thesis about hypothesis testing

The Effect of Statistical Hypothesis Testing on Machine Learning Model Selection

• Conference paper
• First Online: 12 October 2023
• Cite this conference paper

• Marcel Chacon Gonçalves 9 &
• Rodrigo Silva   ORCID: orcid.org/0000-0003-2547-3835 10  

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14196))

Included in the following conference series:

• Brazilian Conference on Intelligent Systems

229 Accesses

Statistical tests of hypothesis play a crucial role in evaluating the performance of machine learning (ML) models and selecting the best model among a set of candidates. However, their effectiveness in selecting models over larger periods of time remains unclear. This study aims to investigate the impact of statistical tests on ML model selection in sequential experiments. Specifically, we examine whether selecting models based on statistical tests leads to higher quality models after a significant number of iterations and explore the effect of the number of tests performed and the preferred statistical test for different experimental time horizons.

The study on binary classification problems reveals that the use of statistical tests should be approached with caution, particularly in challenging scenarios where generating improved models is difficult. The analysis demonstrates that statistical tests may impede progress and impose overly stringent acceptance criteria for new models, hindering the selection of high-quality models. The findings also indicate that the dominance of versions without statistical tests remained consistent, suggesting the need for further research in this area.

Although this study is limited by the number of datasets and the absence of pre-test assumption verification, it emphasizes the importance of understanding the impact of statistical tests on ML model selection.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

• Available as PDF
• Read on any device
• Instant download
• Own it forever
• Available as EPUB and PDF
• Compact, lightweight edition
• Dispatched in 3 to 5 business days
• Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Aygun, B., Gunay, E.K.: Comparison of statistical and machine learning algorithms for forecasting daily bitcoin returns. Avrupa Bilim ve Teknoloji Dergisi (21), pp. 444–454 (2021)

Google Scholar  

Bao, D., et al.: Discriminating between p16-negative oropharyngeal and non-oropharyngeal origins by their metastatic lymph nodes using machine learning approach based on MRI radiomics (2022)

Benavoli, A., Corani, G., Demšar, J., Zaffalon, M.: Time for a change: a tutorial for comparing multiple classifiers through bayesian analysis. J. Mach. Learn. Res. 18 (77), 1–36 (2017). http://jmlr.org/papers/v18/16-305.html

Bender, A., Schneider, N., Segler, M., Patrick Walters, W., Engkvist, O., Rodrigues, T.: Evaluation guidelines for machine learning tools in the chemical sciences. Nat. Rev. Chem. 6 (6), 428–442 (2022)

Article   Google Scholar  

Corani, G., Benavoli, A.: A bayesian approach for comparing cross-validated algorithms on multiple data sets. Mach. Learn. 100 (2–3), 285–304 (2015)

Article   MathSciNet   MATH   Google Scholar  

Dua, D., Graff, C.: UCI machine learning repository (2017). http://archive.ics.uci.edu/ml

Fagerland, M.W.: t-tests, non-parametric tests, and large studies-a paradox of statistical practice? BMC Med. Res. Methodol. 12 (1), 1–7 (2012)

Hair, J.F., Jr., Sarstedt, M.: Data, measurement, and causal inferences in machine learning: opportunities and challenges for marketing. J. Market. Theory Practice 29 (1), 65–77 (2021)

Hopkins, M., Reeber, E., Forman, G., Suermondt, J.: Spambase. UCI Machine Learning Repository (1999). https://doi.org/10.24432/C53G6X

Janosi, A., Steinbrunn, W., Pfisterer, M., Detrano, R., M.D., M.: Heart Disease. UCI Machine Learning Repository (1988). https://doi.org/10.24432/C52P4X

Kim, T.K.: T test as a parametric statistic. Korean J. Anesthesiol. 68 (6), 540–546 (2015)

Article   MathSciNet   Google Scholar  

Morettin, P.A., Bussab, W.O.: Estatística básica. Saraiva Educação SA (2017)

Moro, S., Rita, P., Cortez, P.: Bank Marketing. UCI Machine Learning Repository (2012). https://doi.org/10.24432/C5K306

Trawiński, B., Smetek, M., Telec, Z., Lasota, T.: Nonparametric statistical analysis for multiple comparison of machine learning regression algorithms. Int. J. Appl. Math. Comput. Sci. 22 (4), 867–881 (2012)

Van Rijsbergen, C.J.: Information retrieval. (No Title) (1979)

Virtanen, P., et al.: SciPy 1.0 Contributors: SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17 , 261–272 (2020). https://doi.org/10.1038/s41592-019-0686-2

Wong, T.T., Yeh, P.Y.: Reliable accuracy estimates from k-fold cross validation. IEEE Trans. Knowl. Data Eng. 32 (8), 1586–1594 (2019)

Yeh, I.C.: default of credit card clients. UCI Mach. Learn. Repository (2016). https://doi.org/10.24432/C55S3H

Download references

Acknowledgments

This work was supported by CNPq - National Council for Scientific and Technological Development, CAPES - Coordination for the Improvement of Higher Education Personnel and UFOP - Federal University of Ouro Preto.

Author information

Authors and affiliations.

Graduate Program on Computer Science, Universidade Federal de Ouro Preto, Ouro Preto, Brazil

Marcel Chacon Gonçalves

Department of Computer Science, Universidade Federal de Ouro Preto, Ouro Preto, Brazil

Rodrigo Silva

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Rodrigo Silva .

Editor information

Editors and affiliations.

Federal University of São Carlos, São Carlos, Brazil

Murilo C. Naldi

Centro Universitario da FEI, São Bernardo do Campo, Brazil

Reinaldo A. C. Bianchi

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Cite this paper.

Gonçalves, M.C., Silva, R. (2023). The Effect of Statistical Hypothesis Testing on Machine Learning Model Selection. In: Naldi, M.C., Bianchi, R.A.C. (eds) Intelligent Systems. BRACIS 2023. Lecture Notes in Computer Science(), vol 14196. Springer, Cham. https://doi.org/10.1007/978-3-031-45389-2_28

Download citation

DOI : https://doi.org/10.1007/978-3-031-45389-2_28

Published : 12 October 2023

Publisher Name : Springer, Cham

Print ISBN : 978-3-031-45388-5

Online ISBN : 978-3-031-45389-2

eBook Packages : Computer Science Computer Science (R0)

Share this paper

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Publish with us

Policies and ethics

• Find a journal
• Track your research

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

• Advanced Search
• Journal List
• Ind Psychiatry J
• v.18(1); Jan-Jun 2009

Probability, clinical decision making and hypothesis testing

A. banerjee.

Department of Community Medicine, D. Y. Patil Medical College, Pune - 411018, India

S. L. Jadhav

J. s. bhawalkar.

Few clinicians grasp the true concept of probability expressed in the ‘ P value.’ For most, a statistically significant P value is the end of the search for truth. In fact, the opposite is the case. The present paper attempts to put the P value in proper perspective by explaining different types of probabilities, their role in clinical decision making, medical research and hypothesis testing.

The clinician who wishes to remain abreast with the results of medical research needs to develop a statistical sense. He reads a number of journal articles; and constantly, he must ask questions such as, “Am I convinced that lack of mental activity predisposes to Alzheimer’s? Or “Do I believe that a particular drug cures more patients than the drug I use currently?”

The results of most studies are quantitative; and in earlier times, the reader made up his mind whether or not to accept the results of a particular study by merely looking at the figures. For instance, if 25 out of 30 patients were cured with a new drug compared with 15 out of the 30 on placebo, the superiority of the new drug was readily accepted.

In recent years, the presentation of medical research has undergone much transformation. Nowadays, no respectable journal will accept a paper if the results have not been subjected to statistical significance tests. The use of statistics has accelerated with the ready availability of statistical software. It has now become fashionable to organize workshops on research methodology and biostatistics. No doubt, this development was long overdue and one concedes that the methodologies of most medical papers have considerably improved in recent years. But at the same time, a new problem has arisen. The reading of medical journals today presupposes considerable statistical knowledge; however, those doctors who are not familiar with statistical theory tend to interpret the results of significance tests uncritically or even incorrectly.

It is often overlooked that the results of a statistical test depend not only on the observed data but also on the choice of statistical model. The statistician doing analysis of the data has a choice between several tests which are based on different models and assumptions. Unfortunately, many research workers who know little about statistics leave the statistical analysis to statisticians who know little about medicine; and the end result may well be a series of meaningless calculations.

Many readers of medical journals do not know the correct interpretation of ‘ P values,’ which are the results of significance tests. Usually, it is only stated whether the P value is below 5% ( P < .05) or above 5% ( P > .05). According to convention, the results of P < .05 are said to be statistically significant, and those with P > .05 are said to be statistically nonsignificant. These expressions are taken so seriously by most that it is almost considered ‘unscientific’ to believe in a nonsignificant result or not to believe in a ‘significant’ result. It is taken for granted that a ‘significant’ difference is a true difference and that a ‘nonsignificant’ difference is a chance finding and does not merit further exploration. Nothing can be further from the truth.

The present paper endeavors to explain the meaning of probability, its role in everyday clinical practice and the concepts behind hypothesis testing.

WHAT IS PROBABILITY?

