IX.

Tests of Reliability

The statistician is often called upon to decide whether an assumed hypothesis for some phenomenon is valid or not. The assumed hypothesis leads to a mathematical model; the model, in turn, yields certain predicted or expected values, for example, 10, 15, 25. The corresponding actually observed values are 12, 16, 21. To determine whether the hypothesis is to be kept or rejected, these deviations must be judged as normal fluctuations caused by sampling techniques or as significant discrepancies. Statisticians have devised several tests for the significance or reliability of data. One is the chi-square (c²) test. The deviations (observed values minus expected values) are squared, divided by the expected values, and summed: