Kruskal-Wallis Test

ANOVA - Egg Percent

Data from Çetinkaya & Domjan (2006). The authors investigated the reproductive success of quails.

groups: Fetishistics, nonFetishistics, or Control
egg_percent: Percent of eggs fertilized
latency: Time taken to initiate copulation

ANOVA - egg_percent
Cases	Sum of Squares	df	Mean Square	F	p
groups	6119.688	2	3059.844	6.769	0.002
Residuals	25315.162	56	452.056

Note. Type III Sum of Squares

Descriptives

Descriptives - egg_percent
groups	N	Mean	SD	SE	Coefficient of variation
Fetishistics	17	50.640	25.505	6.186	0.504
NonFetishistics	15	31.926	15.496	4.001	0.485
Control	27	26.790	21.073	4.055	0.787

Raincloud plots

Percent of eggs fertilized:

We know that there are differences between the groups but we don’t know where these differences lie. One way to see which groups differ is to look at raincloud plots (see the output below). If we look at the raincloud plot for this first variable (percentage of eggs fertilized), using the control as our baseline, the medians (which is represented in the boxplots) for the non-fetishistic male quail and the control group were similar, indicating that the non-fetishistic males yielded similar rates of fertilization to the control group. However, the median of the fetishistic males is higher than the other two groups, suggesting that the fetishistic male quail yielded higher rates of fertilization than both the non-fetishistic male quail and the control male quail.

egg_percent

Kruskal-Wallis Test

Percent of eggs fertilized:

For the percentage of eggs fertilized, the test statistic is H = 11.955, with 2 degrees of freedom. The significance value of .003 is less than .05, so we could conclude that the percentage of eggs fertilized was significantly different across the two groups.

Kruskal-Wallis Test
					95% CI for Rank ε²
Factor	Statistic	df	p	Rank ε²	Lower	Upper
groups	11.955	2	0.003	0.206	0.049	0.450

Dunn

Dunn's Post Hoc Comparisons - groups
Comparison	z	W_i	W_j	r_rb	p	p_bonf	p_holm
Fetishistics - NonFetishistics	2.483	41.824	26.967	0.561	0.013	0.039	0.026
Fetishistics - Control	3.362	41.824	24.241	0.564	< .001	0.002	0.002
NonFetishistics - Control	0.501	26.967	24.241	0.128	0.616	1.000	0.616

Note. Rank-biserial correlation based on individual Mann-Whitney tests.

Post-hoc comparisons - percent of eggs fertilized:

We can also look at Dunn's follow-up tests. Let’s look at the pairwise comparisons first for the percentage of eggs fertilized first (see output above). The table shows the average rank within each group: so, for example, the average rank in the fetishistic group was 41.82, and in the non-fetishistic group it was 26.97. In the current example, there are significant differences between the fetishistic group and the control group, and also between the fetishistic group and the non-fetishistic group. There was no significant difference between the control group and the non-fetishistic group. The table shows all of the possible comparisons. The columns labelled p_bonf and p_holm contain the adjusted p-values and it is these columns that we need to interpret (no matter how tempted we are to interpret the one labelled p). Dependent on how strict you want to be about controlling your type-1 error rate, you can look at the Bonferroni (very strict) or Holm (medium strict) corrected p-values. Let's be rigorous and be very strict.Looking at these columns, we can see that significant differences were found between the control group and the fetishistic group, p = .002, and between the fetishistic group and the non-fetishistic group, p = .039 and p = .026. However, the non-fetishistic group and the control group did not differ significantly, p = 1 and p = .616. We know by looking at the raincloud plot and the ranks that the fetishistic males yielded significantly higher rates of fertilization than both the non-fetishistic male quail and the control male quail.

