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I need some help in understanding what kind of post-hoc test I would need to run after an ANOVA.

Let's suppose that I have only 1 group of subjects and as independent variable I have "Condition". "Condition" has 4 levels "Condition_1", "Condition_2", "Condition_3", "Condition_4". As dependent variable, I have reaction times (RT).

To analyze this data I would use a One-Way repeated measures ANOVA. Specifically, in Python I would use the following test:

import pingouin as pg
from pingouin import mixed_anova, read_dataset
df_ANOVA = result.rm_anova(dv='RT', within='Condition', subject='Subjects', detailed=True)

Provided that I have a significant effect, what kind of post-hoc test would you apply? My hypothesis is that Reaction Times increase for each condition. In other words, each condition mean RT is smaller than the mean RT of the following condition: Condition_1 < Condition_2 < Condition_3 < Condition_4.

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Assuming that your global test is statistically significant, the post-hoc tests could simply be three more one-way repeated-measures ANOVAs: using Condition 1 and Condition2; using Condition 2 and Condition 3; and then using Condition 3 and Condition 4.

Because your post-hoc comparisons are specified apriori (beforehand) and the overall global test is statistically significant, I think the risk of Type I error is low.

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