Probability is a recurring theme in medical practice. No doctor who returns home from a busy day at the hospital is spared the nagging feeling that some of his diagnoses may turn out to be wrong, or some of his treatments may not lead to the expected cure. Encountering the unexpected is an occupational hazard in clinical practice. Doctors after some experience in their profession reconcile to the fact that diagnosis and prognosis always have varying degrees of uncertainty and at best can be stated as probable in a particular case.

Critical appraisal of medical journals also leads to the same gut feeling. One is bombarded with new research results, but experience dictates that well-established facts of today may be refuted in some other scientific publication in the following weeks or months. When a practicing clinician reads that some new treatment is superior to the conventional one, he will assess the evidence critically, and at best he will conclude that probably it is true.

Two types of probabilities

The statistical probability concept is so widely prevalent that almost everyone believes that probability is a frequency . It is not, of course, an ordinary frequency which can be estimated by simple observations, but it is the ideal or truth in the universe , which is reflected by the observed frequency. For example, when we want to determine the probability of obtaining an ace from a pack of cards (which, let us assume has been tampered with by a dishonest gambler), we proceed by drawing a card from the pack a large number of times, as we know in the long run, the observed frequency will approach the true probability or truth in the universe. Mathematicians often state that a probability is a long-run frequency, and a probability that is defined in this way is called a frequential probability . The exact magnitude of a frequential probability will remain elusive as we cannot make an infinite number of observations; but when we have made a decent number of observations (adequate sample size), we can calculate the confidence intervals, which are likely to include the true frequential probability. The width of the confidence interval depends on the number of observations (sample size).

The frequential probability concept is so prevalent that we tend to overlook terms like chance, risk and odds, in which the term probability implies a different meaning. Few hypothetical examples will make this clear. Consider the statement, “The cure for Alzheimer’s disease will probably be discovered in the coming decade.” This statement does not indicate the basis of this expectation or belief as in frequential probability, where a number of repeated observations provide the foundation for probability calculation. However, it may be based on the present state of research in Alzheimer’s. A probabilistic statement incorporates some amount of uncertainty, which may be quantified as follows: A politician may state that there is a fifty-fifty chance of winning the next election, a bookie may say that the odds of India winning the next one-day cricket game is four to one, and so on. At first glance, such probabilities may appear frequential ones, but a little reflection will reveal the contrary. We are concerned with unique events, i.e., the likely cure of a disease in the future, the next particular election, the next particular one-day game — and it makes no sense to apply the statistical idea that these types of probabilities are long-run frequencies. Further reflection will illustrate that these statements about probabilities of the election and one-day game are no different from the one about the cure for Alzheimer’s, apart from the fact that in the latter cases an attempt has been made to quantify the magnitude of belief in the occurrence of the event.

It follows from the above deliberations that we have 2 types of probability concepts. In the jargon of statistics, a probability is ideal or truth in the universe which lies beneath an observed frequency — such probabilities may be called frequential probabilities. In literary language, a probability is a measure of our subjective belief in the occurrence of a particular event or truth of a hypothesis. Such probabilities, which may be quantified that they look like frequential ones, are called subjective probabilities. Bayesian statistical theory also takes into account subjective probabilities (Lindley, 1973; Winkler, 1972). The following examples will try to illustrate these (rather confusing) concepts.

A young man is brought to the psychiatry OPD with history of withdrawal. He also gives history of talking to himself and giggling without cause. There is also a positive family history of schizophrenia. The consulting psychiatrist who examines the patient concludes that there is a 90% probability that this patient suffers from schizophrenia.

We ask the psychiatrist what makes him make such a statement. He may not be able to say that he knows from experience that 90% of such patients suffer from schizophrenia. The statement therefore may not be based on observed frequency. Instead, the psychiatrist states his probability based on his knowledge of the natural history of disease and the available literature regarding signs and symptoms in schizophrenia and positive family history. From this knowledge, the psychiatrist concludes that his belief in the diagnosis of schizophrenia in that particular patient is as strong as his belief in picking a black ball from a box containing 10 white and 90 black balls. The probability in this case is certainly subjective probability .

Let us consider another example: A 26-year-old married female patient who suffered from severe abdominal pain is referred to a hospital. She is also having amenorrhea for the past 4 months. The pain is located in the left lower abdomen. The gynecologist who examines her concludes that there is a 30% probability that the patient is suffering from ectopic pregnancy.

As before, we ask the gynecologist to explain on what basis the diagnosis of ectopic pregnancy is suspected. In this case the gynecologist states that he has studied a large number of successive patients with this symptom complex of lower abdominal pain with amenorrhea, and that a subsequent laparotomy revealed an ectopic pregnancy in 30% of the cases.

If we accept that the study cited is large enough to make us assume that the possibility of the observed frequency of ectopic pregnancy did not differ from the true frequential probability, it is natural to conclude that the gynecologist’s probability claim is more ‘evidence based’ than that of the psychiatrist, but again this is debatable.

In order to grasp this in proper perspective, it is necessary to note that the gynecologist stated that the probability of ectopic pregnancy in that particular patient was 30%. Therefore, we are concerned with a unique event just as the politician’s next election or India’s next one-day match. So in this case also, the probability is a subjective probability which was based on an observed frequency . One might also argue that even this probability is not good enough. We might ask the gynecologist to base his belief on a group of patients who also had the same age, height, color of hair and social background; and in the end, the reference group would be so restrictive that even the experience from a very large study would not provide the necessary information. If we went even further and required that he must base his belief on patients who in all respects resembled this particular patient, the probabilistic problem would vanish as we will be dealing with a certainty rather than a probability.

The clinician’s belief in a particular diagnosis in an individual patient may be based on the recorded experience in a group of patients, but it is still a subjective probability. It reflects not only the observed frequency of the disease in a reference group but also the clinician’s theoretical knowledge which determines the choice of reference group (Wulff, Pedersen and Rosenberg, 1986). Recorded experience is never the sole basis of clinical decision making.

GAP BETWEEN THEORY AND PRACTICE

The two situations described above are relatively straightforward. The physician observed a patient with a particular set of signs and symptoms and assessed the subjective probability about the diagnosis in each case. Such probabilities have been termed diagnostic probabilities (Wulff, Pedersen and Rosenberg, 1986). In practice, however, clinicians make diagnosis in a more complex manner which they themselves may be unable to analyze logically.

For instance, suppose the clinician suspects one of his patients is suffering from a rare disease named ‘D.’ He requests a suitable test to confirm the diagnosis, and suppose the test is positive for disease ‘D.’ He now wishes to assess the probability of the diagnosis being positive on the basis of this information, but perhaps the medical literature only provides the information that a positive test is seen in 70% of the patients with disease ‘D.’ However, it is also positive in 2% of patients without disease ‘D.’ How to tackle this doctor’s dilemma? First a formal analysis may be attempted, and then we can return to everyday clinical thinking. The frequential probability which the doctor found in the literature may be written in the statistical notation as follows:

P (S/D+) = .70, i.e., the probability of the presence of this particular sign (or test) given this particular disease is 70%.

P (S/D–) = .02, i.e., the probability of this particular sign given the absence of this particular disease is 2%.

However, such probabilities are of little clinical relevance. The clinical relevance is in the ‘opposite’ probability. In clinical practice, one would like to know the P (D/S), i.e., the probability of the disease in a particular patient given this positive sign. This can be estimated by means of Bayes’ Theorem (Papoulis, 1984; Lindley, 1973; Winkler, 1972). The formula of Bayes’ Theorem is reproduced below, from which it will be evident that to calculate P(D/S), we must also know the prior probability of the presence and the absence of the disease, i.e., P (D+) and P (D–).

P (D/S) = P (S/D+) P (D+) ÷ P (S/D+) P (D+) + P (S/D–) P (D–)

In the example of the disease ‘D’ above, let us assume that we estimate that prior probability of the disease being present, i.e., P (D+), is 25%; and therefore, prior probability of the absence of disease, i.e., P (D–), is 75%. Using the Bayes’ Theorem formula, we can calculate that the probability of the disease given a positive sign, i.e., P (D/S), is 92%.

We of course do not suggest that clinicians should always make calculations of this sort when confronted with a diagnostic dilemma, but they must in an intuitive way think along these lines. Clinical knowledge is to a large extent based on textbook knowledge, and ordinary textbooks do not tell the reader much about the probabilities of different diseases given different symptoms. Bayes’ Theorem guides a clinician how to use textbook knowledge for practical clinical purposes.

The practical significance of this point is illustrated by the European doctor who accepted a position at a hospital in tropical Africa. In order to prepare himself for the new job, he bought himself a large textbook of tropical medicine and studied in great detail the clinical pictures of a large number of exotic diseases. However, for several months after his arrival at the tropical hospital, his diagnostic performance was very poor, as he knew nothing about the relative frequency of all these diseases. He had to acquaint himself with the prior probability, P (D +), of the diseases in the catchment area of the hospital before he could make precise diagnoses.

The same thing happens on a smaller scale when a doctor trained at a university hospital establishes himself in general practice. At the beginning, he will suspect his patients of all sorts of rare diseases (which are common at the university hospital), but after a while he will learn to assess correctly the frequency of different diseases in the general population.

