A parametric test uses a sample to infer something about a population whose data are assumed to follow a specified probability distribution. It can help analysts evaluate group differences or relationships, but its conclusions depend on whether the relevant assumptions fit the data. section 4.2.1 section 4.2
Choose a test that matches the question:
- Use a t-test to compare two group means, including independent groups or paired before-and-after measurements. section 4.2.1
- Use ANOVA to compare means across two or more groups; it can also accommodate multiple factors. section 4.2.1
- Use Pearson’s correlation for a linear relationship between continuous variables. Linear and logistic regression model relationships with continuous and categorical outcomes, respectively. section 4.2.1
Figure 4.19 Parametric statistics assume that the population data follows a specific probability distribution and that you can make inferences about the parameters of that distribution based on your sample data.
The figure links the assumed population distribution to the parameters estimated from a sample—the step on which parametric inference relies. section 4.2.1
Before interpreting a result, inspect the distribution rather than relying on a summary statistic alone. Many parametric tests assume normality, and many assume equal variances; extreme outliers can also matter. A histogram or boxplot can expose problems that a mean hides. Some skewed data can be transformed toward a normal distribution, but transformation is not a guarantee that the assumptions will hold. section 4.2.1 section 4.4
When transformation is not enough
Suppose an app’s user data form bimodal distributions. Square and square-root transformations still leave them far from normal. A one-way ANOVA is then unlikely to give reliable results; consider a test with different or fewer distributional assumptions instead of forcing the data into a familiar method. section 5.1 section 5.0
Why sample size changes interpretation
Two groups of students have mean scores of 80.4 and 79.9, with sample sizes of 45 and 44. Their difference is not statistically significant in the illustrated comparison. Increasing the sample size tenfold makes the result significant: a significance threshold alone does not communicate how large the difference is. section 4.2.1
Treat a p-value as part of an interpretation, not as a guarantee that a finding is important or that assumptions were met. Check whether the test suits the question and data, then describe the result and its limitations precisely to stakeholders. If assumptions remain unmet, evaluate non-parametric or semi-parametric alternatives. section 4.2.1 section 4.4 section 5.1.2
