How to Choose an Appropriate Statistical Test

There are number of tests in biostatistics, but choice mainly depends on characteristics and type of analysis of data. Sometimes, we need to find out the difference between means or medians or association between the variables. Number of groups used in a study may vary; therefore, study design also varies. Hence, in such situation, we will have to make the decision which is more precise while selecting the appropriate test. In appropriate test will lead to invalid conclusions. Statistical tests can be divided into parametric and non- parametric tests. If variables follow normal distribution, data can be subjected to parametric test, and for non- Gaussian distribution, we should apply non-parametric test. Statistical test should be decided at the start of the study. Following are the different parametric test used in analysis of various types of data.

1) Student's ‘t’ Test

Mr. W. S. Gosset, a civil service statistician, introduced‘t’ distribution of small samples and published his work under the pseudonym ‘Student.’ This is one of the most widely used tests in pharmacological investigations, involving the use of small samples. The‘t’ test is always applied for analysis when the number of sample is 30 or less. It is usually applicable for graded data like blood sugar level, body weight, height etc. If sample size is more than 30, ‘Z’ test is applied. There are two types of ‘t’ test, paired and unpaired.

When to apply paired and unpaired

a) When comparison has to be made between two measurements in the same subjects after two consecutive treatments, paired ‘t’ test is used. For example, when we want to compare effect of drug A (i.e. decrease blood sugar) before start of treatment (baseline) and after 1 month of treatment with drug A.

b) When comparison is made between two measurements in two different groups, unpaired ‘t’ test is used. For example, when we compare the effects of drug A and B (i.e. mean change in blood sugar) after one month from baseline in both groups, unpaired ‘t’ test’ is applicable.

2) ANOVA

When we want to compare two sets of unpaired or paired data, the student’s‘t’ test is applied. However, when there are 3 or more sets of data to analyze, we need the help of well-designed and multi-talented method called as analysis of variance (ANOVA). This test compares multiple groups at one time. In ANOVA, we draw assumption that each sample is randomly drawn from the normal population, and also they have same variance as that of population. There are two types of ANOVA.

A) One way ANOVA: It compares three or more unmatchedgroups when the data are categorized in one way. For example, we may compare a control group with three different doses of aspirin in rats. Here, there are four unmatched group of rats. Therefore, we should apply one way ANOVA. We should choose repeated measures ANOVA test when the trial uses matched subjects. For example, effect of supplementation of vitamin C in each subject before, during, and after the treatment. Matching should not be based on the variable you are com paring. For example, if you are comparing blood pressures in two groups, it is better to match based on age or other variables, but it should not be to match based on blood pressure. The term repeated measures applies strictly when you give treatments repeatedly to one subjects. ANOVA works well even if the distribution is only approximately Gaussian. Therefore, these tests are used routinely in many field of science. The P value is calculated from the ANOVA table.

B) Two ways ANOVA: Also called two factors ANOVA, determineshow a response is affected by two factors. For example, you might measure a response to three different drugs in both men and women. This is a complicated test. Therefore, we think that for postgraduates, this test may not be so useful.

Importance of post hoc test

Post tests are the modification of‘t’ test. They account for multiple comparisons, as well as for the fact that the comparison are interrelated. ANOVA only directs whether there is significant difference between the various groups or not. If the results aresignificant, ANOVA does not tell us at what point the difference between various groups subsist. But, post test is capable to pinpoint the exact difference between the different groups of comparison. Therefore, post tests are very useful as far as statistics is concerned. There are five types of post- hoc test namely; Dunnett's, Turkey, Newman-Keuls, Bonferroni, and test for linear trend between mean and column number.

How to select a post test?

1) Select Dunnett's post-hoc test if one column represents control group and we wish to compare all other columns to that control column but not to each other.

2) Select the test for linear trend if the columns are arranged in a natural order (i.e. dose or time) and we want to test whether there is a trend so that values increases (or decreases) as you move from left to right across the columns.

3) Select Bonferroni, Turkey's, or Newman's test if we want to compare all pairs of columns