The authors reported as follows (p. 429):

Kruskal–Wallis analysis of variance (ANOVA) confirmed that female quail partnered with the different types of male quail produced different percentages of fertilized eggs, χ2(2, N = 59) =11.95, p < .05, η2 = 0.20. Subsequent pairwise comparisons with the Mann–Whitney U test (with the Bonferroni correction) indicated that fetishistic male quail yielded higher rates of fertilization than both the nonfetishistic male quail (U = 56.00, N₁ = 17, N₂ = 15, effect size = 8.98, p < .05) and the control male quail (U= 100.00, N₁ = 17, N₂ = 27, effect size = 12.42, p < .05). However, the nonfetishistic group was not significantly different from the control group (U = 176.50, N₁ = 15, N₂ = 27, effect size = 2.69, p > .05)

ANOVA - Latency

ANOVA - latency
Cases	Sum of Squares	df	Mean Square	F	p
groups	3230.046	2	1615.023	17.650	< .001
Residuals	5124.056	56	91.501

Note. Type III Sum of Squares

Descriptives

Descriptives - latency
groups	N	Mean	SD	SE	Coefficient of variation
Fetishistics	17	13.824	2.243	0.544	0.162
NonFetishistics	15	4.867	1.685	0.435	0.346
Control	27	22.926	13.873	2.670	0.605

Raincloud plots

Time taken to initiate copulation:

If we now look at the raincloud for the time taken to initiate copulation, the medians suggest that non-fetishistic males had shorter copulatory latencies than both the fetishistic male quail and the control male. However, these conclusions are subjective. What we really need are some follow-up analyses.

latency

Kruskal-Wallis Test

Time taken to initiate copulation:

For the time taken to initiate copulation the test statistic, H = 32.244, with 2 degrees of freedom. The significance value is < .001 and (assuming we’re using an alpha of 0.05 as our criterion) because this value is less than .05 we could conclude that the time taken to initiate copulation differed significantly across the two groups.

Kruskal-Wallis Test
					95% CI for Rank ε²
Factor	Statistic	df	p	Rank ε²	Lower	Upper
groups	32.244	2	< .001	0.556	0.476	0.667

Dunn

Dunn's Post Hoc Comparisons - groups
Comparison	z	W_i	W_j	r_rb	p	p_bonf	p_holm
Fetishistics - NonFetishistics	4.072	33.471	8.800	1.000	< .001	< .001	< .001
Fetishistics - Control	-1.156	33.471	39.593	0.298	0.248	0.743	0.248
NonFetishistics - Control	-5.591	8.800	39.593	0.941	< .001	< .001	< .001

Note. Rank-biserial correlation based on individual Mann-Whitney tests.

Post-hoc comparisons - time taken to initiate copulation:

Let’s now look at the pairwise comparisons for the time taken to initiate copulation (see output above). The table highlights differences between groups. In the current example, there was not a significant difference between the fetishistic group and the control group. However, there were significant differences between the fetishistic group and the non-fetishistic group, and between the non-fetishistic group and the control. The table shows all of the possible comparisons. Interpret the columns labelled p_bonfand p_holm which contain the p-values adjusted for the number of comparisons. Significant differences were found between the control group and the non-fetishistic group, p < .001, and between the fetishistic group and the non-fetishistic group, p < .001. However, the fetishistic group and the control group did not differ significantly, p = .743. We know by looking at the raincloud plot and the ranks that the non-fetishistic males yielded significantly shorter latencies to initiate copulation than the fetishistic males and the controls.

For the latency data they reported as follows:

A Kruskal–Wallis analysis indicated significant group differences, χ2(2, N = 59) = 32.24, p < .05, η2 = 0.56. Pairwise comparisons with the Mann–Whitney U test (with the Bonferroni correction) showed that the nonfetishistic males had significantly shorter copulatory latencies than both the fetishistic male quail (U = 0.00, N₁ = 17, N₂ = 15, effect size = 16.00, p < .05) and the control male quail (U = 12.00, N₁ = 15, N₂ = 27, effect size = 19.76, p < .05). However, the fetishistic group was not significantly different from the control group (U = 161.00, N₁ = 17, N₂ = 27, effect size = 6.57, p > .05). (p. 430)

These results support the authors’ theory that fetishist behaviour may have evolved because it offers some adaptive function (such as preparing for the real thing).