# Comparing the result of a study which has unequal group sizes

I have conducted two user studies and in my studies I didn't have control over the group sizes. In each study users were put in groups and they were asked to perform some group activities. Here is the way the groups were arranged:

• Study 1 (Control Groups): In this study 20 people participated. The participants were in 2 groups of 4 people, and 4 groups of 3 people.
• Study 2 (Modified Groups): In this study 25 people participated. The participants were in 5 groups of 4 people, and 3 groups of 3 people.

I have gathered two kinds of data during my study:

• Individual data. For example the number of ideas that each person put forward.
• Group related data. For example the time group spent to do something.

I am looking for a method which helps me combine the results for each study and then compare the results. I was wondering if anyone could help me with this ?

The task is Brainstorming ideas about a specific topic. The topic is the same between all of the groups. Users work in a software that I wrote. Test groups see a different version of the software. I am measuring the time it took the group to generate 10 ideas, and I want to see if software version had an effect on it or not. But the main problem is having groups of 3 and groups of 4 users.

• Welcome to the site, @ali. I don't understand how you are describing your groups. EG, what does "2 groups of 4 users. 4 groups of 3 users" mean? Can you say more about what each group is exactly? You may find the following blog post helpful in formulating your question: How to ask a statistics question. You may also want to read our FAQ. Oct 19, 2012 at 3:45
• @gugn thanks for your comment. I tried to make things more clear.
– Ali
Oct 19, 2012 at 3:54
• The results will be more reliable if you kept number of groups to minimum, large sample size per group and fewer specific questions. As the reverse happens, the variability becomes too large and results will be statistically insignificant.
– rnso
Oct 25, 2014 at 9:39

You can separate each study into groups that contained 4 people and groups that contained 3 people. Then compare statistics for each of these sets between the control and modified groups. For example let's say you have data on the time a group spent doing something:

Controls
Times for 3 person control groups: 10,8,11,9 Mean = 9.5
Times for 4 person control groups: 6,8 Mean = 7

Modified
Times for 3 person modified groups: 7,7,10 Mean = 8
Times for 4 person modified groups: 5,6,4,10,5 Mean = 6

Now you can compare the 3 person control mean (9.5) with the 3 person modified mean (8) and do the same for the 4 person groups.

• Thanks Jake for your response. But I was wondering if there is a method that I can use to combine the results of 3 person groups and 4 person groups. If I can't do that then what you say is the best way to do it.
– Ali
Oct 19, 2012 at 17:30
• Unless you can be sure that your modification to the second study affects 3 and 4 person groups in the same way I don't think it is very sound to combine all the data. Can you provide more info about the data or modification to the control group? Oct 19, 2012 at 17:45
• The task is Brainstorming ideas about a specific topic. The topic is the same between all of the groups. Users work in a software that I wrote. Modified groups see a different version of the software. I am measuring the time it took the group to generate 10 ideas, and I want to see if my modifications had an effect on it or not.
– Ali
Oct 19, 2012 at 17:52