Binary vs. Binary (unpaired/independent)
Part 1: Impression of the sample data (cross table)
To begin analysing a potential association between two binary variables, we can start by getting an impression from the sample data using a socalled cross table, or also known as a contingency table. It can be defined as “tables arising when observations on a number of categorical variables are crossclassified” (Everitt, 2004, p.89).
For example, I might be interested to know if gender has an association with the location of the secondary school, and generate the following cross table from my sample.
Female Count 
Female Percent 
Male Count 
Male Percent 
Total Count 
Total Percent 


Valid  The Netherlands  8 
73% 
16 
52% 
24 
57% 
Other  3 
27% 
15 
48% 
18 
43% 

Total  11 
100% 
31 
100% 
42 
100% 
Click here to see how you can create a cross table...
Note that the instructions are for a cross table of two nominal variables, but this works the same as for two binary variables.
with Excel
Excel file: IM  Cross Table.xlsm.
with SPSS
There are a two different ways to create a cross table with SPSS.
using Crosstabs
Data file: Holiday Fair.sav.
using Custom Tables
Data file: Holiday Fair.sav.
From the table we can tell that for example there were 8 Female students who had their secondary school in The Netherlands. This is 73% of the female students in the survey.
Note that in this example the column totals were used to determine the percentages. Alternative the row totals could have been used or the grand total. For example using the row total of 24 for The Netherlands, the Female percentage would then be 8/24 × 100 = 33%, indicating that 33% of those who had their secondary school in the Netherlands were female. If the grand total was used, we get 8/42 × 100 = 19%, indicating that 19% of the respondents were female and had their secondary school in the Netherlands.
Looking at the table, it seems that the percentage vary a bit, but would there be a significant association between gender and secondary school? To find out we would need to run a statistical test, but if you want, you could first visualise the results.
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