PROBABILITY AND HYPOTHESIS TESTING

Besides predictions on individual patients, the doctor is also concerned in generalizations to the population at large or the target population. We may say that probably there may have been life at Mars. We may even quantify our belief and mention that there is 95% probability that depression responds more quickly during treatment with a particular antidepressant than during treatment with a placebo. These probabilities are again subjective probabilities rather than frequential probabilities . The last statement does not imply that 95% of depression cases respond to the particular antidepressant or that 95% of the published reports mention that the particular antidepressant is the best. It simply means that our belief in the truth of the statement is the same as our belief in picking up a red ball from a box containing 95 red balls and 5 white balls. It means that we are, however, almost not totally convinced that the average recovery time during treatment with a particular antidepressant is shorter than during placebo treatment.

The purpose of hypothesis testing is to aid the clinician in reaching a conclusion concerning the universe by examining a sample from that universe. A hypothesis may be defined as a presumption or statement about the truth in the universe. For example, a clinician may hypothesize that a certain drug may be effective in 80% of the cases of schizophrenia. It is frequently concerned about the parameters in the population about which the presumption or statement is made. It is the basis for motivating the research project. There are two types of hypotheses, research hypothesis and statistical hypothesis (Daniel, 2000; Guyatt et al ., 1995).

Genesis of research hypothesis

Hypothesis may be generated by deduction from anatomical, physiological facts or from clinical observations.

Statistical hypothesis

Statistical hypotheses are hypotheses that are stated in such a way that they may be evaluated by appropriate statistical techniques.

Pre-requisites for hypothesis testing

Nature of data.

The types of data that form the basis of hypothesis testing procedures must be understood, since these dictate the choice of statistical test.

Presumptions

These presumptions are the normality of the population distribution, equality of the standard deviations, random samples.

There are 2 statistical hypotheses involved in hypothesis testing. These should be stated a priori and explicitly. The null hypothesis is the hypothesis to be tested. It is denoted by the symbol H 0 . It is also known as the hypothesis of no difference . The null hypothesis is set up with the sole purpose of efforts to knock it down. In the testing of hypothesis, the null hypothesis is either rejected (knocked down) or not rejected (upheld). If the null hypothesis is not rejected, the interpretation is that the data is not sufficient evidence to cause rejection. If the testing process rejects the null hypothesis, the inference is that the data available to us is not compatible with the null hypothesis and by default we accept the alternative hypothesis , which in most cases is the research hypothesis. The alternative hypothesis is designated with the symbol H A .

Limitations

Neither hypothesis testing nor statistical tests lead to proof. It merely indicates whether the hypothesis is supported or not supported by the available data. When we reject a null hypothesis, we do not mean it is not true but that it may be true. By default when we do not reject the null hypothesis, we should have this limitation in mind and should not convey the impression that this implies proof.

Test statistic

The test statistic is the statistic that is derived from the data from the sample. Evidently, many possible values of the test statistic can be computed depending on the particular sample selected. The test statistic serves as a decision maker, nothing more, nothing less, rather than proof or lack of it. The decision to reject or not to reject the null hypothesis depends on the magnitude of the test statistic.

Types of decision errors

The error committed when a true null hypothesis is rejected is called the type I error or α error . When a false null hypothesis is not rejected, we commit type II error, or β error . When we reject a null hypothesis, there is always the risk (howsoever small it may be) of committing a type I error, i.e., rejecting a true null hypothesis. On the other hand, whenever we fail to reject a null hypothesis, the risk of failing to reject a false null hypothesis, or committing a type II error, will always be present. Put in other words, the test statistic does not eliminate uncertainty (as many tend to believe); it only quantifies our uncertainty.

Calculation of test statistic

From the data contained in the sample, we compute a value of the test statistic and compare it with the rejection and non-rejection regions, which have to be specified in advance.

Statistical decision

The statistical decision consists of rejecting or of not rejecting the null hypothesis. It is rejected if the computed value of the test statistic falls in the rejection region, and it is not rejected if the value falls in the non-rejection region.

If H 0 is rejected, we conclude that H A is true. If H 0 is not rejected, we conclude that H 0 may be true.

The P value is a number that tells us how unlikely our sample values are, given that the null hypothesis is true. A P value indicating that the sample results are not likely to have occurred, if the null hypothesis is true, provides reason for doubting the truth of the null hypothesis.

We must remember that, when the null hypothesis is not rejected, one should not say the null hypothesis is accepted. We should mention that the null hypothesis is “not rejected.” We avoid using the word accepted in this case because we may have committed a type II error. Since, frequently, the probability of committing error can be quite high (particularly with small sample sizes), we should not commit ourselves to accepting the null hypothesis.

INTERPRETATIONS

With the above discussion on probability, clinical decision making and hypothesis testing in mind, let us reconsider the meaning of P values. When we come across the statement that there is statistically significant difference between two treatment regimes with P < .05, we should not interpret that there is less than 5% probability that there is no difference, and that there is 95% probability that a difference exists, as many uninformed readers tend to do. The statement that there is difference between the cure rates of two treatments is a general one, and we have already discussed that the probability of the truth of a general statement (hypothesis) is subjective , whereas the probabilities which are calculated by statisticians are frequential ones. The hypothesis that one treatment is better than the other is either true or false and cannot be interpreted in frequential terms.

To explain this further, suppose someone claims that 20 (80%) of 25 patients who received drug A were cured, compared to 12 (48%) of 25 patients who received drug B. In this case, there are two possibilities, either the null hypothesis is true, which means that the two treatments are equally effective and the observed difference arose by chance; or the null hypothesis is not true (and we accept the alternative hypothesis by default), which means that one treatment is better than the other. The clinician wants to make up his mind to what extent he believes in the truth of the alternative hypothesis (or the falsehood of the null hypothesis ). To resolve this issue, he needs the aid of statistical analysis. However, it is essential to note that the P value does not provide a direct answer. Let us assume in this case the statistician does a significance test and gets a P value = .04, meaning that the difference is statistically significant ( P < .05). But as explained earlier, this does not mean that there is a 4% probability that the null hypothesis is true and 96% chance that the alternative hypothesis is true. The P value is a frequential probability and it provides the information that there is a 4% probability of obtaining such a difference between the cure rates, if the null hypothesis is true . In other words, the statistician asks us to assume that the null hypothesis is true and to imagine that we do a large number of trials. In that case, the long-run frequency of trials which show a difference between the cure rates like the one we found, or even a larger one, will be 4%.

Prior belief and interpretation of the P value

In order to elucidate the implications of the correct statistical definition of the P value, let us imagine that the patients who took part in the above trial suffered from depression, and that drug A was gentamycin, while drug B was a placebo. Our theoretical knowledge gives us no grounds for believing that gentamycin has any affect whatsoever in the cure of depression. For this reason, our prior confidence in the truth of the null hypothesis is immense (say, 99.99%), whereas our prior confidence in the alternative hypothesis is minute (0.01%). We must take these prior probabilities into account when we assess the result of the trial. We have the following choice. Either we accept the null hypothesis in spite of the fact that the probability of the trial result is fairly low at 4% ( P < .05) given the null hypothesis is true, or we accept the alternative hypothesis by rejecting the null hypothesis in spite of the fact that the subjective probability of that hypothesis is extremely low in the light of our prior knowledge.

It will be evident that the choice is a difficult one, as both hypotheses, each in its own way, may be said to be unlikely, but any clinician who reasons along these lines will choose that hypothesis which is least unacceptable: He will accept the null hypothesis and claim that the difference between the cure rates arose by chance (however small it may be), as he does not feel that the evidence from this single trial is sufficient to shake his prior belief in the null hypothesis.

Misinterpretation of P values is extremely common. One of the reasons may be that those who teach research methods do not themselves appreciate the problem. The P value is the probability of obtaining a value of the test statistic as large as or larger than the one computed from the data when in reality there is no difference between the different treatments. In other words, the P value is the probability of being wrong when asserting that a difference exists.

Lastly, we must remember we do not establish proof by hypothesis testing, and uncertainty will always remain in empirical research; at the most, we can only quantify our uncertainty.

Source of Support: Nil

Conflict of Interest: None declared.

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, generate accurate citations for free.

• Knowledge Base
• Choosing the Right Statistical Test | Types & Examples

Choosing the Right Statistical Test | Types & Examples

Published on January 28, 2020 by Rebecca Bevans . Revised on June 22, 2023.

Statistical tests are used in hypothesis testing . They can be used to:

• determine whether a predictor variable has a statistically significant relationship with an outcome variable.
• estimate the difference between two or more groups.

Statistical tests assume a null hypothesis of no relationship or no difference between groups. Then they determine whether the observed data fall outside of the range of values predicted by the null hypothesis.

If you already know what types of variables you’re dealing with, you can use the flowchart to choose the right statistical test for your data.

Statistical tests flowchart

Table of contents

What does a statistical test do, when to perform a statistical test, choosing a parametric test: regression, comparison, or correlation, choosing a nonparametric test, flowchart: choosing a statistical test, other interesting articles, frequently asked questions about statistical tests.

Statistical tests work by calculating a test statistic – a number that describes how much the relationship between variables in your test differs from the null hypothesis of no relationship.

It then calculates a p value (probability value). The p -value estimates how likely it is that you would see the difference described by the test statistic if the null hypothesis of no relationship were true.

If the value of the test statistic is more extreme than the statistic calculated from the null hypothesis, then you can infer a statistically significant relationship between the predictor and outcome variables.

