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This is the results of my anova(glm()) and the post-hoc analyses emmeans() :      

         Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
NULL                                 515     1336.6              
Type_product        3   32.544       512     1304.0 4.019e-07 ***
Exhaustion_product  9   92.167       503     1211.8 5.977e-16 ***
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Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1[/code]

gl=glm(Effort ~  Type_product +  Exhaustion_product, family=poisson , data=vect)
library("emmeans")
emmp <- emmeans( gl, pairwise ~ Type_product)
summary( emmp, infer=TRUE)

 contrast    estimate         SE  df    asymp.LCL   asymp.UCL z.ratio p.value
 c - f    -0.14084934 0.04221684 Inf -0.249305743 -0.03239295  -3.336  0.0047
 c - m     0.33882907 0.08050197 Inf  0.132016967  0.54564118   4.209  0.0002
 c - s     0.31167356 0.12274400 Inf -0.003659682  0.62700680   2.539  0.0541
 f - m     0.47967842 0.08339482 Inf  0.265434484  0.69392235   5.752  <.0001
 f - s     0.45252290 0.12076017 Inf  0.142286189  0.76275962   3.747  0.0010
 m - s    -0.02715551 0.14317625 Inf -0.394979861  0.34066883  -0.190  0.9976

There is significant effect of Effort and Type_product (χ2(3)=32.5, p<0.001). Post-hoc test report decreasing Effort of C comparing to F.

Firstly, I want to be sure that my GLM reporting is correct.

After that, I can't found any APA format reporting for post-hoc test (p-value, estimate?)

How to report these values ?

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I think in your paper you should show a table of the EMMs and SEs, and another table showing the comparisons among them and their Tukey-adjusted P values. Possibly you should do them with type = “response" so that the results are on a more interpretable scale. A graph or two might help as well.

In submitting a paper to a journal, your responsibility is to show the reviewers as clearly as possible what you did and how you justify your findings. If the journal wants the results expressed more succinctly to save pages, that’s understandable, and can be accomplished later. It should not come at the expense of the reviewers and editors’ clear understanding of the methods and procedures being used.

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