# Comparing count data from multiple groups, Kruskal-Wallis with Dunn post-hoc or GLM with Poisson distribution?

Stats novice. I am comparing counts of microplastic artefacts from multiple independent sites, my null hypothesis is that there is no difference in counts between the sites.

So far I have tried Kruskal-Wallis with Dunn's post-hoc test (I have only included comparable results):

site.comp<-kruskal.test(MP.kg~ Core, data = sample.counts)

Kruskal-Wallis rank sum test

data:  MP.kg by Core
Kruskal-Wallis chi-squared = 135.78, df = 12, p-value < 2.2e-16

library(FSA)
post.site.comp<-dunnTest(MP.kg ~ Core, data = sample.counts)

Dunn (1964) Kruskal-Wallis multiple comparison
p-values adjusted with the Holm method.

1    112 - 13  2.3742473 1.758477e-02 6.506363e-01
3    13 - 131  4.1807014 2.906113e-05 1.772729e-03
5    13 - 137  2.2647170 2.353005e-02 8.000217e-01
8     13 - 20 -3.4055623 6.602794e-04 3.367425e-02
12    13 - 34  1.6496563 9.901325e-02 1.000000e+00
17    13 - 35  2.5808428 9.855945e-03 4.139497e-01
23   13 - 405  0.6292214 5.292041e-01 1.000000e+00
30    13 - 55  0.3182703 7.502799e-01 1.000000e+00
38    13 - 61 -2.1837093 2.898362e-02 8.695086e-01
47    13 - 70  0.1383227 8.899854e-01 1.000000e+00
57    13 - 83 -2.2207813 2.636578e-02 8.437050e-01
68    13 - 98  3.6223826 2.919019e-04 1.547080e-02


and GLM with quasipoisson distribution (quasi to deal with overdispersion, aliased to Core 13):

site.depth<-glm(MP.kg ~ Core, data = sample.counts, family = quasipoisson)
Call:
glm(formula = MP.kg ~ Core, family = quasipoisson, data = sample.counts)

Deviance Residuals:
Min       1Q   Median       3Q      Max
-58.569  -23.381   -7.192   10.640  231.000

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)   7.4473     0.1495  49.801  < 2e-16 ***
Core98       -1.6183     0.3827  -4.229 2.93e-05 ***
Core20        0.1636     0.2080   0.787 0.431958
Core34       -0.9963     0.2983  -3.340 0.000919 ***
Core35       -1.3016     0.3504  -3.714 0.000234 ***
Core55       -0.6826     0.2509  -2.721 0.006800 **
Core61       -0.0941     0.2119  -0.444 0.657156
Core70       -0.1925     0.2356  -0.817 0.414336
Core83       -0.1565     0.2261  -0.692 0.489246
Core112      -0.1702     0.2270  -0.750 0.453721
Core131      -1.8366     0.4204  -4.369 1.60e-05 ***
Core137      -0.6449     0.2575  -2.504 0.012680 *
Core405      -0.7299     0.2709  -2.694 0.007367 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for quasipoisson family taken to be 1265.69)

Null deviance: 460310  on 400  degrees of freedom
Residual deviance: 344189  on 388  degrees of freedom
AIC: NA

Number of Fisher Scoring iterations: 6


The results of Dunn's post-hoc and the GLM do not agree.

Why is there this disparity and which test should I trust?

The FSA dunnTest has adjusted the p-values with the holm method, could this be the source of the difference?

• (1) The p-values are different because these are completely different statistical procedures that make different assumptions about the data's distribution. (2) Is it fair to say you don't have a good sense of the data's distribution? If so, K-W seems more appropriate, being a fully nonparametric test. Using a quasipoisson GLM assumes you know the mean is proportional to the variance. – Paul Jun 14 '17 at 12:58
• Looking at a histogram of the count data, it is very clearly poisson distributed, as I would expect from count data. Beyond that, I do not have a clear sense of the distribution. The residuals on the GLM are homoscedastic, if that helps? If the K-W is more robust, maybe I should go with that. Apologies if I haven't really addressed your question about the distribution, as I say I am still a novice! – Gavin Senior Jun 14 '17 at 13:31