I've got some data. My data passed Shapiro-Wilk test i.e. my data is normal. I am about to standardize it using SPSS, but not sure on what steps to follow in order to standardize it based on t-scores, not z-ones. As I assume SPSS will do it to variables based on z-scores as default. After data standardization being done I am going to use Student's t-test between independent groups. Any help or reference would be appreciated.
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$\begingroup$ Why do you need to standardize it for analysis? And why does it need to be according to t-scores instead of z-scores? $\endgroup$– Mark WhiteCommented Apr 1, 2020 at 15:58
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$\begingroup$ Hi. well first of all it has to be based on t-scores because the total number (populiation) of sample I have is N = 20, which is very few items, so t-distribution (t-scores) would be better solution as a sign of good practice. Secondly, I will have to compare to different data types, basically two types of scales with different measuring units that in such scenario would require standardization. $\endgroup$– Web MasterCommented Apr 1, 2020 at 16:19
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I think there may be a little confusion I could clear up here: The t-distribution is the distribution that the test statistic is assumed to come from. The the dependent variable itself does not need to be t-distributed or scaled to be as such. You will get the same results of the t-test, in terms of test statistic, degrees of freedom, p-value, and standardized effect size (e.g., Cohen's d) regardless of any linear transformation you do to the data.
answered Apr 1, 2020 at 17:02
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$\begingroup$ Thanks for quick reply. As far as I did understood you, Student t-test does not require the normal data to be standardized in order to find a statistical differences in between two variables. Basically I have two variables: one as independent and one as dependent, each has different measuring units, so following your answer I am allowed to ignore the fact those two variables are not folllowing t-distribution. Correct if I am wrong. Thank you. $\endgroup$ Commented Apr 1, 2020 at 17:17
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1$\begingroup$ @WebMaster yes, you’ve got it. The independent variable is categorical with to groups. The dependent is normally distributed. There’s no need to standardize the dependent variable. In fact, if you standardize by condition, you are ensuring that both groups have a mean of zero. So no transformation necessary if the dependent variable is normal. $\endgroup$ Commented Apr 1, 2020 at 17:21