I would like to compare two population means or two groups of populations by a genetic diversity index, for example expected heterozygosity(He) or allelic richness (Ar)...etc. For example, I calculate He for pop 1 and pop 2, and I want to find out whether pop 1 has significantly higher He than pop 2. I want to use a single variable, with about 20-30 values (one mean value per population if I calculate for groups), to find significant difference or similarity.
I know that ANOVA is not good because it is for more than two populations, but what about t-test of f-test? I found that t-test is good to comparing the means of two populations, while f-test can compare two populations variance. What about the Kolmogorov–Smirnov test?
The t-test (for 2 independent samples, or for 1 sample of matched pairs) or F-test (for more than 2 independent samples) requires the distributions of your indexes to be (fairly) normal. Inspect the histograms. If visually not normal and a sign. Shapiro test, you can use a nonparametric test: a Wilcoxon-Mann-Whitney for 2 independent samples and a Kruskal-Wallis one-way analysis of variance for k-samples. The Kolmogorov-Smirnov is a nonparametric one-sample test, e.g. for the differences between 2 groups (matched pairs). Use this latter when the distributions of differences are not normal. Otherwise us a t-test for matched pairs.
The example you give : 'I calculate HE for pop1 and pop2', implies to use a t-test or a Wilcoxon-Mann-Whitney, both for 2 independent samples.
Better you can go to Non Parametric Test.
Parametric tests (means) and Nonparametric tests (medians):
1-sample t test = 1-sample Sign,1-sample Wilcoxon.
2-sample t test = Mann-Whitney test.
One-Way ANOVA = Kruskal-Wallis, Mood's median test.
Factorial DOE with one factor and one blocking variable = Friedman test .
Dear Jos Feys and Victor Seelan, Thank you for the valuable answers. Best, Endre
It really depends upon in what way you wish to see if they are different.
The Wilcoxon-Mann-Whitney test does not test the same null hypothesis as a t-test.
If you want to know if the means differ, use a test of means. If you wish to know if the medians differ, use a test of medians. If you wish to use if the overall distriibutions differ, use e.g. Kolmogorov–Smirnov. And so on.
The test you choose depends upon what you want to know.
Thank you Salvatore S. Mangiafico , My plan is to compare the mean He of two population group, to find out whether they significantly differ or not. I think t-test would be a good choice, do you agree?
Best wishes, Endre
The t-test may be appropriate to compare the means of two samples. In reality it depends upon what kind of variable "expected heterozygosity" (He) is.
Having re-read your question carefully, I think it will benefit you to provide more information.
One question: From what I've looked up, He appears to be the product of frequencies. Does it behave like a continuous variable?
Dear Dr. Endre,
First point is what is the measurement scale you are using? is it nominal or ordinal or Interval, ratio scale.
For raking, yes/no, male/female kind of scales you need apply non-parametric tests such as Mann-Whitney's test, Krushal -Wallis test.
For continues variables which has varied numerical values such as blood glucose values, serum cholesterol, tensile strength of a material, temperature of different places, etc. you need to apply parametric tests such as Student-T-Test, ANOVA etc.
Test for variance
1. 1 sample case you can Chi-squre test
2. for comparing variance/heterogenicity of two groups you can apply F- test.
Test for equality of means
1. For checking the equality of two means you can apply t-test.
2. ANOVA for means of 2 or more groups.
Regards
Vishwanatha
Dear Dr. Vishwanath shastry G.L. , Thank you for your advice. Finally, I carried out an independent sample t-test to compare group means. Best wishes, Endre
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