Spearman’s?
Chi-squared?
Mann-Whitney?
Choosing
Your Test
Choosing the correct technique
• Choose your technique BEFORE
collecting your data!
• Your choice will depend on:
What you want to test
What sort of data you can collect
• Once you’ve chosen your test, it will tell
you how much data you must collect
What do you want to test?
• For Correlation
(e.g. between hours in day-care and GCSE scores)
• For Association
(e.g. is there an association between gender of
advertiser in personal ads, and whether physical
attraction or resources are advertised)
• For a Difference Between Two
Cases
(e.g. difference in recall of semantically similar and
dissimilar words)
Click here for a flow chart on choosing tests
Testing for Correlation
Correlation can be positive, negative or zero
 Positive correlation: as one variable
increases, so does the other.
E.g. the higher the parental IQ, the higher the child’s IQ
 Negative correlation: as one variable
increases, the other decreases.
E.g. the more hours in daycare per week, the lower the
GCSE points score
 No correlation: one variable increasing has
no consistent effect on the other
Types of correlation
Two kinds of correlation:
Straight Line correlation
This measures how close your data are to a
straight line graph.
Data must be continuous, interval
Rank correlation
This measures whether things are in the same
order, but they don’t have to be in a straight line.
Data do not have to be continuous – but they
must be ordinal
Choosing A Correlation Coefficient
• Straight line correlation - Pearson’s Product
Moment Correlation Coefficient
Best to use if data actually are near a straight line
If you have lots of data, easier to calculate than Spearman’s
(use a spreadsheet)
Lets you work out the equation of a “best-fit” line
• Rank correlation - Spearman’s Rank Correlation
Coefficient
Data do not need to be close to a straight line
Needs absolute minimum of 4 data pairs – but more is better
Not valid if you have too many “ties”
Testing for Association
Chi-Squared Association Index
• This lets you investigate whether there’s any
association between two factors – are they linked?
 E.g.: Are gender and what is advertised in a “Personal Ad”
linked?
 If they are associated, it means that if we know if an
advertiser is female, they are more likely to advertise
physical attractiveness, say
• To do this test, we need:
 Numbers of people/items etc in categories (in the example,
it would be numbers of ads from each sex advertising
resources or physical attractiveness)
 An average of at least 5 in each category
 The data needs only to be nominal/categorical
Testing For A Difference
• Difference between numbers of items in
two or more categories
(e.g. numbers of males and females choosing a
certain A-level)
• Difference between averages (mean or
median)
(e.g. difference in scores on a memory test for
semantically similar and dissimilar words)
Difference between numbers of
items in 2+ categories
Your data need only be nominal/categorical
• Chi-squared – testing for a difference
• Sign Test
In either case, the null hypothesis is that there will be
no difference between the categories – so in the first
example there must be equal numbers of images classified
as “beginning”, “middle” and “end”, and in the second,
there must be approximately equal numbers of male and
female students
Which one to use?
Chi-squared – testing for a difference
 Use this if there are 3 or more categories (e.g. when
comparing number of images recalled from the
beginning, middle and end of a sequence)
 You can also use it to compare 2 categories
 Data must be frequencies – numbers of people/items
• Sign Test
 Use to see whether there’s significantly more
individuals in one category rather than another – e.g.
more males than females doing a particular A-level
Difference Between Averages
To choose the right test for averages, you must ask:
Frequency
 Are the data paired or not?
E.g.: Data on “matched pairs”
Two test results for the same person (repeated measures)
 For paired data, is the size of the difference important, or just
the fact there is a difference?
E.g.: for a change in pulse rate, the size is important
for a change in self-esteem, just “better” or “worse” is more
useful
 Are the data likely to be normally distributed?
 Only continuous data can be normal
 Can check visually whether normal by diagram
Value
Which Test for Averages?
• Paired Data
 If the size of the difference is unimportant (or you only
have ordinal data), use the sign test.
 If the size of the difference is important, but the data is
not normally distributed, use the Wilcoxon Signed Rank
 If the data is normally distributed, use the paired t-test
• Unpaired Data
 If the data is not normally distributed, use the MannWhitney U-test
 If the data is normally distributed, use the unpaired t-test