If the value of the test statistic is less extreme than the one calculated from the null hypothesis, then you can infer no statistically significant relationship between the predictor and outcome variables.

Receive feedback on language, structure, and formatting

Professional editors proofread and edit your paper by focusing on:

• Academic style
• Vague sentences
• Style consistency

See an example

You can perform statistical tests on data that have been collected in a statistically valid manner – either through an experiment , or through observations made using probability sampling methods .

For a statistical test to be valid , your sample size needs to be large enough to approximate the true distribution of the population being studied.

To determine which statistical test to use, you need to know:

• whether your data meets certain assumptions.
• the types of variables that you’re dealing with.

Statistical assumptions

Statistical tests make some common assumptions about the data they are testing:

• Independence of observations (a.k.a. no autocorrelation): The observations/variables you include in your test are not related (for example, multiple measurements of a single test subject are not independent, while measurements of multiple different test subjects are independent).
• Homogeneity of variance : the variance within each group being compared is similar among all groups. If one group has much more variation than others, it will limit the test’s effectiveness.
• Normality of data : the data follows a normal distribution (a.k.a. a bell curve). This assumption applies only to quantitative data .

If your data do not meet the assumptions of normality or homogeneity of variance, you may be able to perform a nonparametric statistical test , which allows you to make comparisons without any assumptions about the data distribution.

If your data do not meet the assumption of independence of observations, you may be able to use a test that accounts for structure in your data (repeated-measures tests or tests that include blocking variables).

Types of variables

The types of variables you have usually determine what type of statistical test you can use.

Quantitative variables represent amounts of things (e.g. the number of trees in a forest). Types of quantitative variables include:

• Continuous (aka ratio variables): represent measures and can usually be divided into units smaller than one (e.g. 0.75 grams).
• Discrete (aka integer variables): represent counts and usually can’t be divided into units smaller than one (e.g. 1 tree).

Categorical variables represent groupings of things (e.g. the different tree species in a forest). Types of categorical variables include:

• Ordinal : represent data with an order (e.g. rankings).
• Nominal : represent group names (e.g. brands or species names).
• Binary : represent data with a yes/no or 1/0 outcome (e.g. win or lose).

Choose the test that fits the types of predictor and outcome variables you have collected (if you are doing an experiment , these are the independent and dependent variables ). Consult the tables below to see which test best matches your variables.

Parametric tests usually have stricter requirements than nonparametric tests, and are able to make stronger inferences from the data. They can only be conducted with data that adheres to the common assumptions of statistical tests.

The most common types of parametric test include regression tests, comparison tests, and correlation tests.

Regression tests

Regression tests look for cause-and-effect relationships . They can be used to estimate the effect of one or more continuous variables on another variable.

Comparison tests

Comparison tests look for differences among group means . They can be used to test the effect of a categorical variable on the mean value of some other characteristic.

T-tests are used when comparing the means of precisely two groups (e.g., the average heights of men and women). ANOVA and MANOVA tests are used when comparing the means of more than two groups (e.g., the average heights of children, teenagers, and adults).

Correlation tests

Correlation tests check whether variables are related without hypothesizing a cause-and-effect relationship.

These can be used to test whether two variables you want to use in (for example) a multiple regression test are autocorrelated.

Non-parametric tests don’t make as many assumptions about the data, and are useful when one or more of the common statistical assumptions are violated. However, the inferences they make aren’t as strong as with parametric tests.

Prevent plagiarism. Run a free check.

This flowchart helps you choose among parametric tests. For nonparametric alternatives, check the table above.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient
• Null hypothesis

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

Statistical tests commonly assume that:

• the data are normally distributed
• the groups that are being compared have similar variance
• the data are independent

If your data does not meet these assumptions you might still be able to use a nonparametric statistical test , which have fewer requirements but also make weaker inferences.

A test statistic is a number calculated by a  statistical test . It describes how far your observed data is from the  null hypothesis  of no relationship between  variables or no difference among sample groups.

The test statistic tells you how different two or more groups are from the overall population mean , or how different a linear slope is from the slope predicted by a null hypothesis . Different test statistics are used in different statistical tests.

Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test . Significance is usually denoted by a p -value , or probability value.

Statistical significance is arbitrary – it depends on the threshold, or alpha value, chosen by the researcher. The most common threshold is p < 0.05, which means that the data is likely to occur less than 5% of the time under the null hypothesis .

When the p -value falls below the chosen alpha value, then we say the result of the test is statistically significant.

Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).

Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).

You need to know what type of variables you are working with to choose the right statistical test for your data and interpret your results .

Discrete and continuous variables are two types of quantitative variables :

• Discrete variables represent counts (e.g. the number of objects in a collection).
• Continuous variables represent measurable amounts (e.g. water volume or weight).

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

Bevans, R. (2023, June 22). Choosing the Right Statistical Test | Types & Examples. Scribbr. Retrieved April 15, 2024, from https://www.scribbr.com/statistics/statistical-tests/

Is this article helpful?

Rebecca Bevans

Other students also liked, hypothesis testing | a step-by-step guide with easy examples, test statistics | definition, interpretation, and examples, normal distribution | examples, formulas, & uses, what is your plagiarism score.

Tutorial Playlist

Statistics tutorial, everything you need to know about the probability density function in statistics, the best guide to understand central limit theorem, an in-depth guide to measures of central tendency : mean, median and mode, the ultimate guide to understand conditional probability.

A Comprehensive Look at Percentile in Statistics

The Best Guide to Understand Bayes Theorem

Everything you need to know about the normal distribution, an in-depth explanation of cumulative distribution function, a complete guide to chi-square test, a complete guide on hypothesis testing in statistics, understanding the fundamentals of arithmetic and geometric progression, the definitive guide to understand spearman’s rank correlation, a comprehensive guide to understand mean squared error, all you need to know about the empirical rule in statistics, the complete guide to skewness and kurtosis, a holistic look at bernoulli distribution.

All You Need to Know About Bias in Statistics

A Complete Guide to Get a Grasp of Time Series Analysis

The Key Differences Between Z-Test Vs. T-Test

The Complete Guide to Understand Pearson's Correlation

A complete guide on the types of statistical studies, everything you need to know about poisson distribution, your best guide to understand correlation vs. regression, the most comprehensive guide for beginners on what is correlation, what is hypothesis testing in statistics types and examples.

Lesson 10 of 24 By Avijeet Biswal

Table of Contents

In today’s data-driven world , decisions are based on data all the time. Hypothesis plays a crucial role in that process, whether it may be making business decisions, in the health sector, academia, or in quality improvement. Without hypothesis & hypothesis tests, you risk drawing the wrong conclusions and making bad decisions. In this tutorial, you will look at Hypothesis Testing in Statistics.

What Is Hypothesis Testing in Statistics?

Hypothesis Testing is a type of statistical analysis in which you put your assumptions about a population parameter to the test. It is used to estimate the relationship between 2 statistical variables.

Let's discuss few examples of statistical hypothesis from real-life - 

• A teacher assumes that 60% of his college's students come from lower-middle-class families.
• A doctor believes that 3D (Diet, Dose, and Discipline) is 90% effective for diabetic patients.

Now that you know about hypothesis testing, look at the two types of hypothesis testing in statistics.

Hypothesis Testing Formula

Z = ( x̅ – μ0 ) / (σ /√n)

• Here, x̅ is the sample mean,
• μ0 is the population mean,
• σ is the standard deviation,
• n is the sample size.

How Hypothesis Testing Works?

An analyst performs hypothesis testing on a statistical sample to present evidence of the plausibility of the null hypothesis. Measurements and analyses are conducted on a random sample of the population to test a theory. Analysts use a random population sample to test two hypotheses: the null and alternative hypotheses.

The null hypothesis is typically an equality hypothesis between population parameters; for example, a null hypothesis may claim that the population means return equals zero. The alternate hypothesis is essentially the inverse of the null hypothesis (e.g., the population means the return is not equal to zero). As a result, they are mutually exclusive, and only one can be correct. One of the two possibilities, however, will always be correct.

Your Dream Career is Just Around The Corner!

Null Hypothesis and Alternate Hypothesis

The Null Hypothesis is the assumption that the event will not occur. A null hypothesis has no bearing on the study's outcome unless it is rejected.

H0 is the symbol for it, and it is pronounced H-naught.

The Alternate Hypothesis is the logical opposite of the null hypothesis. The acceptance of the alternative hypothesis follows the rejection of the null hypothesis. H1 is the symbol for it.

Let's understand this with an example.

A sanitizer manufacturer claims that its product kills 95 percent of germs on average. 

To put this company's claim to the test, create a null and alternate hypothesis.

H0 (Null Hypothesis): Average = 95%.

Alternative Hypothesis (H1): The average is less than 95%.

Another straightforward example to understand this concept is determining whether or not a coin is fair and balanced. The null hypothesis states that the probability of a show of heads is equal to the likelihood of a show of tails. In contrast, the alternate theory states that the probability of a show of heads and tails would be very different.

Become a Data Scientist with Hands-on Training!

Hypothesis Testing Calculation With Examples

Let's consider a hypothesis test for the average height of women in the United States. Suppose our null hypothesis is that the average height is 5'4". We gather a sample of 100 women and determine that their average height is 5'5". The standard deviation of population is 2.

