I was conducting a statistical analysis with R.
First of all, I checked the assumption of equality of normality, I found no equality :
then checking the one of the variance, i found equality of varirance.
I dicided to carry out a non parametric test to check weither or not there were difference in the mean. Thus, I used Kruskal.test, i found a p-value of 0.31, higher than 0.05. So I concluded that there is no significant difference in the means. But looking at the value I found :
=c(114, 120, 66,
84, 72, 60,
81, 78, 191,
71, 70, 72,
70, 60, 80,
50, 40, 75,
70, 60, 90)
I wished to rank the means. So I carried out a LSD test with agricolae. Bingo, it found different letters for the means (a, ab, b). However, HSD found no difference(a) for all means.
I am a bit confused, because, all article a visited said that LSD is a post anova test in the case if we observed a significant difference.
Is my methodology logical and statistically acceptable.
Kind regards,
Evans
There is a long list of available multiple comparison procedures. They are not all equal. The LSD test fails to control the experimentwise error rate. If the null hypothesis is true, then there is a 1 in 20 chance (0.05) of a type I error (assuming significance is declared at 0.05). With independent tests, the chance of a type I error increases for every pairwise comparison made. The error rate will be 1-(1-alpha)^n where n is the number of pairwise comparisons. Tukey's HSD test controls the experimentwise error rate to 0.05, but the cost is that the error rate for any individual pairwise comparison is less than 0.05. So it is not surprising that LSD shows a significant difference while HSD does not.
In general, tests that make more assumptions will be more capable of detecting small differences in data that conform to the assumptions. There is a cost to making fewer assumptions.
This is about matching the assumptions of the multiple comparison method to your data, and understanding the costs and benefits to different approaches to this problem. Here is a fairly good start: http://support.sas.com/documentation/cdl/en/statug/63347/HTML/default/viewer.htm#statug_glm_a0000000867.htm. However, there are many other multiple comparison methods available.
Thank you very usefull!
I have a better understanding of the question with your simulation.
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