Introduction
This topic covers parametric hypothesis tests, the assumptions they rest on, how to choose the right test for a given study design and data type, and the Student's t-test in its three forms: one-sample, paired and independent-samples. Examiners expect you to name the test, justify the choice, write the hypotheses, and interpret the result correctly.
What parametric tests are
Parametric tests assume that the data come from a population with a known distribution, usually the normal distribution, described by parameters such as the mean and the standard deviation. Because they use these parameters, they are more powerful than their distribution-free counterparts when the assumptions hold. The main assumptions are:
- Measurement scale: the outcome is continuous (interval or ratio), not ordinal or categorical.
- Normality: the outcome is approximately normally distributed in each group, or the sample is large enough for the test to be robust (the central limit theorem helps for the mean, but not for very small or strongly skewed samples).
- Independence: observations are independent of each other, except in designs that are paired on purpose.
- Homogeneity of variance: the groups have similar variances (required for the classic pooled t-test and for ANOVA).