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For an experiment, I have two groups of participants (one group with pain, one without pain) who are going to perform three tasks. One task is under normal conditions, one task is with overstated visual feedback and one task is with understated visual feedback. I want to compare for each task whether the two groups are different, and if the difference between overstated to normal AND understated to normal is different between groups, and if the difference between overstated and normal AND the difference between understated and normal is different within groups. I think I will need a mixed method ANOVA design for the last two questions, and a two way ANOVA for the first comparison. Am I correct?

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From the information you have given, it would appear that you wish to compare differences across categorical variables, i.e. normal conditions, overstated visual feedback, and understated visual feedback.

In this regard, your analysis might be better served by using a chi-square test, which is designed to test for differences between categories.

If you were to run a chi-square test (I'm using R for this example), you first have your data sorted into a contingency table (one which shows the frequencies of the different categories across groups):

tbl = table(mydata$Groups, mydata$Tasks) tbl chisq.test(tbl)

Then, your null and alternative hypothesis is as follows:

H0: Groups A and B are independent.

HA: Groups A and B are not independent.

Should you yield an x2 symbol greater than the critical value (or a p-value lower than 0.05 at the 5% level of significance), then this indicates support for your alternative hypothesis - that the two groups are not independent from each other.

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