ANOVA - Binary / dichotomous dependent variable

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dama
Posts: 11
Joined: Wed Apr 07, 2021 5:12 pm

ANOVA - Binary / dichotomous dependent variable

Post by dama »

Hi,

thanks for your great work on Jamovi.

How would I go about comparing a control with two treatment conditions, where the dependent variable is dichotomous, i.e. yes or no.

I would like to compare the frequencies of yes and nos for the three different conditions. Would it work to use ANOVA?

Thanks for your help!
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MAgojam
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Joined: Thu Jun 08, 2017 2:33 pm
Location: Parma (Italy)

Re: ANOVA - Binary / dichotomous dependent variable

Post by MAgojam »

Hey dama,
I think your request can best be satisfied with an independence chi-square test.
Take a look at the screenshot ...
chi2_capture.PNG
chi2_capture.PNG (79 KiB) Viewed 2462 times
Cheers,
Maurizio
dama
Posts: 11
Joined: Wed Apr 07, 2021 5:12 pm

Re: ANOVA - Binary / dichotomous dependent variable

Post by dama »

Many thanks Maurizio, much appreciated.

Best,
Daniel
dama
Posts: 11
Joined: Wed Apr 07, 2021 5:12 pm

Re: ANOVA - Binary / dichotomous dependent variable

Post by dama »

If I were to make it a tad more complicated.. I'm sorry to get back to you @MAgojam.

So, there are three conditions with three levels where participants can give a dichotomous reply.

So, for condition 1, control (level 1), treatment 1 (level 2) and treatment 2 (level 3) will be able to give a yes or no. Is it still the independent chi-square test?

Thx!
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MAgojam
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Location: Parma (Italy)

Re: ANOVA - Binary / dichotomous dependent variable

Post by MAgojam »

dama wrote:So, there are three conditions with three levels where participants can give a dichotomous reply.
Hi Daniel,
from what I see it seems that yours are three categorical variables (3x3x2).
If so, I suggest you move towards the log-linear analysis which is basic in jamovi, with a look at the example in the first screenshot.
log-linear_3x3x2.PNG
log-linear_3x3x2.PNG (131.01 KiB) Viewed 2401 times
Log-linear analysis is a multidimensional extension of the classic chi-square cross-tabulation test.
While the latter can only consider two variables at a time, log-linear models can determine complex interactions in multidimensional contingency tables with more than two categorical variables.
Log-linear models combine the characteristics of cross-tabulation chi-square tests (determining the fit between observed and predicted cell counts) with those of the analysis of variance (ANOVA; simultaneous testing of the main effects and interactions within the multifactorial design), which is why they are sometimes informally called ANOVA for categorical data.
Instead of Pearson's chi-squared statistic, log-linear models use the statistical likelihood ratio of chi-squared, which is calculated differently, but has approximately the same distribution when the number of observations is large.

If in jamovi you install the gamlj module by Marcello Gallucci (fantastic module, indispensable for me) you can also look at your variables from the ribbon by selecting
Linear Models>Generalized Linear Model>Frequencies (Poisson) as in the example of the second screenshot.
glm_3x3x2.PNG
glm_3x3x2.PNG (183.41 KiB) Viewed 2401 times
Cheers,
Maurizio
dama
Posts: 11
Joined: Wed Apr 07, 2021 5:12 pm

Re: ANOVA - Binary / dichotomous dependent variable

Post by dama »

Much appreciated! Many thanks!
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