Is there any reference for the statement "During the testing of variables either using x2 or t-test, the significant variable are taken to the model and the insignificant are not"
I do not think you could find a reference for this. An insignificant variable before might get significance after entering in the model due to confounding.
Moreover, it is much more important to check the shape of the relationship between the dependent and the independent variable (possibly conditionnally on other covariates) on the logit scale. Scatterplots and smoothing techniques are very useful for this purpose.
If your dependent variable is a sigmoid (e.g., a probability), do the logit transform and then you can run PCA, t-test, chi-square, manova, or even correlation to identify significant covariates or their linear combinations. The problem with using the standard tests on raw dependent variable in your case is that the dependent variable is not linear (it's a sigmoid), meaning that you will lose sensitivity at the tails. Logit transformation will give you a dependent variable whose sensitivity to covariates does not depend on its own value.
