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riveragmn
Level I

Comparing 5 means of a small sample size

I sampled animal behavior for approximately 37 hours in 20 days while exposing them to 5 different "treatments". The treatments were different structures and I wanted to see how they used those, especially how frequently they used them. I would change the "treatment" every two days for a total of two trials per treatment. There were a total of 10 study subjects and they were not exposed to the treatment for the same amount of time (simply because they were not always available) and I did not have the treatments up for the same amount of time (i.e., weather related events).

 

I want to compare the average rate of events (let's call them crossing events) among treatments and see if there is a statistically significant difference between these. I calculated the rate of events given that the treatments were not sampled for an equal amount of time and the study subjects were also not exposed to the treatments for the same amount of time. 

 

Ho: The average crossing rate is the same for each treatment.

Ha: The average crossing rate is not the same for each treatment.

 

I have organized my data this way to compare means (this is just a brief example, not real data):

 

DayTreatmentEventsTime sampled (mins)Rate of events
1A3850.035
2A2600.033
3B0750.00
4B71150.06
5C121250.096
6C1900.011
7A02000.00
8A21100.018
9D61200.05
10D51050.047

 

Since I have five means to compare I decided to conduct a Kruskal-Wallis test (my data is not normally distributed) and use the Bonferroni correction. However, when I run this it says "small sample sizes. Refer to statistical tables for tests rather than large-sample approximation." Should I be organizing my data in a different way? Such as by study subject instead of crossings by day? That would give me about 50 rows of data and it would include that individual variation instead of pooling everything by day. Should I simply go by statistical tables? I am wondering what the best approach would be for this. 

 

Thank you! Let me know any questions.

2 REPLIES 2

Re: Comparing 5 means of a small sample size

This appears to be a classic case for a Poisson log-linear regression. JMP provides it through a generalized linear model (GLM). You model the count of events directly. I copied your data into a JMP data table.

 

table.PNG

 

The time of observation varied for each treatment. This variation is known as 'opportunity' and is modeled with an offset. The offset is the log( opportunity).

 

Then select Analyze > Fit Model and change the launch dialog to look like this one.

 

launch.PNG

 

Here are the results of the regression.

 

glm.PNG

 

The effect of the treatments is not significant at alpha = 0.05 (Whole Model Test and Effect Tests). The 'over-dispersion' is significant, meaning that the variance is greater than expected for a Poisson distribution of the response. The deviance is also significant, which indicates lack of fit. There could be lurking variables that were changing along with the treatments.

Re: Comparing 5 means of a small sample size

Similarly, a scatter plot of the event per time versus treatment does not exhibit a clear effect.

 

gb.PNG