# Hypothesis testing for ordinal proportions for multiple independent subjects divided between two groups

I have two biological groups - each with multiple subjects (7 in one and 10 in another). Each subject provides 40-80 observations, which can be classified into either of two ordinal categories. I have converted the individual observations of a subject into a proportion falling in one category (resulting in one degree of freedom). Thus, I have several subjects in one group, each with a unique proportion. I have two such groups. As my subject numbers are low, and I want to include the variability in the proportion measurements across group members in my hypothesis testing, what test should I be considering?

I don't have any theoretical estimation of the expected proportion, nor do I want to pool all individual observations in a group (regardless of subject identity) to calculate an overall proportion and do a Z-test.

I look forward to your inputs. Thanks in advance!

• What are the two ordinal categories and what are the two groups? A little more description would make this easier to think through and discuss. Apr 21, 2022 at 0:24
• Thanks @MattF. for your interest. The two broader groups are control animals and trained animals. Within each of these groups, I have several animals from which I get multiple data points (40-80). Each data point corresponds to the number of partners that a synaptic structure makes. Instead of dividing the data into multiple bins (number of partners 1, 2, 3, 4, 5... and so on) which reduces my power, I have binned the data as having one partner or more than one partner. My research question is whether average number of partners increase after training. I hope this helps!
– ARay
Apr 22, 2022 at 19:27

## 1 Answer

From your comments, I would ask the question as: “I have 7 trained and 10 untrained animals. In each animal I observe 40-80 synapses as having either a single partner or multiple partners. I hypothesize that the proportion of multiply-partnered synapses is higher in the trained animals than the untrained. How can I test this hypothesis?”

With that framing, the Mann-Whitney U Test would be one reasonable way to compare the rankings of those proportions among the two groups.