Hello Miguel Mejías

Given your specific hypothesis about dominance and the setup where only one species takes the shell per trial, the Chi-Square Goodness-of-Fit Test seems the most appropriate choice. It simplifies the analysis by focusing on whether the observed dominance (shell-taking) differs from an expected distribution.

This test compares observed frequencies against expected frequencies for a single categorical variable.

It is more appropriate for your experiment as it allows you to test whether the observed frequency of shell-taking by each species deviates from your expected proportions (e.g., a 50/50 distribution).

Example of Goodness-of-Fit Analysis:

Suppose you expect both species(e.g. A, B) to take the shell equally (50/50), and you conduct 40 trials. Your expected frequency for each species taking the shell would be:

Expected frequency for Species A = 20 (50% of 40)

Expected frequency for Species B = 20 (50% of 40)

Your contingency table for the goodness-of-fit test would look like the picture below:

Where:

X is the actual number of times Species A took the shell.

Y is the actual number of times Species B took the shell.

After that, you can Conduct the Goodness-of-Fit Test by calculating the Chi-Square Statistic and Compare to the Critical Value With 1 degree of freedom (since there are 2 categories), from the Chi-Square distribution table at your chosen significance level (e.g., 0.05), or using any programme to do so.

If the calculated is greater than the critical value (P_value or sig less than significance level (e.g., 0.05)), you reject the null hypothesis, indicating that the observed frequencies differ significantly from the expected frequencies, therefore the Species hermit crabs that have frequency highest is being more dominant, vice versa.

I hope this helps you.

Hi Douaa Arrouk ,

Thank you for your clear and detailed response! I really appreciate it. I will definitely take this route when it comes to this analyses.

If you don't mind, may I ask you one last question? For a separate crab study, I am hoping to do a similar hermit crab and shell experiment. The main difference is that this experiment will test shell exchange frequencies with just ONE hermit crab species.

I’m hoping to test if shell condition (i.e., damaged or undamaged) affects shell exchanges. The general prediction would be that hermit crabs with damaged shells would be more likely to change shells if an empty, undamaged one was available. For this tank experiment, I’m thinking of testing the frequency of shell swaps among 4 groups: (1) a crab with a damaged shell being offered a whole, empty shell, (2) a crab with a whole shell offered a damaged shell, (3) a crab with a damaged shell being offered another damaged shell, and (4) a crab with a whole shell being offered another whole shell. For simplicity, I’m planning to offer the same shell species, and ensure the size of offered shells are about the same as the one study crab are wearing. I’m thinking of running 20 trials, per group (i.e., 80 trials),

My last question is, is the Chi-Square Goodness-of-Fit Test still the right test for this study?

Thanks again for your help. I look forward to hearing from you.

Regards,

Miguel

Hi Miguel Mejías

The Chi-Square Test of Independence is more suitable in this case because the Chi-Square Test of Independence is used to determine if there is a significant association between two categorical variables - in your experiment, the condition of the shell (damaged vs. whole) and the frequency of shell exchanges-.

You would create a contingency table with the four groups and the observed frequencies of shell exchanges (yes or no) and then use the Chi-Square Test of Independence to determine if the frequency of shell exchanges is independent of the shell condition (damaged vs. whole) or the type of shell offered (damaged vs. whole).

if you have small sample sizes in any of the cells in your contingency table (expected frequency less than 5) you can use Fisher's Exact Test.