Paired t Test on Z normalized values

Question

I have 2 sets of data, each consist of 92 data points. Pearson's correlation between them is 0.22. My hypothesis is the data sets are not significantly different, so I've normalized each datasets with Z score, and then did a paired t-test.

Here is the outcome post z score generation:

Pearson Correlation = 0.227190366262831
Observed Mean Difference = 7.61468183193993E-16
Variance of the Differences = 1.54561926747434
df = 91
t Stat = 5.87481796014581E-15
P (T<=t) one-tail = 0.5
t Critical one-tail = 1.66177115506169
P (T<=t) two-tail = 1
t Critical two-tail = 1.98637715441862

If I had used raw values then the outcome looks like this:

Pearson Correlation = 0.227190366262831
Observed Mean Difference = 18.2867152592913
Variance of the Differences = 239.53919514091
df = 91
t Stat = 11.3329069579844
P (T<=t) one-tail = 2.18898629577025E-19
t Critical one-tail = 1.66177115506169
P (T<=t) two-tail = 4.3779725915405E-19
t Critical two-tail = 1.98637715441862

What I can infer from this? Is this a correct approach to test these 2 datasets.

Answer 1

I am assuming these are numeric values since you z-transformed them. You do not need to transform them to use a t-test, in fact you shouldn't, since that will center each one on 0, which is why the p-values for the z-transformed data are 0.5 or 1.

The p-value for the two-tailed t-test on the raw values tells you that the means of the two data sets are different. As for correlation, you can use a correlation test to test whether that is different from 0.