CHAPTER TWELVE
ANALYSING DATA I: QUANTITATIVE DATA ANALYSIS
QUANTITATIVE ANALYSIS
Analysis should always have a purpose:
• Describe.
• Compare.
• Examine similarities.
• Examine differences.
The issue is not just HOW do we collect data, but how do we
generate useful information?
DESCRIPTIVE STATISTICS
Summarise and organise data.
Measures of central tendency
• Mean − average sum of scores/number of scores.
• Mode − most common value − ‘typical’ value.
• Median − middle value.
Findings can be presented in a number of ways:
Frequency tables
How often do
you go training
in a week?
1
2
3
(n = number of responses)
Always provide a table of results.
n
17
29
22
%
25.0
42.7
32.3
USING GRAPHS AND CHARTS
Only present a graph/chart if it illustrates something.
These describe data − they do not explain anything.
INFERENTIAL STATISTICS
Allow you to make inferences from data.
Uses at least 2 variables.
‘What affect does the independent variable have on the
dependent variable?’ − Causality − is A caused by B?
TYPES OF TEST
1. Parametric tests. These tests use interval or ratio data
(see Chapter 6 for a reminder). Parametric tests assume
that the data is drawn from a normally distributed
population (i.e. the data is not skewed) and have the
same variance (or spread) on the variables being
measured.
2. Non-parametric tests. These are used with ordinal or
nominal data, and do not make any assumptions about
the characteristics of the sample in terms of its
distribution.
TESTS OF ASSOCIATION
CORRELATION
Correlations investigate the relationship between two
variables consisting of interval or ratio data.
A correlation can indicate:
• Whether there is a relationship between the two
variables.
• The direction of the relationship, i.e. whether it is positive
or negative.
• The strength, or magnitude of the relationship.
Correlation scores range from 1 to -1
R=1
strong
positive
correlation
R= -1
strong
negative
correlation
R=0
no
correlation
A strong correlation does not necessarily mean a
relationship!
e.g. lectures attended positively correlates with final grade.
May be:
more lectures attended = more interest
more interest = higher grade
Spuriousness relationship.
TESTING DIFFERENCES
Tests of difference generally assess whether differences
between two samples are likely to have occurred by chance,
or whether they are the result of the effect of a particular
variable.
THE INDEPENDENT SAMPLES T-TEST
This examines whether the mean scores of two different
groups can be considered as being significantly different.
It can be used when:
• The data is interval or ratio in nature.
• The groups are randomly assigned (hence, you should
use an ANOVA rather than a t-test to compare
differences between males and females, as gender is not
randomly determined when you come to assign your
groups).
• The two groups are independent of each other.
• The variance, or spread, in the two groups is equal.
PAIRED SAMPLES T-TEST
The paired t-test measures whether the mean of a single
group is different when measured at different times.
ANALYSIS OF VARIANCE (ANOVA)
ANOVA is similar in nature to the independent t-test,
however it allows you to ascertain differences between
more than two groups.
If you are looking to explore gender differences, then this
is a more appropriate test to use than an independent ttest as it does not assume that participants have been
randomly assigned to each group.
THE MANN-WHITNEY TEST
An alternative to the independent t-test.
Used when data is ordinal and non-parametric.
This test works on ranking the data rather than testing the
actual score, and scoring each rank (so the lowest score
would be ranked ‘1’, the next lowest ‘2’ and so on)
ignoring the group to which each participant belonged.
The principle of the test is that if the groups were equal,
then the sum of the ranks should also be the same.
THE WILCOXON SIGNED RANK TEST
Similar to the Mann-Whitney test, however it examines
differences where the two sets of scores are from the same
participants (effectively it is non-parametric alternative to a
one sample t-test).
THE KRUSKAL-WALLIS TEST
This is a non-parametric alternative to the ANOVA test, and
can be used to identify differences between three or more
independent groups.
WHICH TEST SHOULD I USE?
The type of data that you collect will be important in your
final choice of test:
Nominal
Consider a chi-squared test if you are interested in
differences in frequency counts using nominal data, for
example comparing whether month of birth affects the
sport that someone participates in.
Ordinal
If you are interested in the relationship between groups,
then use Spearman’s correlation.
If you are looking for differences between independent
groups, then a Mann-Whitney test may be appropriate.
If the groups are paired, however, then a Wilcoxon
Signed rank test is appropriate.
If there are three or more groups then consider a KruskalWallis test.
Interval or ratio
Are you looking to identify relationships between two
variables? If so, consider the use of a Pearson’s
correlation.
If there are three or more variables, then consider multiple
regression.
If you are concerned with differences between scores,
then t-tests or ANOVA may be appropriate.
If you want to identify differences within one group, then a
paired samples t-test should be used.
If you are comparing two randomly assigned groups, then
use an independent samples t-test.
If you are looking to compare two non-randomly assigned,
or three or more groups, then use ANOVA.
INTERPRETING THE FINDINGS
SPSS/excel will tell you the correlation and tell you if it is
significant or not.
Significance is the likelihood of something not being due
to chance.
Take two groups and measure average height… height of
group A is 165cm and the other is 155cm…
are they different?
You will be given a score, e.g. p=0.05
5% likelihood the finding was due to chance
95% likelihood that it was as a consequence of treatment.
MISTAKES SOMETIMES MADE IN QUANTITATIVE
ANALYSIS
• Choosing an incorrect statistical test, often through
applying parametric tests to non-parametric data.
• Designing the questionnaire so that the data is in the
incorrect format for the appropriate statistical test, thus the
format of the response may provide you with ordinal data
when you require interval data.
• Misinterpreting a p-value, or deciding upon an
inappropriate level of significance.
• Deciding upon a level of significance after undertaking the
analysis.
• Using parametric tests for non-parametric data.
SUMMARY
1. Descriptive statistics allow you to organise and
summarise your data. Inferential statistics allow you to
draw inferences regarding the association or difference
between two or more variables.
2. Inferential tests will provide you with a ‘p-value’. The pvalue indicates the likelihood that any association or
difference (depending upon the test) was down to chance
or not. A p-value of 0.05 indicates that in 95 cases out of
100 you could be confident that there was an actual
difference or association, rather than a chance difference
or association.