To calculate the z-score, we would use the following formula:

z = ( x̅ – μ0 ) / (σ /√n)

z = (5'5" - 5'4") / (2" / √100)

z = 0.5 / (0.045)

 We will reject the null hypothesis as the z-score of 11.11 is very large and conclude that there is evidence to suggest that the average height of women in the US is greater than 5'4".

Steps of Hypothesis Testing

Step 1: specify your null and alternate hypotheses.

It is critical to rephrase your original research hypothesis (the prediction that you wish to study) as a null (Ho) and alternative (Ha) hypothesis so that you can test it quantitatively. Your first hypothesis, which predicts a link between variables, is generally your alternate hypothesis. The null hypothesis predicts no link between the variables of interest.

Step 2: Gather Data

For a statistical test to be legitimate, sampling and data collection must be done in a way that is meant to test your hypothesis. You cannot draw statistical conclusions about the population you are interested in if your data is not representative.

Step 3: Conduct a Statistical Test

Other statistical tests are available, but they all compare within-group variance (how to spread out the data inside a category) against between-group variance (how different the categories are from one another). If the between-group variation is big enough that there is little or no overlap between groups, your statistical test will display a low p-value to represent this. This suggests that the disparities between these groups are unlikely to have occurred by accident. Alternatively, if there is a large within-group variance and a low between-group variance, your statistical test will show a high p-value. Any difference you find across groups is most likely attributable to chance. The variety of variables and the level of measurement of your obtained data will influence your statistical test selection.

Step 4: Determine Rejection Of Your Null Hypothesis

Your statistical test results must determine whether your null hypothesis should be rejected or not. In most circumstances, you will base your judgment on the p-value provided by the statistical test. In most circumstances, your preset level of significance for rejecting the null hypothesis will be 0.05 - that is, when there is less than a 5% likelihood that these data would be seen if the null hypothesis were true. In other circumstances, researchers use a lower level of significance, such as 0.01 (1%). This reduces the possibility of wrongly rejecting the null hypothesis.

Step 5: Present Your Results 

The findings of hypothesis testing will be discussed in the results and discussion portions of your research paper, dissertation, or thesis. You should include a concise overview of the data and a summary of the findings of your statistical test in the results section. You can talk about whether your results confirmed your initial hypothesis or not in the conversation. Rejecting or failing to reject the null hypothesis is a formal term used in hypothesis testing. This is likely a must for your statistics assignments.

Types of Hypothesis Testing

To determine whether a discovery or relationship is statistically significant, hypothesis testing uses a z-test. It usually checks to see if two means are the same (the null hypothesis). Only when the population standard deviation is known and the sample size is 30 data points or more, can a z-test be applied.

A statistical test called a t-test is employed to compare the means of two groups. To determine whether two groups differ or if a procedure or treatment affects the population of interest, it is frequently used in hypothesis testing.

Chi-Square 

You utilize a Chi-square test for hypothesis testing concerning whether your data is as predicted. To determine if the expected and observed results are well-fitted, the Chi-square test analyzes the differences between categorical variables from a random sample. The test's fundamental premise is that the observed values in your data should be compared to the predicted values that would be present if the null hypothesis were true.

Hypothesis Testing and Confidence Intervals

Both confidence intervals and hypothesis tests are inferential techniques that depend on approximating the sample distribution. Data from a sample is used to estimate a population parameter using confidence intervals. Data from a sample is used in hypothesis testing to examine a given hypothesis. We must have a postulated parameter to conduct hypothesis testing.

Bootstrap distributions and randomization distributions are created using comparable simulation techniques. The observed sample statistic is the focal point of a bootstrap distribution, whereas the null hypothesis value is the focal point of a randomization distribution.

A variety of feasible population parameter estimates are included in confidence ranges. In this lesson, we created just two-tailed confidence intervals. There is a direct connection between these two-tail confidence intervals and these two-tail hypothesis tests. The results of a two-tailed hypothesis test and two-tailed confidence intervals typically provide the same results. In other words, a hypothesis test at the 0.05 level will virtually always fail to reject the null hypothesis if the 95% confidence interval contains the predicted value. A hypothesis test at the 0.05 level will nearly certainly reject the null hypothesis if the 95% confidence interval does not include the hypothesized parameter.

Simple and Composite Hypothesis Testing

Depending on the population distribution, you can classify the statistical hypothesis into two types.

Simple Hypothesis: A simple hypothesis specifies an exact value for the parameter.

Composite Hypothesis: A composite hypothesis specifies a range of values.

A company is claiming that their average sales for this quarter are 1000 units. This is an example of a simple hypothesis.

Suppose the company claims that the sales are in the range of 900 to 1000 units. Then this is a case of a composite hypothesis.

One-Tailed and Two-Tailed Hypothesis Testing

The One-Tailed test, also called a directional test, considers a critical region of data that would result in the null hypothesis being rejected if the test sample falls into it, inevitably meaning the acceptance of the alternate hypothesis.

In a one-tailed test, the critical distribution area is one-sided, meaning the test sample is either greater or lesser than a specific value.

In two tails, the test sample is checked to be greater or less than a range of values in a Two-Tailed test, implying that the critical distribution area is two-sided.

If the sample falls within this range, the alternate hypothesis will be accepted, and the null hypothesis will be rejected.

Become a Data Scientist With Real-World Experience

Right Tailed Hypothesis Testing

If the larger than (>) sign appears in your hypothesis statement, you are using a right-tailed test, also known as an upper test. Or, to put it another way, the disparity is to the right. For instance, you can contrast the battery life before and after a change in production. Your hypothesis statements can be the following if you want to know if the battery life is longer than the original (let's say 90 hours):

• The null hypothesis is (H0 <= 90) or less change.
• A possibility is that battery life has risen (H1) > 90.

The crucial point in this situation is that the alternate hypothesis (H1), not the null hypothesis, decides whether you get a right-tailed test.

Left Tailed Hypothesis Testing

Alternative hypotheses that assert the true value of a parameter is lower than the null hypothesis are tested with a left-tailed test; they are indicated by the asterisk "<".

Suppose H0: mean = 50 and H1: mean not equal to 50

According to the H1, the mean can be greater than or less than 50. This is an example of a Two-tailed test.

In a similar manner, if H0: mean >=50, then H1: mean <50

Here the mean is less than 50. It is called a One-tailed test.

Type 1 and Type 2 Error

A hypothesis test can result in two types of errors.

Type 1 Error: A Type-I error occurs when sample results reject the null hypothesis despite being true.

Type 2 Error: A Type-II error occurs when the null hypothesis is not rejected when it is false, unlike a Type-I error.

Suppose a teacher evaluates the examination paper to decide whether a student passes or fails.

H0: Student has passed

H1: Student has failed

Type I error will be the teacher failing the student [rejects H0] although the student scored the passing marks [H0 was true]. 

Type II error will be the case where the teacher passes the student [do not reject H0] although the student did not score the passing marks [H1 is true].

Level of Significance

The alpha value is a criterion for determining whether a test statistic is statistically significant. In a statistical test, Alpha represents an acceptable probability of a Type I error. Because alpha is a probability, it can be anywhere between 0 and 1. In practice, the most commonly used alpha values are 0.01, 0.05, and 0.1, which represent a 1%, 5%, and 10% chance of a Type I error, respectively (i.e. rejecting the null hypothesis when it is in fact correct).

Future-Proof Your AI/ML Career: Top Dos and Don'ts

A p-value is a metric that expresses the likelihood that an observed difference could have occurred by chance. As the p-value decreases the statistical significance of the observed difference increases. If the p-value is too low, you reject the null hypothesis.

Here you have taken an example in which you are trying to test whether the new advertising campaign has increased the product's sales. The p-value is the likelihood that the null hypothesis, which states that there is no change in the sales due to the new advertising campaign, is true. If the p-value is .30, then there is a 30% chance that there is no increase or decrease in the product's sales.  If the p-value is 0.03, then there is a 3% probability that there is no increase or decrease in the sales value due to the new advertising campaign. As you can see, the lower the p-value, the chances of the alternate hypothesis being true increases, which means that the new advertising campaign causes an increase or decrease in sales.

Why is Hypothesis Testing Important in Research Methodology?

Hypothesis testing is crucial in research methodology for several reasons:

• Provides evidence-based conclusions: It allows researchers to make objective conclusions based on empirical data, providing evidence to support or refute their research hypotheses.
• Supports decision-making: It helps make informed decisions, such as accepting or rejecting a new treatment, implementing policy changes, or adopting new practices.
• Adds rigor and validity: It adds scientific rigor to research using statistical methods to analyze data, ensuring that conclusions are based on sound statistical evidence.
• Contributes to the advancement of knowledge: By testing hypotheses, researchers contribute to the growth of knowledge in their respective fields by confirming existing theories or discovering new patterns and relationships.

Limitations of Hypothesis Testing

Hypothesis testing has some limitations that researchers should be aware of:

• It cannot prove or establish the truth: Hypothesis testing provides evidence to support or reject a hypothesis, but it cannot confirm the absolute truth of the research question.
• Results are sample-specific: Hypothesis testing is based on analyzing a sample from a population, and the conclusions drawn are specific to that particular sample.
• Possible errors: During hypothesis testing, there is a chance of committing type I error (rejecting a true null hypothesis) or type II error (failing to reject a false null hypothesis).
• Assumptions and requirements: Different tests have specific assumptions and requirements that must be met to accurately interpret results.

