Introduction

Have you ever given the same test to two different groups of students in order to see if they were at the same level of ability? Or have you ever have given two different tests to the same group to find out if the group was better in one area of ability than another? Or perhaps to see if the scores from the two tests were correlated? Situations such as these, in which we would like to make inferences about differences in ability, or about relationships between constructs on the basis of test scores, are very common, not only in language assessment, but in language teaching and other areas of applied linguistics research, as well. In order to answer such questions with statistics, we need to understand how we can use the descriptive statistics and correlations obtained from samples, described in Chapters 2 and 3, to make inferences and test hypotheses about differences and relationships between different samples.

In situations such as those mentioned above, where we are interested in differences in group performance, we typically compare the average (mean, median or mode) of one distribution of scores with that of another distribution. Or, if we are interested in investigating the relationship between two sets of test scores, we would compute the appropriate correlation coefficient. However, because it is possible that the differences or the correlations we find may simply be due to chance, we need to use statistical inference to determine how likely it is that these differences or correlations are real.