# Can Chi Square be Used for a Mixed Design with Repeated Measures?

• Math Is Hard
In summary, the conversation discusses a study in which participants were divided into two groups and put into either a positive or neutral mood. Both groups then had to solve two moral dilemmas. The authors used a chi square analysis to analyze the results, which caused confusion for the lab partners as they were only familiar with ANOVA. However, upon further examination, it was discovered that the authors only looked at one level of the independent variable at a time. The lab partners then decided to use a different measure for the dependent variable in their own experiment.
Math Is Hard
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My lab partner and I are trying to recreate this experiment:
http://www.blackwell-synergy.com/doi/pdf/10.1111/j.1467-9280.2006.01731.x?
This appears to be a mixed design.
Half the participants were put in a positive mood and half were put into a neutral mood. After the mood induction, each group solved two moral dilemmas (the Footbridge Dilemma and the Trolley Dilemma).
The type of dilemma is one of the independant variables and is a repeated measure because each group has to solve both moral dilemmas.

Now, it seems the authors use a chi square to analyze the results, and my lab partner and I are really struggling because neither of us ever learned to use chi squares (just ANOVA). I called up a friend who is a stats prof and he says that he seems to recall that a chi square can't be used if there are repeated measures in the design.

But somehow the authors are doing it. From the table on the 2nd page of article, it looks like they only analyze one level of the "type of dilemma" IV at a time. (i.e., they just looked only at responses to the Footbridge Dilemma and then looked only at reponses to the Trolley Dilemma).
So, I guess you can use chi square for a design that involves repeasted measures for one of the IVs?
thanks.

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oh, and we were planning on only two reponse choices for a dilemma: "appropriate" or "inappropriate", just as the authors did.

ok, never mind. we are going to use a different measure for the dependent variable.

## 1. What is a Chi square test?

A Chi square test is a statistical method used to determine if there is a significant relationship between two categorical variables. It is often used to analyze data from experiments or surveys.

## 2. What is a mixed design in a Chi square test?

A mixed design in a Chi square test refers to a study or experiment that includes both between-subjects factors (where different groups of participants are exposed to different conditions) and within-subjects factors (where the same participants are exposed to multiple conditions).

## 3. How is a Chi square test used in a mixed design?

In a mixed design, a Chi square test can be used to analyze the relationship between categorical variables for both the between-subjects and within-subjects factors. This allows researchers to examine the main effects and interactions of these variables on the outcome being measured.

## 4. What are the assumptions of a Chi square test?

The assumptions of a Chi square test are that the data is categorical, the observations are independent, and the expected frequencies for each category are at least 5. If these assumptions are not met, the results of the Chi square test may be inaccurate.

## 5. What is the interpretation of a Chi square test in a mixed design?

The interpretation of a Chi square test in a mixed design is similar to that of a regular Chi square test. If the p-value is less than the chosen alpha level (typically 0.05), then there is a significant relationship between the variables being studied. If the p-value is greater than the alpha level, there is not enough evidence to conclude that there is a significant relationship.