Statistical Analysis for Education and Psychology Researchers

also shown and the pragmatic consequences of particular violations, some of which are
more serious than others, are discussed.
In summary, each statistical procedure is introduced and discussed using the following
subheadings:

• when to use the test;


• statistical inference (and null hypothesis);


• test assumptions;


• example from the literature;


• worked example (simplified data);


• interpretation (using statistical tables);


• computer analysis (real data);


• interpretation of computer output.

We begin this chapter with tests appropriate for one-group (sample) designs using binary
or nominal data. These tests are appropriate when the research question is concerned with
either association between two variables (or correlation), or differences between
proportions, or percentages. We then consider tests for two-group (sample) designs, both
related and independent groups with binary and nominal data. Research questions may
again relate to association or to differences and comparisons between the two groups.
Finally, multiple group designs are considered for binary and nominal data. These tests
are appropriate when interest focuses on differences or association between three or more
groups which may be either related or independent.

6.1 Chi-square Tests for Contingency Tables

In this section both the One-sample Chi-square test of independence and the Two-
sample Chi-square test of homogeneity are considered together because of their
similarity in both computation and interpretation.

When to Use

The Chi-square test (χ^2 is pronounced ky similar to by) is an approximate test of
significance for association between two categorical variables when data is in the form of
frequency counts and interest focuses on how many subjects fall into different categories.
The precise hypothesis tested depends upon the sampling design used. Observed
frequencies in a 2×2 table (the first ‘2’ indicates the number of rows in the table and the
second ‘2’ refers to the number of columns) may arise from a number of different
research designs and this often causes confusion. Two common sampling designs are the
χ^2 test of independence with random row and column marginal totals and the χ^2 test of
homogeneity of proportions with either fixed row or fixed column marginal totals.

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