I have done a two variable t-test for two states(Newyork and Connecticut) to check whether the AQI(Air quality index ) is same for both of them or not, The calculated p value is 0.03 which is less than 0.05 so able to reject null hypothesis. I want to know is there any performance index for this method(Two variable t-test) so that I can improve my test results.
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1$\begingroup$ I suggest you don't try to improve your test results, the test result is what it is, it tells you that the air quality depends on state and you shouldn't change what the data is telling you. $\endgroup$– Rui BarradasCommented May 2, 2020 at 5:48
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$\begingroup$ Some details might be helpful. How many AQI values for each state. A few cities in each state, or scattered throughout voth states. Do you have NY and CT on the same days? If so, especially for neighboring states, it might be appropriate to use days as pairs. You say you did 2-sample t. If pairing is appropriate/possible you might get a more powerful test. Are AQI values subject to far outliers? $\endgroup$– BruceETCommented May 2, 2020 at 6:42
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$\begingroup$ The aim is not to minimize p value! $\endgroup$– Michael MCommented May 2, 2020 at 15:05
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is there any performance index for this method
It sounds like you are asking how to improve your p-value.
You must accept the p-value for what is is. The probability of obtaining results as extreme or more extreme than the results you obtained is 0.03.
In general, if you want to increase statistical power (the ability to detect a real effect if a real effect is there), you can increase sample size, increase the precision of your instruments, or (in some cases) use a more powerful test.
Work on gathering more data, if you can.
