Look up multinomial logistic regression if your outcome variable is nominal, or ordinal logistic regression if the categories are ordered. Both yield odds ratios as measures of effect size. HTH.

With a categorical variable you are left to use logistic regression to determine if there is an association with your continuous variables. This will provide an OR as your effect estimate.

No if the DV is categorical you want a generalized linear model often some form of logistic regression. To cover all the bases, see:

https://statisticsbyjim.com/regression/choosing-regression-analysis/

Best, David Booth

David Eugene Booth Roberto J Vidri Bruce Weaver I cannot use logistic regression due to some limitations in assumptions. My problem is a bit complex to explain so in short I cannot use any ML model to do this. I am using ANOVA but want someone to confirm if the other way interpretation of ANOVA is valid or not.

Okay so i will explain here why i felt that ANOVA is useful in this case also. Suppose we are having a drug A,B,C given to Groups A,B,C. For 50 people in each group. We have reaction continous variable like % of insomnia occurred. Now, ideally it is like whether group A , B and C is clearly from same normal distribution or not is the ANOVA result. Which is like whether groupA ,B and C has some difference in % insomnia occurred. Now that can also be applied in my case also ie whether outcome_variable=1 is having some difference in continuous Independent variable as compared to outcome_variable=0 category. (Whether they are from same distribution or not).

I feel its just the way to say things are happening but it is like pearson correlation coefficient (Symmetric).

ANOVA measures whether two sets of groups have things drawn from same normal distribution or not. If we take this exact ANOVA statistician interpretation behind formulae, cant we apply because we are measuring distance between this two distributions from which they are drawn and if that distance is far from critical value, we say that there is difference between groups. If we say there is difference in continuous_var_independent more than necessary between group A and group B, we say that both have some different behavior whcih means outcome_var =1 has different sales velocity as compared to outcome_var =0.

Utsav Patel, I do not understand at all why you think logistic regression is precluded. But if you must estimate an ANOVA model with a binary outcome, look up linear probability model. The resources I'm aware of stress the importance of using a robust covariance matrix. E.g.,

• https://www.econometrics-with-r.org/11-1-binary-dependent-variables-and-the-linear-probability-model.html
• https://pdfs.semanticscholar.org/abf7/b1dcaeef7f2d75152368903bee4e54ab9552.pdf

Those sources talk about linear regression, but ANOVA and regression are just special cases of the General Linear Model (GLM). So I think they are applicable to your situation.

HTH.

Anova is a “Analysis of Variance”. Would be looking at the variance in the outcome (continuous) to be able to interpret correctly. I also, don’t quite understand how a logistic model cannot be used in your particular situation with a categorical/binary outcome.

Roberto and Bruce have given you very good answers, ANOVA basically provide information on level of variability within regression model and thats what forms the basis of significance testing. Hence, it is said that if you are reporting ANOVA you should not report regression on same data. If you do not want to use regression and want to build ANOVA model try using following equation, total sum of square (SST) = model sum of square(SSM) +error sum of square (SSE). The square of the sample correlation is equal to the ratio of the model sum of squares to the total sum of squares: r² = SSM/SST

I hope it helps.