Statistical Analysis for Education and Psychology Researchers

6.3 Fisher’s Exact Test 181

A test for studying differences in two independent groups (2×2

contingency table) and is particularly useful when sample sizes are

small. Data should be in the form of frequency counts.

6.4 Proportions Test 187

A two-sample test for binomial data, used to estimate the difference

between two sample proportions or percentages. A response variable

is counted as present or absent for subjects and a group proportion (or

percentage) is calculated.

6.5 Sign Test 192

A nonparametric repeated measures test of direction of difference

between two measures. It is useful when actual measurement is

difficult but it is possible to determine, for each pair of measures,

which measure is smaller in some meaningful sense. The response

variable should be at least theoretically continuous.

Multiple-Sample Tests^

6.6 r×k Sample χ

(^2) test

196

This is a direct extension of the r×2 Sample χ^2 test when there are

more than two groups (samples).^

6.7 Cochran’s Q Test 199

A procedure for comparing three or more related groups on a binary

response variable. The proportions in each treatment group

(measurement occasion) are compared.

Introduction

Many research studies in the social sciences use observations or measures that are in the
form of count data. Whenever data is obtained from a population which can be thought of
as discrete in nature, then any statistical inferences we make using data such as frequency
counts, percentages or proportions are, in fact, inferences that involve count data. For
example, if we were interested in a possible difference between the proportions (or
percentages) of male and female students studying Advanced Level (A-level) science
subjects, then the parameters about which we would make inferences are the population
proportions and data sampled from the population would be in the form of counts or
frequencies.
Count data can be binary when only two mutually exclusive categories exist, for
example, gender. Count data may also be: nominal, when counts can be classified into
more than two mutually exclusive groups and there is no order implied in the groupings

Statistical analysis for education and psychology researchers 160