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vital statistics

Hypothesis testing using Student’s t-test

When two sets of data are compared, how do you decide whether they are really different or whether any differences are just attributable to chance? Senior teaching fellow Robert Spooner describes how to address this using the t-test

The Student t-test began as a way to compare malt yield from varieties of barley

Figure 1 compares one population of data (orange) with another population (blue). Orange is a control situation (e.g. enzyme activity under standard conditions; distance jumped by grasshoppers) and blue is a test condition (enzyme activity at high pH; distance jumped when confronted by a large spider). On the left are idealised normal distributions of the data as smoothed curves. The upper panel shows populations that seem to be very similar. The lower panel indicates two distinct populations of data. The populations represented in the middle panel are difficult to judge because the data overlap. The mean values are shown as columns, with error bars representing the standard deviation (SD). This emphasises how similar the two datasets are in the upper panels.

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