R-ticulate

5Two‐Sample and One‐Sample Tests

One‐ and two‐sample tests were the early cornerstones in statistical data analysis. Nowadays, however, our experimental designs tend to be more complex than what these simple tests can handle. Nonetheless, these tests, the famous Student's t‐test in particular, provide excellent entry points into statistical modelling, since the underlying principle can be understood quite easily and they get you into the swing of understanding hypothesis testing and the interpretation of test statistics such as t‐, z‐, F‐, ‐values, etc.

5.1 The t‐Statistic

The t‐statistic boils down to a simple signal‐to‐noise ratio where the difference between two group means (the signal or effect) is normalized (divided) by the pooled standard deviation of the two groups (the noise, Figure 5.3).

(5.1)

This test‐statistic follows a symmetric, bell‐shaped distribution similar to the normal distribution but with longer tails that is called Student's t‐distribution. The number of degrees of freedom () is the shape defining parameter of the t‐distribution (Figure 5.1).

5.2 Two Sample Tests: Comparing Two Groups

5.2.1 Student's t‐Test

Student's t‐test is applied in situations ...