After reading this tutorial, you would have a much better understanding of hypothesis testing, one of the most important concepts in the field of Data Science . The majority of hypotheses are based on speculation about observed behavior, natural phenomena, or established theories.

If you are interested in statistics of data science and skills needed for such a career, you ought to explore Simplilearn’s Post Graduate Program in Data Science.

If you have any questions regarding this ‘Hypothesis Testing In Statistics’ tutorial, do share them in the comment section. Our subject matter expert will respond to your queries. Happy learning!

1. What is hypothesis testing in statistics with example?

Hypothesis testing is a statistical method used to determine if there is enough evidence in a sample data to draw conclusions about a population. It involves formulating two competing hypotheses, the null hypothesis (H0) and the alternative hypothesis (Ha), and then collecting data to assess the evidence. An example: testing if a new drug improves patient recovery (Ha) compared to the standard treatment (H0) based on collected patient data.

2. What is hypothesis testing and its types?

Hypothesis testing is a statistical method used to make inferences about a population based on sample data. It involves formulating two hypotheses: the null hypothesis (H0), which represents the default assumption, and the alternative hypothesis (Ha), which contradicts H0. The goal is to assess the evidence and determine whether there is enough statistical significance to reject the null hypothesis in favor of the alternative hypothesis.

Types of hypothesis testing:

• One-sample test: Used to compare a sample to a known value or a hypothesized value.
• Two-sample test: Compares two independent samples to assess if there is a significant difference between their means or distributions.
• Paired-sample test: Compares two related samples, such as pre-test and post-test data, to evaluate changes within the same subjects over time or under different conditions.
• Chi-square test: Used to analyze categorical data and determine if there is a significant association between variables.
• ANOVA (Analysis of Variance): Compares means across multiple groups to check if there is a significant difference between them.

3. What are the steps of hypothesis testing?

The steps of hypothesis testing are as follows:

• Formulate the hypotheses: State the null hypothesis (H0) and the alternative hypothesis (Ha) based on the research question.
• Set the significance level: Determine the acceptable level of error (alpha) for making a decision.
• Collect and analyze data: Gather and process the sample data.
• Compute test statistic: Calculate the appropriate statistical test to assess the evidence.
• Make a decision: Compare the test statistic with critical values or p-values and determine whether to reject H0 in favor of Ha or not.
• Draw conclusions: Interpret the results and communicate the findings in the context of the research question.

4. What are the 2 types of hypothesis testing?

• One-tailed (or one-sided) test: Tests for the significance of an effect in only one direction, either positive or negative.
• Two-tailed (or two-sided) test: Tests for the significance of an effect in both directions, allowing for the possibility of a positive or negative effect.

The choice between one-tailed and two-tailed tests depends on the specific research question and the directionality of the expected effect.

5. What are the 3 major types of hypothesis?

The three major types of hypotheses are:

• Null Hypothesis (H0): Represents the default assumption, stating that there is no significant effect or relationship in the data.
• Alternative Hypothesis (Ha): Contradicts the null hypothesis and proposes a specific effect or relationship that researchers want to investigate.
• Nondirectional Hypothesis: An alternative hypothesis that doesn't specify the direction of the effect, leaving it open for both positive and negative possibilities.

Find our Data Analyst Online Bootcamp in top cities:

About the author.

Avijeet is a Senior Research Analyst at Simplilearn. Passionate about Data Analytics, Machine Learning, and Deep Learning, Avijeet is also interested in politics, cricket, and football.

Recommended Resources

Free eBook: Top Programming Languages For A Data Scientist

Normality Test in Minitab: Minitab with Statistics

Machine Learning Career Guide: A Playbook to Becoming a Machine Learning Engineer

• PMP, PMI, PMBOK, CAPM, PgMP, PfMP, ACP, PBA, RMP, SP, and OPM3 are registered marks of the Project Management Institute, Inc.

Hypothesis Testing in Healthcare Decision-Making Essay

Introduction.

Hypothesis testing plays a proficient role in the deductive and inductive derivation of insights across distinctive industries. Research indicates that developing a hypothesis in the healthcare sector is a statistical inference encompassing the comparative analysis of a causal or correlation perspective (Liu et al., 2022). Primarily, hypothesis testing is an initiative optimally utilized to quantify the strength of evidence parallel to the sample data. Therefore, the practice is a conductive factor in effective decision-making in medical care due to its attribution of establishing objective overviews on pertinent matters. The testing of a thesis is a strategic initiative that profoundly contributes to sustainable management and advancement in the healthcare mainframe.

Over the decades, the dynamism of sociocultural and economic practices fostered the emergence of various medical problems. One of the critical outliers to solving the challenges in the healthcare sector enshrines objectively demonstrating the interplay between the independent and dependent variables. Transcendentally, researchers agree that the use of hypothesis renders the identification of vital elements in the spectral issue while ascertaining the core approach to determine effective and functional decision-making among the practitioners (Prieto et al., 2021). An excellent example is a comparative analysis between obesity and lifestyle habits. The development of a hypothesis that addresses the pivotal effect between lifestyle habits and obesity further maps the trickle-down effect on individuals’ well-being.

In conclusion, it is the responsibility of professionals to exploit hypothesis testing strategies due to the objective effects. One of the primary virtues in the healthcare sector enshrines promoting the welfare of the patients. Therefore, it is critical to establish factorial baselines affirming correlations and causal perspectives. As a result, the stakeholders access ultimately actionable intelligence for sustainable decision-making. Hypothesis testing is an initiative that significantly influences the quality of medical care as a multidimensional phenomenon.

Liu, X., Zhang, Z., & Wang, L. (2022). Bayesian hypothesis testing of mediation: Methods and the impact of prior odds specifications . Behavior Research Methods , 1-13. Web.

Prieto, C., Kavetski, D., Le Vine, N., Álvarez, C., & Medina, R. (2021). Identification of dominant hydrological mechanisms using Bayesian inference, multiple statistical hypothesis testing, and flexible models . Water Resources Research , 57 (8), e2020WR028338. Web.

• Chicago (A-D)
• Chicago (N-B)

IvyPanda. (2024, April 1). Hypothesis Testing in Healthcare Decision-Making. https://ivypanda.com/essays/hypothesis-testing-in-healthcare-decision-making/

"Hypothesis Testing in Healthcare Decision-Making." IvyPanda , 1 Apr. 2024, ivypanda.com/essays/hypothesis-testing-in-healthcare-decision-making/.

IvyPanda . (2024) 'Hypothesis Testing in Healthcare Decision-Making'. 1 April.

IvyPanda . 2024. "Hypothesis Testing in Healthcare Decision-Making." April 1, 2024. https://ivypanda.com/essays/hypothesis-testing-in-healthcare-decision-making/.

1. IvyPanda . "Hypothesis Testing in Healthcare Decision-Making." April 1, 2024. https://ivypanda.com/essays/hypothesis-testing-in-healthcare-decision-making/.

Bibliography

IvyPanda . "Hypothesis Testing in Healthcare Decision-Making." April 1, 2024. https://ivypanda.com/essays/hypothesis-testing-in-healthcare-decision-making/.

• Trickle-Down vs. Grassroots Organization' Approaches
• The Concept of Actionable Information in Economy
• Drug Efficacy: Factorial Analysis of Variance
• The Trickle-Down Economics Definition and Aspects
• Groups Leadership: Factorial Analysis of Variance
• Multi-Factorial Model and Diagnosis of Illnesses
• Studying the Conductive Polymers
• Stereotype-Conductive Behavior
• ANCOVA and Factorial ANOVA: A Case Study
• What Does Husserl Mean by Individualized Consciousness?
• The Hospital of the University of Pennsylvania
• The Colposcopy Clinics Expansion
• The Eastern Chestnut Regional Health System's Merger
• An Analytic Strategy for the New Medical Center
• Empowering Healthcare Through Democratic Leadership

Thesis Vs Hypothesis: Understanding The Basis And The Key Differences

Hypothesis vs. thesis: They sound similar and seem to discuss the same thing. However, these terms have vastly different meanings and purposes. You may have encountered these concepts in school or research, but understanding them is key to executing quality work. 

As an inexperienced writer, the thought of differentiating between hypotheses and theses might seem like an insurmountable task. Fortunately, I am here to help. 

In this article, I’ll discuss hypothesis vs. thesis, break down their differences, and show you how to apply this knowledge to create quality written works. Let’s get to it!

Thesis vs. Hypothesis: Understanding the Basis

The power of a thesis.

A thesis is a foundational element in academic writing and research. It also serves as the linchpin of your argument, encapsulating the central idea or point you aim to prove or disprove throughout your work. 

A thesis statement is typically found at the end of the introduction in an essay or research paper, succinctly summarizing the overarching theme.

