Chi-Squared Test Using JASP: Further Results

Exploring Chi-Squared results further

The worksheet called Chi-Squared Tests Using JASP, 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 Frequencies menu select Contingency Tables:

Make sure personality is in the Rows box and colour is in the Columns box. It doesn’t matter which way round we do them.

Then open the Statistics tab, and make sure the option is ticked. However, this time, also tick the option to obtain ‘Phi and Cramer’s V’:

Now open the Cells tab, and for the ‘Percentages’, tick ‘Row’:

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 ‘Nominal’ 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.

Since we have a 2x4 table (2 rows and 4 columns) we use a Cramer’s V of 0.422. Phi’s coefficient is NaN as our table is not 2x4, not 2x2 as required to obtain a coefficient. 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 for this value in the column labelled df in the table below and look along the row labelled 1. 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

Table derived from Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed).

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 association was a 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