Chi-squared Tests Using SPSS: Further Results

Exploring Chi-squared results further

The worksheet called Chi-Squared Tests Using SPSS, showed how to run a Chi-squared test. Evidence was found that there is an association between colour and personality type. However, this does not tell us about the nature of that association. This worksheet shows you how to discover more.

Example

Perform the Chi-Squared test again: from the Analyze menu select Descriptive Statistics then Crosstabs:

Make sure personality is in the Row(s) box and colour is in the Column(s) box. It doesn’t matter which way round we do them. Then click the Statistics button, and make sure the Chi_square option is ticked. However, this time, also tick the option to obtain Phi and Cramer’s V:

Click Continue to return to the main dialogue. Now click the Cells button, and under Percentages, tick Row:

Click on Continue then OK.

Examining the Output

The output tables differ to those in the previous worksheet:

The row percentages demonstrate that more than half of the extroverts prefer the colour red (60%), while in contrast, almost three-quarters of introverts (74%) prefer blue (44%) and green (30%).

Phi and Cramer’s V provide a measure of the effect size (see the Symmetric Measures table below). Both measure strength of association between two categorical variables, but are used for different sized tables:

Phi is used with 2 X 2 tables (and is equivalent to the correlation coefficient r).
Cramer’s V is used with larger tables (like ours).

Since our cross tabulation table is a 2x4 table (2 rows and 4 columns excluding totals) we use Cramer’s V = 0.422. We can interpret what this means using Cohen’s guidelines in the table below. To use that table we need to determine what our degrees of freedom (df) is. To determine the df, we choose the smallest of the number of rows (2) and the number of columns (4); in this case the smallest is 2. We then minus 1 from this to get our df = 2-1 = 1. Hence, we look down the column labelled 1 in the table below. Our Cramer’s V of 0.42 is between the table values 0.3 and 0.5, so our effect size is medium to large.

Cohen’s (1988) implied guidelines for interpreting Phi and Cramer’s V

df	small	medium	large
1	0.10	0.30	0.50
2	0.07	0.21	0.35
3	0.06	0.17	0.29
4	0.05	0.15	0.25
5	0.04	0.13	0.22

Edited from source: https://peterstatistics.com/CrashCourse/3-TwoVarUnpair/NomNom/NomNom-2c-Effect-Size.html

Reporting Results

We could now add this additional information to the reporting of our results as:

“A Chi-squared test was undertaken to examine the relationship between personality type and colour preference. There is strong evidence that colour preference is associated with personality type, χ^2(3, N=400) = 71.20, p<0.001. This is medium to strong association (V=0.42) where introverts seem more likely to prefer blue (40%) and green (34%) whereas extroverts are more likely to prefer red (60%).”

For more resources, see sigma.coventry.ac.uk Adapted from material developed by Coventry University Creative Commons License