Crafting a strong thesis

• Understand the research: Begin by thoroughly comprehending the requirements and objectives of your research. Having a clear understanding of the topic you are arguing or analyzing is crucial.
• Choose a clear topic: Choose one that interests you and aligns with the research’s scope. Clarity and focus are essential in crafting a strong thesis.
• Conduct research: Gather relevant information and sources to develop a deep understanding of your topic. This research will provide the evidence and context for your thesis.
• Identify your position: Determine your stance or position on the topic. Your thesis should express a clear opinion or argument you intend to support throughout your work.
• Narrow down your focus: Refine your topic and thesis more precisely. Avoid broad, generalized statements. Instead, aim for a concise and specific thesis that addresses a particular aspect of the topic.
• Test for validity: Ensuring that you can argue and provide evidence to support your thesis is crucial. It should not be a self-evident or universally accepted fact.
• Write and revise: Craft your thesis statement as a clear, concise sentence summarizing your main argument. Revise and refine it as needed to improve its clarity and strength.

Remember that a strong thesis serves as the foundation for your entire piece of writing, guiding your readers and keeping your work focused and organized.

Hypothesis: The scientific proposition

In contrast, a hypothesis is a tentative proposition or educated guess. It is the initial step in the scientific method, where researchers formulate a hunch to test their assumptions and theories. 

A hypothesis is an assertion that can be proven or disproven through experimentation and observation.

Formulating a hypothesis

• Identify the research question: Identify the research question or problem you want to investigate. Clearly define the scope and boundaries of your inquiry.
• Review existing knowledge: Conduct a literature review to gather information about the topic. Understand the existing body of knowledge and literature in the field.
• Formulate a tentative explanation: Based on your research and understanding of the topic, create a tentative explanation or educated guess about the phenomenon you are studying. This should be a statement that can be falsifiable through experimentation or observation.
• Make it testable: Ensure that your hypothesis is testable and falsifiable. In other words, designing experiments or gathering data supporting or refuting your hypothesis should be possible.
• Specify variables and predictions: Clearly define the variables involved in your hypothesis and make predictions about how changes in these variables will affect the outcome. It also helps in designing experiments and collecting data to test your hypothesis.

Formulating a hypothesis is a crucial step in the scientific method since it directs research and guides efforts to validate theories or uncover new knowledge.

Key Differences Between Thesis vs. Hypothesis

1. Nature of statement

• Thesis: A thesis presents a clear and definitive statement or argument that summarizes the main point of a research paper or essay.
• Hypothesis: A hypothesis is a tentative and testable proposition or educated guess that suggests a possible outcome of an experiment or research study.
• Thesis: The primary purpose of a thesis is to provide a central focus and roadmap for the entire piece of academic writing.
• Hypothesis: The main purpose of a hypothesis is to guide scientific research by proposing a specific prediction that can be tested and validated.

3. Testability

• Thesis: A thesis is not typically subjected to experimentation but serves as a point of argumentation and discussion.
• Hypothesis: A hypothesis, on the other hand, is explicitly designed for testing through experimentation or observation, making it a fundamental part of the scientific method.

4. Research stage

• Thesis: A thesis is usually formulated after extensive research and analysis as a conclusion or summary of findings.
• Hypothesis: A hypothesis is formulated at the beginning of a research project to establish a basis for experimentation and data collection.
• Thesis: A thesis typically encompasses the entire research paper or essay, providing an overarching theme throughout the work.
• Hypothesis: A hypothesis addresses a specific aspect of a research question or problem, guiding the focus of experiments or investigations.

6. Examples

• Thesis: Example of a thesis statement: “The impact of climate change on marine ecosystems is irreversible.”
• Hypothesis: Example of a hypothesis: “If increased temperatures continue, coral reefs will experience bleaching events.”
• Thesis: The thesis represents a conclusion or a well-supported argument and does not aim to be proven or disproven.
• Hypothesis: On the other hand, a hypothesis aims to be tested and validated through empirical evidence. Besides, it can be proven true or false based on the results of experiments or observations.

These differences highlight the distinct roles that the thesis and hypothesis play in academic writing and scientific research, with one providing a point of argumentation and the other guiding the scientific inquiry process.

Can a hypothesis become a thesis?

Yes. A hypothesis can develop into a thesis as it accumulates substantial evidence through research.

Do all research papers require a thesis?

Not necessarily. While most academic papers benefit from a clear thesis, some, like purely descriptive papers, may follow a different structure.

Can a thesis be proven wrong?

Yes. The purpose of a thesis is not only to prove but also to encourage critical analysis. It can be proven wrong with compelling counterarguments and evidence.

How long should a thesis statement be?

A thesis statement should be concise and to the point, typically one or two sentences.

Is a hypothesis only used in scientific research?

Although hypotheses are typically linked to scientific research, they can also be used to verify assumptions and theories in other areas.

Can a hypothesis be vague?

No. When creating a hypothesis, it’s important to make it clear and able to be tested. Developing experiments and making conclusions based on the results can be difficult if the hypothesis needs clarification.

Final Thoughts

In conclusion, understanding the differences between a hypothesis and a thesis is vital to crafting successful research projects and academic papers. While they may seem interchangeable at first glance, these two concepts serve distinct purposes in the research process. 

A hypothesis serves as a testable prediction or explanation, whereas a thesis is the central argument of a paper or project. Your work can lack clarity and purpose without understanding the difference. 

So, the next time you embark on a research project, take the time to ensure that you understand the fundamental difference between a hypothesis and a thesis. Doing so can lead to more focused, meaningful research that advances knowledge and understanding in your field.

You can also learn more about how long a thesis statement should be .

Thanks for reading.

You may also like:

• Discover Where Thesis Statement Is Located In An Essay
• Master’s Thesis Length: How Long Should A Master’s Thesis Be?
• How Long Is A Thesis Paper: Factors Involved & Formatting Tips
• Moral Argument – Examples And Benefits
• Examples of Work Ethic: Everyone Loves a Good Employee

People Also Read:

Why Do Waiters Get Paid So Little [+ How To Make More Money]

Navigating Workplace Norms: Can You Email A Resignation Letter?

Difference Between Roles And Responsibilities

Does Suspension Mean Termination?

Moral Claim: Definition, Significance, Contemporary Issues, & Challenges

Why Can’t You Flush The Toilet After A Drug Test?

The Plagiarism Checker Online For Your Academic Work

Start Plagiarism Check

Editing & Proofreading for Your Research Paper

Get it proofread now

Online Printing & Binding with Free Express Delivery

Configure binding now

• Academic essay overview
• The writing process
• Structuring academic essays
• Types of academic essays
• Academic writing overview
• Sentence structure
• Academic writing process
• Improving your academic writing
• Titles and headings
• APA style overview
• APA citation & referencing
• APA structure & sections
• Citation & referencing
• Structure and sections
• APA examples overview
• Commonly used citations
• Other examples
• British English vs. American English
• Chicago style overview
• Chicago citation & referencing
• Chicago structure & sections
• Chicago style examples
• Citing sources overview
• Citation format
• Citation examples
• College essay overview
• Application
• How to write a college essay
• Types of college essays
• Commonly confused words
• Definitions
• Dissertation overview
• Dissertation structure & sections
• Dissertation writing process
• Graduate school overview
• Application & admission
• Study abroad
• Master degree
• Harvard referencing overview
• Language rules overview
• Grammatical rules & structures
• Parts of speech
• Punctuation
• Methodology overview
• Analyzing data
• Experiments
• Observations
• Inductive vs. Deductive
• Qualitative vs. Quantitative
• Types of validity
• Types of reliability
• Sampling methods
• Theories & Concepts
• Types of research studies
• Types of variables
• MLA style overview
• MLA examples
• MLA citation & referencing
• MLA structure & sections
• Plagiarism overview
• Plagiarism checker
• Types of plagiarism
• Printing production overview
• Research bias overview
• Types of research bias
• Example sections
• Types of research papers
• Research process overview
• Problem statement
• Research proposal
• Research topic
• Statistics overview
• Levels of measurment
• Frequency distribution
• Measures of central tendency
• Measures of variability
• Hypothesis testing
• Parameters & test statistics
• Types of distributions
• Correlation
• Effect size
• Hypothesis testing assumptions
• Types of ANOVAs
• Types of chi-square
• Statistical data
• Statistical models
• Spelling mistakes
• Tips overview
• Academic writing tips
• Dissertation tips
• Sources tips
• Working with sources overview
• Evaluating sources
• Finding sources
• Including sources
• Types of sources

Your Step to Success

Plagiarism Check within 10min

Printing & Binding with 3D Live Preview

Hypothesis Testing – Step by Step Guide

How do you like this article cancel reply.

Save my name, email, and website in this browser for the next time I comment.

Hypothesis testing is mainly used to eliminate sampling error (chance) as a possible explanation for any fallouts obtained from a research study. As you will see in this article, hypothesis testing is a method often relied upon to help student researchers establish whether a given treatment contains an effect on the subjects of a population. Apart from getting its official definition and a suitable example, you will also get to learn about the steps followed in hypothesis testing.

Inhaltsverzeichnis

• 1 Hypothesis Testing – FAQs
• 2 Hypothesis Testing: Definition
• 3 Hypothesis Testing: Step by Step Guide
• 4 Hypothesis Testing: Example
• 5 Hypothesis Testing: In a Nutshell

Hypothesis Testing – FAQs

How do you write a hypothesis test.

