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Please consider this experimental result of biological cell counts on differently treated areas:

            R2      R3          R4          R5      R6
Replicate1  115421  1582        14989       2997    0
Replicate2  12460   60312       51621       1424    4272
Replicate3  42721   19580       20104       8900    13402

enter image description here

There is a trend in the data, but i have difficulties showing its significance (well, maybe there is none). As you can see, i am working with just three replicates and very high within-sample variance.

I tried linear models with glht() with Tukey Contrasts and correction for high heteroscedasticity:

library(multcomp)
library(sandwich)
library(MASS)

amod <- glm.nb(value ~ variable, data=data4.melt)
amod <- glm(value ~ variable, data=data4.melt, family="poisson")
res <- glht(amod, mcp( variable = "Tukey"), vcov = vcovHC)

for both poisson and negativ binomial distribution assumptions. The result was consistenst between the two models, that only R5 and R2 were different from each other. My PI asked my what the reason was for R6 not behaving like R5. I only could guess its related to one of the replicates being zero and an overall high variance.

Is there a better explanation? And most importantly, did i treat my data right? Is there even a justification for asking such a skewed dataset these questions?

nouse
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    Well, R5 and R6 aren't statistically different, so your results are not inconsistent with your PI's expectations. You can't answer all the world's questions with a minuscule dataset. – Russ Lenth Oct 02 '15 at 20:24
  • Sorry, the question was more directed to the observation that if R5 and R2 are significantly different, why R6 is not different from R2 as well. But the most important part was if i did my math right, anyway. – nouse Oct 02 '15 at 23:38
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    I suggest you try to get more comfortable with the inherent uncertainty of statistical conclusions. You can't escape it. – Russ Lenth Oct 02 '15 at 23:42
  • Statistical significance is not transitive: https://stats.stackexchange.com/questions/387415/transitivity-of-statistical-significance, https://stats.stackexchange.com/questions/159821/transitive-property-in-statistical-comparisons – kjetil b halvorsen Jun 27 '22 at 14:44

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