Statnote 7: chi-square contingency tables

When the data are counts or the frequencies of particular events and can be expressed as a contingency table, then they can be analysed using the chi-square distribution. When applied to a 2 x 2 table, the test is approximate and care needs to be taken in analysing tables when the expected frequencies are small either by applying Yate’s correction or by using Fisher’s exact test. Larger contingency tables can also be analysed using this method. Note that it is a serious statistical error to use any of these tests on measurement data!

Statnote 1: is the data normal?

Testing whether an observed distribution of observations deviates from normality is a common type of statistical test available in statistics software. Most software offer two ways of judging whether there are significant deviations of the observed from the expected distributions, viz., chi-square and the KS test. These tests have different sensitivities and problems and often give conflicting results. The results of these tests together with observations of the shape of the observed distribution should be used to judge normality.

Statnote 34 : the Kolmogorov-Smirnov (KS) test

The Kolmogorov-Smirnov (KS) test is a non-parametric test which can be used in two different circumstances. First, it can be used as an alternative to chi-square (?2) as a ‘goodness-of-fit’ test to compare whether a given ‘observed’ sample of observations conforms to an ‘expected’ distribution of results (KS, one-sample test). An example of the use of the one-sample test to determine whether a sample of observations was normally distributed was described previously. Second, it can be used as an alternative to the Mann-Whitney test to compare two independent samples of observations (KS, two-sample test). Hence, this statnote describes the use of the KS test with reference to two scenarios: (1) to compare the observed frequency (Fo) of soil samples containing cysts of the protozoan Naegleria collected each month for a year with an expected equal frequency (Fe) across months (one-sample test), and (2) to compare the abundance of bacteria on cloths and sponges sampled in a domestic kitchen environment (two-sample test).