Selection should be based on the desired biological interpretation!

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Cecil Shannon Barber
5 years ago
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The median intensity? Or something else?

1 Statistical tools to compare levels of parasitism Jen_ Reiczigel,, Lajos Rózsa Hungary What to compare? The prevalence? The mean intensity? The median intensity? Or something else? And which statistical test to use if there are more of them? Selection should be based on the desired biological interpretation!

2 Comparing prevalence between two (or more) populations Interpretation: comparing frequency of infection Chi-square test All expected counts should be 5 Approximate p-values are obtained Fisher s exact test Computer time expensive Example: No. of infected No. of uninfected Total Sample Sample Sample Both tests are based on this k x 2 table. Note that Fisher s exact test is available for k x 2 tables (not only for 2 x 2 tables)!

3 Comparing mean intensity between two populations Interpretation: comparing parasite population sizes Student s t-test Normal (=Gaussian) distribution of intensity or large samples ( 30) Equality of variances Welch t-test (t-test for unequal variances) Normal (=Gaussian) distribution of intensity or large samples ( 30) Bootstrap t-test Model should be specified (shift, stretch, etc.) Few computer programs available Student s t-test on transformed data (square root, log, etc.) does not compare mean intensities! Mann-Whitney U-test (=Wilcoxon s rank sum test) does not compare mean intensities in general!

4 Comparing mean intensity in several populations Interpretation: comparing parasite population sizes ANOVA Normal (=Gaussian) distribution of intensity Equality of variances Bootstrap ANOVA Practically no computer program available ANOVA on transformed data (square root, log, etc.) does not compare mean intensities! Kruskal-Wallis test does not compare mean intensities in general!

5 Comparing median intensity in two (or more) populations Interpretation: comparing typical states of hosts Mood s median test Few computer programs available Mann-Whitney U-test (=Wilcoxon s rank sum test) does not compare median intensities in general! Kruskal-Wallis test does not compare median intensities in general! Procedures similar to Mood s median test can be applied for the comparison of quantiles (quartiles, percentiles, etc.). Testing for differences in the tails of the parasite distributions. Testing for differences in population proportions beyond a certain intensity threshold. Such questions arise if there is a certain effect but it does not affect the whole population, just a part of it. In this case neither the population mean nor the median may appropriately reflect the situation.

6 Example: Here neither the difference between the means nor that between the medians is significant (p = and p = ). However, choosing a threshold at 60 and applying Fisher s exact test to the above 2 x 2 table results in p = Choose always a natural threshold to get interpretable results! If choosing the threshold optimally with respect to the sample at hand, the obtained p-value will be biased, leading to wrong conclusions. (This may be the case in the above example it is just for illustration.)

7 Comparing distribution of intensity in two populations Interpretation: comparing typical states of hosts in terms of stochastic equality or dominance Stochastic equality means that if choosing randomly a host from population A and another from population B, then P(host from A has more parasites) = P(host from B has more parasites) Stochastic dominance means that if choosing randomly 2 hosts in the same way, then P(host from A has more parasites) > P(host from B has more parasites) Mann-Whitney U test (=Wilcoxon s rank sum test) Welch t-test on ranks Bootstrap WMW test Intensity distributions are of the same shape, the difference is a pure shift (almost never holds in parasitology!) Wider area of application but not clearly understood properties Under preparation Model should be specified (shift, stretch, etc.) Mann-Whitney U-test compares mean or median intensities only under very special (and unrealistic!) conditions, like e.g. the shift model. In general circumstances it is not at all a location test! (There exist distributions such that A < B < C < A in terms of stochastic dominance.) Mann-Whitney U-test is invariant to monotone transformations. Student s t-test on ranks is equivalent with Mann-Whitney U-test. (An idea if someone has no computer program for the Mann-Whitney test.)

8 Comparing distribution of intensity in several populations Interpretation: comparing typical states of hosts in terms of stochastic homogeneity or dominance Kruskal-Wallis test Intensity distributions are of the same shape, the differences are pure shifts (almost never holds in parasitology!) Kruskal-Wallis test compares mean or median intensities only under very special (and unrealistic!) conditions, like e.g. the shift model. Kruskal-Wallis test is invariant to monotone transformations. Comparing distribution of intensity in 2 or more populations Interpretation: comparing states of hosts Chi-square test Intensities should be categorized All expected counts should be 5 Approximate p-values are obtained

Non-parametric tests, part A:

Two types of statistical test: Non-parametric tests, part A: Parametric tests: Based on assumption that the data have certain characteristics or "parameters": Results are only valid if (a) the data are