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## t Test for 2 Means - Hypothesis Writting

Hi all, I have a question regarding the hypothesis writting order for the below 2 samples t-test. Is that matter with the sequence/order for the hypothesis writting, something like we put Before or After on the left, whcich is showing in the below Example A & B?

Basically, both Example A & B are the same except the sequence/order. Question is which one should be the correct one?

Example A:

H0 (null) : µAfter µBefore

HA (alternative): µAfter < µBefore

Example B:

H0 (null) : µBefore ≤ µAfter

HA (alternative): µBefore > µAfter 1 ACCEPTED SOLUTION

Accepted Solutions
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## Re: t Test for 2 Means - Hypothesis Writting

As I said, it is your call. Since you were hoping to demonstration a decrease afterward, then it is

H0: mean before less than or equal to mean after

H1: mean before is greater than mean after

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4 REPLIES 4
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## Re: t Test for 2 Means - Hypothesis Writting

Only you could know the correct hypothesis test. That is why JMP provides three results. The null and alternative hypotheses are stated or proposed before you collect any data from the two populations. If your alternative hypothesis proposes any difference in the mean Test Time, then the two-tailed test is the appropriate test. If you proposed that the mean Test Time would decrease afterward, then Example A is correct. Finally, if you proposed that the mean Test Time would increase afterward, then Example B is correct.

What did you propose would happen afterward?

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## Re: t Test for 2 Means - Hypothesis Writting

Everything that Mark said is correct.

However, whenever I see "Before" and "After", I wonder if you actually should be conducting a PAIRED t-test. The analysis that you show and Mark discusses is for two independent populations.

Look at your data. Could you rearrange the values in the After column (without changing the Before column) and still have the results make sense? If so, then you are fine, continue with the two independent populations t-test. If the results would NOT make sense, then you have a paired t-test and you should change your analysis. All of Mark's advice on the hypotheses and the p-values would still hold.

Dan Obermiller
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## Re: t Test for 2 Means - Hypothesis Writting

Hi Mark,

Thanks for your reply. I try to write the hypothesis based on the 3 scenarios that listed in your earlier reply. Please correct me if I am wrong. :)

If your alternative hypothesis proposes any difference in the mean Test Time, then the two-tailed test is the appropriate test. The hypothesis writting should be something like below:

H0 (null) : µAfter = µBefore

HA (alternative): µAfter ≠ µBefore

If you proposed that the mean Test Time would decrease afterward, then Example A is correct.

Example A:

H0 (null) : µAfter  µBefore

HA (alternative): µAfter < µBefore

Finally, if you proposed that the mean Test Time would increase afterward, then Example B is correct. I believe it should be something like below and not the Example B:

H0 (null) : µAfter  µBefore

HA (alternative): µAfter > µBefore

The earlier Example B is identical to Example A, the difference is on the sequence for Before & After. For Example A, we put After on the left while for Example B, we put Before on the left. The intention is to check whether mean test time would decrease afterward. Are we allow to write the hypothesis as Example B in below, or we have to strictly follow the Example A?

Example B:

H0 (null) : µBefore ≤ µAfter

HA (alternative): µBefore > µAfter

Highlighted

## Re: t Test for 2 Means - Hypothesis Writting

As I said, it is your call. Since you were hoping to demonstration a decrease afterward, then it is

H0: mean before less than or equal to mean after

H1: mean before is greater than mean after

Learn it once, use it forever!
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