My PhD thesis contain a cross-culture research between two nationalities witch requires me to standardized my data to avoid the issue of responses type a cross-cultures for that i did the Z-score to standardized my data in Spss. So my question is: is it right to run T-test and Correlations directly to the standardized data or is it just for raw data?
This is a good point and I think it depends on exactly how you are z-scoring. take, for example, a common sort of design in my line of work, where multiple people will participate in a study and each person will provide a bunch of data points for 2 conditions. So you have one repeated-measures fixed effect (Condition) and one random effect (Subject). If you z-scored the data by pooling all the data from condition A, substracting the mean of that pool and dividing by the sd of that pool (and then repeating this same procedure for condition B), then you will have erased any between-conditions differences, just as Rainer described. On the other hand, if you z-score the data by participant instead of by condition (i.e., you pool the data for subject 1, including both conditions, and z-score that... then repeat the process for subject 2, for subject 3, etc.), then you have eliminated between-subjects differences but preserved between-conditions differences. (For example, if condition A elicited higher DV values than condition B in subject 1, than subject 1's z-scores for condition A will be positive and for condition B will be negative.) Indeed, some people do this.
Personally I usually don't feel it's necessary; I just use a mixed effects model to handle the between subjects differences. But it can be done. You just need to be specific about how you are z-scoring, because unlike some other transformations (like log, sqrt, etc.), "z-scoring" is not a monolithic thing, it means something different depending on how you are organizing your data for it.
Sorry, I erased my previous answer, because it was not thought out well. So Stephen refers to my first answer.
In principle, you could use the z-transformed variable for t-tests but it makes not always sense! You have to take care how you transform the variable. Just think about the variables: after transformation each variable has a mean of 1 and a standard deviation of 0. What will happen if you compare two independent samples: right the difference of 0-0 is 0, so the t-test makes no sense! So, if you use z-transformed dependent variables, the z-transformation has to be done across all groups.
It is very similar with the dependent t-test, especially for highly or not correlated variables. With a high correlation, both variables will look nearly the same. For example, take a random variable, create a second one by adding a fixed value. If you run a t-test on this raw data, you will probably find a difference. Now z-transform those two variables and run again the t-test, the difference will be zero.
Thank you so much Mr.Stephen Politzer-Ahles & Mr.Rainer Duesing it becomes clear now.
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