# Comparing means of 3 dependent percentages

This is an example of the data that I have.

30 plants are a sample. Each plant has been categorized as percentage of green, brown or yellow color (percentages per plant sum to 100). For example:

plant %green   %brown   %yellow
1        30       30        40
2        50       25        25
3        15       70        15


How can I test if there is a significant difference between categories (green, brown and yellow)?

I have trouble because I think the percentage of each category is dependent on the other.

• I think it's necessary to display your data as counts instead of percentage. Unless your percentages are somewhat exact (knowing the exact repartition), they are not useful without the sample size for each type of plant. Jun 16, 2015 at 16:43
• I'd back up and tell us what is of real biological interest to you. Is it really whether mean % green = mean % brown? Jun 16, 2015 at 17:20

You can find means and sd for all 3 colors. If all were equal, the means should be 33 in each. So you can test each with Student t-test separately to see if its mean is different from 33. In R you can do it as follows:

> red = c(30,33,30,26,23,10)
> t.test(red, mu=33)

One Sample t-test

data:  c(30, 33, 30, 26, 23, 10)
t = -2.2663, df = 5, p-value = 0.07278
alternative hypothesis: true mean is not equal to 33
95 percent confidence interval:
16.63715 34.02952
sample estimates:
mean of x
25.33333

• Ok, thank you. However I forgot to add something in the question. I have also samples at different months, 30 plants each month and 6 months, so I have a percentage of all diferent colors for each plant. I want to know,1: does the color composition varies between sampling months??, 2 which month differ from the other? and if there is no variation between month , then I want to know if the percentage of colors differs overall, so I can do what you post above. do you have any suggestions for testing the month effect??? thanks! Jun 16, 2015 at 20:24
• Regression is likely to be a good method to see interaction between different factores.
– rnso
Jun 17, 2015 at 17:34