Student Services, The University of Queensland
CHOOSING THE RIGHT ELEMENTARY STATISTICAL TEST
The first step in determining what statistical test to use is to determine the type of research question to be answered by the statistical analysis. In
elementary courses, the two basic types of questions are:
1. the degree of relationship or dependence among variables (H0 = there is no relationship or dependence, and the statistical test answers the question
as to whether any relationship or dependence found is sufficiently different from zero that it can be considered “statistically significant”.)
2. the significance of group differences (H0 = there is no difference between groups. The statistical test answers the question as to whether an
observed difference is probably due just to random factors, or is large enough to be considered “statistically significant” and due to the treatment
factor.)
The next step is to determine the nature(s) of the variables under discussion, and whether they meet the assumptions of a particular test (e.g. the data are
normally distributed).
Types/levels of data:
nominal = unordered categories (e.g. religion; country of birth; etc.)
ordinal = ordered categories (e.g. level of agreement on an opinion survey; proficiency level at a martial art as measured by the colour of one‟s belt)
For nominal and ordinal data, what is usually recorded is the number of occurrences of a particular result (e.g. number of Christians, number of
Buddhists etc. but these numbers are not the values of the variable. In this case, variable = religion, values = Christian, Buddhist, …and the
numbers are the number of occurrences of a particular value.)
interval = ordinal + distance between values is of constant size (e.g. temperature)
ratio = interval + (i) there is a meaningful zero and (ii) the ratio between two numbers is meaningful (e.g. weight, distance, number of children)
ratio and interval data can be either discrete (i.e. there are gaps between values, e.g. number of children) or continuous (i.e. there are no gaps
between values (e.g. weight, height).
Type of Question
Level of Data /
Assumptions
Examples
Statistical Test
Degree of relationship or
dependence among variables
Is there a relationship between one trait
and another? (I.e. does the observed
frequency of one trait depend on the
frequency of another?)
Both nominal or one
nominal and one ordinal
(i) Is eye colour independent of hair colour?
(ii) Is opinion about a government policy independent of political
affiliation?
Contingency table
Is there a relationship between two
continuous variables?
interval, ratio
(i) Does GPA depend on IQ?
(ii) Does weight depend on height?
t-test for correlations
using Pearson‟s
correlation coefficient
Is there a relationship between two ordinal
variables?
ordinal
(i) How strong is the relationship between the starting grid position
of a race driver and their finishing position?
t-test for correlations
using Spearman‟s rs
