Which parametric test

The investigator should then ask "are the data independent? Thus results from a crossover trial, or from a case-control study in which the controls were matched to the cases by age, sex and social class, are not independent. The next question is "what types of data are being measured?

The choice of test for matched or paired data is described in Table 1 and for independent data in Table 2. It is helpful to decide the input variables and the outcome variables. For example, in a clinical trial the input variable is the type of treatment - a nominal variable - and the outcome may be some clinical measure perhaps Normally distributed. The required test is then the t -test Table 2.

However, if the input variable is continuous, say a clinical score, and the outcome is nominal, say cured or not cured, logistic regression is the required analysis. A t -test in this case may help but would not give us what we require, namely the probability of a cure for a given value of the clinical score. As another example, suppose we have a cross-sectional study in which we ask a random sample of people whether they think their general practitioner is doing a good job, on a five point scale, and we wish to ascertain whether women have a higher opinion of general practitioners than men have.

The input variable is gender, which is nominal. The outcome variable is the five point ordinal scale. Each person's opinion is independent of the others, so we have independent data. Note, however, if some people share a general practitioner and others do not, then the data are not independent and a more sophisticated analysis is called for.

Note that these tables should be considered as guides only, and each case should be considered on its merits. However, they require certain assumptions and it is often easier to either dichotomise the outcome variable or treat it as continuous. Parametric tests are those that make assumptions about the parameters of the population distribution from which the sample is drawn. This is often the assumption that the population data are normally distributed. Table 3 shows the non-parametric equivalent of a number of parametric tests.

Non-parametric tests are valid for both non-Normally distributed data and Normally distributed data, so why not use them all the time? It would seem prudent to use non-parametric tests in all cases, which would save one the bother of testing for Normality. Typical parametric tests can only assess continuous data and the results can be significantly affected by outliers. Conversely, some nonparametric tests can handle ordinal data, ranked data, and not be seriously affected by outliers. Be sure to check the assumptions for the nonparametric test because each one has its own data requirements.

This can be the case when you have both a small sample size and nonnormal data. However, other considerations often play a role because parametric tests can often handle nonnormal data. Finally, if you have a very small sample size, you might be stuck using a nonparametric test.

Please, collect more data next time if it is at all possible! Your chance of detecting a significant effect when one exists can be very small when you have both a small sample size and you need to use a less efficient nonparametric test!

Minitab Blog. Nonparametric analysis to test group medians. Hypothesis Tests of the Mean and Median Nonparametric tests are like a parallel universe to parametric tests. Parametric analyses Sample size guidelines for nonnormal data 1-sample t test Greater than 20 2-sample t test Each group should be greater than 15 One-Way ANOVA If you have groups, each group should be greater than If you have groups, each group should be greater than Parametric tests are suitable for normally distributed data.

Choosing Between Parametric and Nonparametric Tests Deciding whether to use a parametric or nonparametric test depends on the normality of the data that you are working with. Therefore, the first step in making this decision is to check normality. One option is to perform a simple check based on a histogram. If your histogram is roughly symmetrical, it is safe to assume that the data is relatively normally distributed, and a parametric test will be appropriate.

If the histogram is not symmetrical, then a nonparametric test will be more appropriate. Get started with Alchemer today. Brand Experience CX Prediction Start making smarter decisions Contact sales Start a free trial. Contact Sales. By accessing and using this page, you agree to the Terms of Use. Your information will never be shared.