Before it comes to printing & binding your dissertation you need to do your research, which often includes hypothesis tests. There is no variation in the manner in which hypothesis tests are performed or written. In hypothesis testing, the researcher should start by stating the hypothesis that they intend to examine. From here, they will need to formulate a plan on how to conduct the analysis, and then study their sample data. Sample data analysis is then followed by the acceptance or rejection of the null hypothesis established earlier.

How Do You Formulate a Hypothesis?

An examinable hypothesis is never a simple statement. The researcher needs to come up with an intricate statement capable of providing a flawless overview of the scientific experiment at hand. It should also state the intentions of the experiment and the outcomes likely to be achieved. During hypothesis testing, you will need to consider the following: I. Start by stating the problem you would like to solve II. If possible, ensure the hypothesis you craft appears in the form of an if-then statement III. Outline all your variables

What Is a Simple Hypothesis?

The simple hypothesis refers to the prediction of the association that exists amongst two variables, namely the dependent variable and the independent one.

What Are the 3 Main Parts of Any Good Hypothesis?

A good hypothesis ought to comprise of three main distinct sections: problem definition, proposed solutions, and the outcome (result).

What Are The Steps of Hypothesis Testing?

Scientists often use it to study specific predictions known as “hypotheses,” which they formulate from theories. The hypothesis testing process mainly involves five steps: I. State the research hypothesis by specifying whether it is an alternate (Ha) hypothesis or a null (H0) hypothesis. II. Gather data in a manner that is designed to help you examine the hypothesis III. Conduct a suitable statistical test IV. Elect whether your null hypothesis is refuted or supported V. Put forward what you have found in your discussion or results section

Hypothesis Testing: Definition

In statistics, hypothesis testing is considered an act where an analyst or researcher attempts to study a statement related to a given population parameter. The reason for this analysis and the data currently available determines the research methodology that the analyst will apply.

Hypothesis Testing: Step by Step Guide

As mentioned elsewhere in this article, hypothesis testing is a process used to examine the concepts that a researcher has about the world and the population around them.

Hypothesis Testing 1st Step: Start by Stating the Hypotheses

You will need to state the hypotheses according to the following order:

I. Research Hypothesis II. Null Hypothesis III. And last but not least the Alternate Hypothesis

As you state the hypotheses, there will also be a need for you to recall what differentiates a general hypothesis that can’t be reversed following a single investigation and the alternate and null hypothesis.

Hypothesis Testing 2nd Step: Assumptions

For hypothesis testing, you will need to include:

i. Data level measurements ii. Distributions that underlie your information iii. Available data or the lack of information related to population features iv. Sample methods and size v. Sample features needed to apply your measurement statistics vi. testing significance

Hypothesis Testing 3rd Step: Confidence Interval Structure or Test Statistic

Here you are required to specify:

• The structure you will need to use for you to test the set of confidence intervals or test significance levels (ensure you also include the notation and the required equations).
• All the special conditions that the statistic will need to meet.

Hypothesis Testing 4th Step: Probability Statement or Rejection Region

A rejection region refers to the expected measure of your examination statistic as made by the critical valve or tables for a confidence interval. Before you can start performing your calculations, it will be necessary for you to let the reader know how that particular test will be applied to discard the null hypothesis. Also, ensure you communicate the critical value you intend to use to make your determination.

Hypothesis Testing 5th Step: Annotated Spreadsheet (Calculations)

An annotated spreadsheet refers to the actual confidence interval or test statistic measure that you will generate. It should include a detailed specification of any extra equations applied as well as their notation. In some cases, you can also incorporate the sample calculations.

The process of solving a problem can be viewed as an art or as a skill. In terms of skills, you will need to break your problem down into tiny modules or parts. Once broken down, you will need to ensure you keep on checking on them using a hand calculator, sample calculations, or any other methods you may have in mind. It helps to ascertain that your solution doesn’t have any errors.

As mentioned earlier, problem-solving can also be viewed as art. Depending on your skill level, you will find that there are numerous ways of laying out a given task. Applying some elegance to this process guarantees that even the uninformed reader will understand what it is that you are trying to do. Furthermore, a problem that has been broken down into constituent sections always appears simple.

Hypothesis Testing 6th Step: Conclusions

The final step is all about making a statement of your results. It’s also known as the acceptance or discarding of your null hypothesis. In this last step, a researcher also gets to provide a direction for any research they intend to conduct in the future.

When making conclusions, it’s important to provide a summary of your results in mapped, graphical, or tabular form. Make sure also to include a discussion of where the research has taken you.

Providing an answer without taking the time to make a good discussion and/or presentation will not prove very useful. Textbooks often make the mistake of focusing on the correct numbers while failing to provide a thoughtful discussion or making a full presentation.

Hypothesis Testing: Example

Peppermint Essential Oil

Chamomile, lavender, and peppermint are some of the most popular essential oils available today. Having heard about their ability to reduce anxiety, you may want to prove whether this essential oil does indeed have some healing powers.

In this case, the hypothesis is likely to go as below:

I. The null hypothesis—As an essential oil, peppermint doesn’t assist in reducing anxiety pangs II. The alternative hypothesis—Peppermint is capable of reducing anxiety pangs III. Level of significance—Place the significance level at 0.25 (this will provide you with a better opportunity to prove the alternative hypothesis). IV. P-value—It’s calculated as 0.05 V. Conclusion—Once one of the groups is proven using a placebo and the other with peppermint oil, you will need to differentiate the two according to the self-reported anxiety levels. Using your calculations, any difference that exists between the two test groups will be statistically important when it has a 0.05 p-value. This is well-below the pre-defined 0.25 alpha level. The conclusion will, therefore, note that the results of your examination support the alternative hypothesis.

TIP: Always use transition words to properly connect the sentences and paragraphs in your thesis or essay.

Hypothesis Testing: In a Nutshell

• Sample data is used to evaluate whether a hypothesis is plausible
• Statistical analysts study hypotheses by examining and measuring randomly generated samples of the population under scrutiny
• The examination supplies evidence related to the credibility of a hypothesis based on available data.
• Hypothesis testing works by analyzing statistical samples to supply evidence on whether a null hypothesis is plausible or not.

We use cookies on our website. Some of them are essential, while others help us to improve this website and your experience.

• External Media

Individual Privacy Preferences

Cookie Details Privacy Policy Imprint

Here you will find an overview of all cookies used. You can give your consent to whole categories or display further information and select certain cookies.

Accept all Save

Essential cookies enable basic functions and are necessary for the proper function of the website.

Show Cookie Information Hide Cookie Information

Statistics cookies collect information anonymously. This information helps us to understand how our visitors use our website.

Content from video platforms and social media platforms is blocked by default. If External Media cookies are accepted, access to those contents no longer requires manual consent.

Privacy Policy Imprint

File(s) under embargo

until file(s) become available

Porous Materials via Freeze Casting: 3D MXene, Ceramics, and Their Composites for Energy Storage Applications

 Freeze casting, an innovative materials processing technique, offers significant potential to create porous structures with high surface-to-volume ratio for high performance devices. This thesis presents a comprehensive study on the fabrication of porous structures using 2D MXene nanomaterials, silica, and alumina, with a focus on achieving controllable interconnected porosity and demonstration of such structures for steelmaking and energy storage. This thesis is divided into three sections. The first part of the thesis examines the freeze casting process for fabricating porous ceramics using silica and camphene. A full-factorial design of experiments is conducted to correlate freeze casting parameters with pore characteristics. Variables like solid loading, particle size, cooling temperature, and distance from the cooling surface are scrutinized. The fabricated samples are cross-sectioned and analyzed using scanning electron microscopy and image processing, yielding detailed data on areal porosity, pore size, shape, and orientation. The study successfully demonstrates the ability to steer pore orientation using bidirectional freezing, supported by a finite-element model, providing a quantitative understanding of the effects of freeze casting parameters on the part porosity. In the second part, the research establishes the suitability of freeze-cast alumina for high-temperature applications such as structural ceramics for molten metal and glass processing. Specific tests such as gas permeability, dilatometry and steel penetration tests for porous alumina are carried out in collaboration with Vesuvius Plc., a global leader in molten metal flow engineering and technology, towards this goal. By varying process parameters like solid loading and freezing conditions, the study creates alumina with microscale, interconnected, and directional pores, achieving controlled gas permeability and mechanical strength. The optimized alumina exhibits 70% porosity, impressive gas permeability, high compressive strength, and a suitable dynamic elastic modulus; along with consistent performance under high temperatures, as evidenced by the steel penetration tests. These findings highlight the potential of freeze-cast alumina in advanced industrial applications. The final part of the thesis addresses the challenge of assembling MXene nanomaterials in 3D space without restacking. A novel material system is introduced, comprising a 3D MXene network on a porous ceramic backbone, fabricated using freeze casting. This MXene-infiltrated porous silica (MX-PS) system demonstrates high conductivity and effective performance as supercapacitor electrodes. The successful creation of 3D architectures of 2D MXenes opens new avenues in various fields, including energy storage and catalysis. Overall, this thesis contributes significantly to the literature on porous ceramics and MXene-based nanomaterials, providing valuable insights into their controllable and scalable manufacturing, characterization, and application in high-performance devices and industrial settings. 

Degree Type

• Dissertation
• Mechanical Engineering

Degree Name

• Doctor of Philosophy (PhD)

Usage metrics