I'm conducting a "typical" statistical analysis in my research, but I have a few questions regarding appropriateness of the tests I'm using and whether or not I'm doing things the correct way. I don't know which test is appropriate to determine two things: significance in a variable between two groups AND the strength of that association. (Note I use SPSS for my analyses)
Without getting into details, I have dichotomous outcomes/groups, lets call them 0 or 1. I'm investigating several continuous and categorical variables, and I want to test if there is a significant difference between the two groups in any of these variables. So to test significance in continuous variables, I used either the Independent Samples t-test or the Mann-Whitney U test (depending on normality, variance, etc.), and Chi-square for categorical. I found several variables "significant" as a result of these tests, using p < 0.05 as cutoff.
Next, I wanted to determine how much "weight" each variable had, so someone suggested I calculate Odds Ratio. I know that when conducting logistic regression, some say it's appropriate to "standardize" your continuous variables so that it makes more sense when comparing Odds Ratio between these variables. So I standardized my continuous variables using "Z-score standardization" and for each variable, ran a "Univariable Logistic Regression", which gave me Odds Ratio.
In my next step, I'm interested in doing a "Multivariable Logistic Regression" to identify independent variables.
Some concerns I have:
1) I noticed that some of the "significant" variables I identified using "t-tests" did not have significant p-values in the univariable logistic regression. Is this normal??
2) I've read some journal articles that use "Univariate Logistic Regresssion" to select only the significant parameters for "Multivariate Logistic Regression" instead of "t-tests"? So this begs the question, should I be using logistic regression instead to identify significant variables. What's the advantage of doing this and is it even appropriate?
3) Does it make sense to standardize your variables if you want to compare variables measured on different scales when considering Odds Ratio?
4) Are there other ways of determining "how significant" a variable is other than Odds Ratio?
5) What are the best tests to use to answer my questions: which variables are significantly different between the groups, and which of these significant variables have the "strongest" association?