Hello everyone,
I have a group of fish (n=28 per group). I have measured the amount of time that each fish spent exploring two different objects (A and B) in a squared shape tank. Then I have calculated an exploration index as: (time spent with A) / (time spent with B + time spent with A).
Now I have some proportional data and I am going to test whether a fish spent time with A more than chance level (0.5) to see if they have a preference for object A. To see if there is a difference between exploration ratios and chance level, I am gonna run one sample t-test. However, as I read some papers, I think I should do arcsin transformation (arcsine square root transformation) for my data. However, when I transform my data and run one-sample t-test I get odd results. For example, my raw exploration ratios show that they are below chance level (mean: 0.322 and SD:0.12) while after transformation of data I see that the ratio are now higher than chance level. I am really confused and I do not now how I should treat with my data. I would really appreciate it if you can advise me
You need to transform the data because you are applying a parametric test that requires the fulfillment of two main assumptions: normality and homocedasticity.
The angular transformation (or arcsine transformation) is suitable for proportional data, like yours, because they are restricted in the range 0-1.
I think your confusion is regarding the value to which to compare your proportions after the transformation.
Angular transformation: W = [ASIN (SQRT (p))]
Being: W = transformed value; p = the original proportion.
For p = 0.5 (the value you will use for your test)
W = [ASIN (SQRT (0.5))] = 0.785. That value W = 0.785 will be the one used in your
one-sample t-test.
I hope that is your doubt.
Regards !
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