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I've time and again rejected or failed to reject the null hypothesis. In the failure to reject case, you conclude that there isn't sufficient evidence for rejection and you "move on" (i.e., either gather more data, end the experiment etc.,)

But when you "do" reject the null hypothesis, providing some evidence for the alternative hypothesis you can't really "prove" that your alternative hypothesis indeed holds true.

So, what are the common next steps once you reject the null hypothesis? What tools/techniques does one adopt to "analyze the problem further" to make more the findings more conclusive? What are the logical "next steps" as a statistician warranting further analysis?

For example:

$H_0: \mu_1 = \mu_0$

$H_1: \mu_1 > \mu_0$ (say we know the expected direction)

Once we reject the null hypothesis at some level of significance we have "some evidence" for the alternative to be true, but we cancan't draw that conclusion. If I really want to draw that conclusion conclusively (pardon the double word play) what should I do?

I've never pondered this question during my undergrad days but now that I'm doing a fair deal of hypotheses testing I can't help but wonder what's ahead :)

I've time and again rejected or failed to reject the null hypothesis. In the failure to reject case, you conclude that there isn't sufficient evidence for rejection and you "move on" (i.e., either gather more data, end the experiment etc.,)

But when you "do" reject the null hypothesis, providing some evidence for the alternative hypothesis you can't really "prove" that your alternative hypothesis indeed holds true.

So, what are the common next steps once you reject the null hypothesis? What tools/techniques does one adopt to "analyze the problem further" to make more the findings more conclusive? What are the logical "next steps" as a statistician warranting further analysis?

For example:

$H_0: \mu_1 = \mu_0$

$H_1: \mu_1 > \mu_0$ (say we know the expected direction)

Once we reject the null hypothesis at some level of significance we have "some evidence" for the alternative to be true, but we can draw that conclusion. If I really want to draw that conclusion conclusively (pardon the double word play) what should I do?

I've never pondered this question during my undergrad days but now that I'm doing a fair deal of hypotheses testing I can't help but wonder what's ahead :)

I've time and again rejected or failed to reject the null hypothesis. In the failure to reject case, you conclude that there isn't sufficient evidence for rejection and you "move on" (i.e., either gather more data, end the experiment etc.,)

But when you "do" reject the null hypothesis, providing some evidence for the alternative hypothesis you can't really "prove" that your alternative hypothesis indeed holds true.

So, what are the common next steps once you reject the null hypothesis? What tools/techniques does one adopt to "analyze the problem further" to make more the findings more conclusive? What are the logical "next steps" as a statistician warranting further analysis?

For example:

$H_0: \mu_1 = \mu_0$

$H_1: \mu_1 > \mu_0$ (say we know the expected direction)

Once we reject the null hypothesis at some level of significance we have "some evidence" for the alternative to be true, but we can't draw that conclusion. If I really want to draw that conclusion conclusively (pardon the double word play) what should I do?

I've never pondered this question during my undergrad days but now that I'm doing a fair deal of hypotheses testing I can't help but wonder what's ahead :)

Source Link
PhD
PhD
  • 14.9k
  • 21
  • 51
  • 48

Now that I've rejected the null hypothesis what's next?

I've time and again rejected or failed to reject the null hypothesis. In the failure to reject case, you conclude that there isn't sufficient evidence for rejection and you "move on" (i.e., either gather more data, end the experiment etc.,)

But when you "do" reject the null hypothesis, providing some evidence for the alternative hypothesis you can't really "prove" that your alternative hypothesis indeed holds true.

So, what are the common next steps once you reject the null hypothesis? What tools/techniques does one adopt to "analyze the problem further" to make more the findings more conclusive? What are the logical "next steps" as a statistician warranting further analysis?

For example:

$H_0: \mu_1 = \mu_0$

$H_1: \mu_1 > \mu_0$ (say we know the expected direction)

Once we reject the null hypothesis at some level of significance we have "some evidence" for the alternative to be true, but we can draw that conclusion. If I really want to draw that conclusion conclusively (pardon the double word play) what should I do?

I've never pondered this question during my undergrad days but now that I'm doing a fair deal of hypotheses testing I can't help but wonder what's ahead :)