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One of my hypotheses is:

There is a significant difference in metabolical syndrome (dependent variable, quantitative, resultant range from 0 to 5) between patients and control group (one independent variable: 0 = patient id, 1 = control group) regarding to gender (independent variable, 0 = male, 1 = female).

Can someone please tell me which test in SPSS should I use to check that hypothesis? Should I use two way ANOVA or is chi-squared test sufficient?

My sample is N = 80.

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If metabolic syndrome is an ordered categorical variable with six levels (0, 1, ..., 5) then a model for ordinal logistic regression would be better than purely doing $\chi^2$ which is responsive to any deviation whereas you want to know if the patient group have higher odds of having a worse metabolic syndrome profile. You can then add sex into your model as a covariate. I have no idea whether you can do this in SPSS but I imagine an online search for SPSS ordinal logistic regression will turn up something.

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So from what you've written it sounds like a two-way ANOVA would be the way to go.

Im not following whether your response variable is discrete or continuous? If continuous, then a standard general linear model is probably fine to approach this data (although make sure to test normality, constant variance). If it is discrete then you will have to use a generalized linear model, possibly with a poisson distribution.

Make sure to include the interaction term (although based off the question I expect it would be non-significant). If it is significant, then thats a really cool result. If non-significant, then move on to evaluating each main effect.

Also, you said in your question you want to evaluate differences 'regarding' to gender. Do you mean controlling for gender? If so, then you should probably use type I sums of squares, and enter gender first in the model. This is all completely superfluous if you have a balanced design though.

Hope this helps

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