Inferential statistics

The different methods have distinct requirements with respect to to the scale level of the data (see page on Scale levels):

Testing of difference hypotheses

• Methods for nominal data: If differences of frequency in the occurrence of certain attributes or attribute combinations are to be analysed (e.g. Are more female or more male students enrolled in social science courses? Has the number of non-smokers increased after an educational advertising campaign?), then the methods of χ2 are applied to data with a nominal scale.

• Methods for ordinal data (distribution-free methods): If two independent samples are to be compared with respect to their central tendency (e.g. Do the students in one class have better scores than those in another class?), then the Mann-Whitney’s U-test  is used. If two dependent samples are to be compared (e.g. Do the students obtain better scores after training compared  to the scores before training?), then the Wilcoxon-test is used.

• Methods for interval and ratio data: In order to compare two independent sample means (e.g Do the students in a class need more time to solve a task than those in another class?), the t-test for independent samples is used; in a comparison of two dependent sample means (e.g. Do the students need more time before the training to solve a task than after the training?) the t-test for dependent samples is used.
  

Testing of correlational hypotheses

• Methods for nominal data: As a measure of characterising the correlation between two attributes (e.g. is the field of study chosen dependent on gender?) the contingency coefficient is used on nominal-scale data.

• Methods for ordinal data: The correlation between two ordinal-scaled attributes (e.g. Is the popularity of pupils associated with school-leaving qualifications?) is captured using Spearman's ranking correlation coefficient.

• Methods for interval and ratio data: The correlation between pieces of interval or ratio data (e.g. Is the time taken to solve a task linked to age?) is captured using Pearson's product moment correlation coefficient.