Flowcharts are a useful means of taking you through many of the key questions you should be asking on deciding which hypothesis test(s) to use for your data. A couple of these can be found below.

Which hypothesis test 1

Please note carefully from this flowchart that when comparing two groups of continuous (equivalently, scale or measurement) data, the requirement to test for Normality before choosing a hypothesis test is waived provided both groups are of size at least 30. This result is a corollary from the Central Limit Theorem (see video) which states that for a sufficiently large sample size, the distribution of the sample mean approximates to Normality regardless of the distribution of the population from which that sample was taken. This is a powerful theorem and can save you some work.  For smaller sample sizes, testing the Normality of your data is a means of obtaining evidence that your sample has been taken from a larger population (the parent population) which is itself Normally distributed.  This is important because you can then conclude that the distribution of the sample mean for all samples taken from the population is Normal. It is this result that justifies use of a t-test.  However, the Central Limit Theorem tells us that for sufficiently large samples, the distribution of the sample mean approximates to Normality anyhow, regardless of whether or not the parent population is Normal.  This is a handy finding, as for sufficiently large groups, an independent samples t-test or paired samples t-test can be used without the need to test for Normality.

However, before applying the Central Limit Theorem to your data, it makes best sense to check that your data really appear continuous by plotting a histogram for each group of interest. If the histogram consists of blocks of data with gaps in between, your data may be better represented in categorical form.

Note. I may be splitting hairs here, but I say ‘at least 30’ as opposed to ‘greater than 30’ (cf. content of above video) in setting the cut-off for allowing you to apply the Central Limit Theorem. There is in fact more disagreement than I would care to describe here about where the limit should lie and the choice is not really integral to the statement of the Central Limit Theorem. Let me be that little more more lenient when it comes to setting requirements for student projects!

Once you have used the above flowchart to decide which type of t-test to perform, if appropriate, you can refer to the StatsforMedics page HYPOTHESIS TESTS FOR COMPARING TWO GROUPS OF MEASUREMENT OR ORDINAL DATA in order to learn how to perform them and interpret and present your findings in a statistically sound way.

Which Hypothesis Test 2: Comprehensive flowchart on ANOVA  

This chart contains the term residuals, to gain a simple and clear understanding of the meaning of residuals in statistics, please refer to the Wikipedia page Errors and residuals in statistics. Use should also find the resource The ANOVA helpful in supporting your understanding of the different ANOVA designs provided in this flowchart, including when to use them.

Please note that no flowchart can exhaustively tackle all of the issues that ought to be considered in the choice of statistical methodology for any project. For example, instead of tests of difference, you may need to consider tests of agreement. It is therefore very much worthwhile using these charts as a starting point rather than an end-point when seeking advice from the Medical Statistician.

Using the flowcharts: If you are planning to compare two groups of data, please take time out to carefully consider the information provided in the box on the top left-hand side of the page for the first flowchart, where you will find that the difference between independent and related groups has been clearly explained. As you will see from the box on the top right-hand side of the page for the second flow-chart, the terms between subjects and within subjects are used when considering an Analysis of Variance (ANOVA) for independent and related groups, respectively. 

Flowcharts for choosing hypothesis tests by Margaret MacDougall is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.