Dear Shahidul,

Since you don’t have normality in your data, you cannot use paired samples t-test for your hypothesis tests. Instead you should use the non-parametric equivalent which is Wilcoxon Sign Test. For more information see https://www.statisticssolutions.com/the-wilcoxon-sign-test-in-spss/

I fully agree with Stamatis Ntanos . But, if the differences between income before and income after (for each subject) look quite normal (by histogram and QQ-plot, and maybe the Shapiro test), you could run the one-sample t-test, i.e., test whether the mean of these differences is equal to zero (null hypothesis).

https://libguides.library.kent.edu/SPSS/OneSampletTest

https://www.statisticssolutions.com/manova-analysis-one-sample-t-test/

Note also that the t-test is quite robust. If the 'abnormality' of the data is not too obvious, you could rely upon the paired t-test. It has more power than the Sign test or the Wilcoxon signed ranks test.

Income distributions often are highly skewed, and a classic way to deal with this is to take the natural logarithm. If that produces reasonably symmetric distributions, then you can use a paired t-Test.

What does your graph look like? Have you tried a Kolmogorov-Smirnov test? If so try a transformation to normality, Google Box-cox transformation selection program. Best, David Booth PS Prof Morgan has offered good advice thus Box-Cox should probably choose a log transformation. You can compare your results with more Goodness of fit tests. As Prof Morgan indicates if this works paired t is fine. Best, D. Booth PS a refrence to this Stuff is:

https://www.amazon.com/Applied-Linear-Statistical-Models-Michael/dp/007310874X/ref=sr_1_2?keywords=Kutner+Applied+linear+Statistical+models&qid=1561297643&s=books&sr=1-2

you cannot use paired samples t-test for your hypothesis tests. you should use the non-parametric equivalent which is Wilcoxon Sign Test.

If the sample size is sufficiently large then you can safely use paired t test utilising the Central Limit Theorem..

According to the Central limit theorem, if sample size large enough then you should use Paired t-test otherwise non-parametric test like as Wilcoxon Sign Test use.

Hi Shahidul,

You have got all brilliant responses to resolve your problems. I would like to add that first you have to log transformed your income data and check normality. If income still does not follow normal distribution, you should go for non-parametric test of Wilcoxon Sign Rank-Sum Test, which is equivalent to paired t-test. Note that you have to compare two medians now instead of two means as they are non-normal data.

All the best!

Rakib