hypothesis testing confusion
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December 28, 2005 at 6:44 am #41834
while testing hypothesis’, if the pvalue is less than .05, then we reject the null hypothesis, otherwise we fail to reject it.
If the null hypothesis is Ho: Mean A = Mean B
Alternate is Ha: Mean A <> Mean B
And we get a pvalue of .02, what is the conclusion apart from the final conclusion that we reject the null hypothesis? For example, are we saying that the probability that the two samples are different is less than 2%? If so, then how have we tested the alternative hypothesis?
Thanks
neo0December 28, 2005 at 7:09 am #131640Hypothesis testing is not just about rejecting the null hypothesis and accepting the alternative when p is 0.02. What it means is, you don’t have sufficient evidence to show that Mean A = Mean B and that there is more evidence in favour of Mean A Mean B. Hope this explanation helps.
0December 28, 2005 at 7:18 am #131641Raj,
I understand the part about there being not enough evidence to reject the null hypothesis.
What I want to know is that what does this p value mean statistically?
Ram0December 28, 2005 at 7:48 am #131643Hi Neo,
The Hypothesis test is based on the theory that ‘ Unless proven, the person is not guity of the charges ‘.
The example quoted by you, has the Alternate hypothesis as Mean A not equal to mean B. So we have to look whether enough evidence is available to proven the alternate hypothesis.
The pvalue of 0.02 indicates that for Alpha value of 5%, enough evidence is available to say that the two means are significantly different. We donot check the alternate hypothesis, we only check the Null hypothesis. The inference drawn by you needs correction – There is 2% probability that the two means are same. i.e only 2% chances that null hypothesis holds true.
AVY0December 28, 2005 at 10:54 am #131650
domanoidParticipant@domanoid Include @domanoid in your post and this person will
be notified via email.Hi,
first of all I do not know, how clear Hypothesis Testing is for U. U do not test the alternative Hypothesis. The test result does not tell you anything about the alternative hypothesis. It says if you should reject or not reject the H0 Hypothesis.
Type I error: A conclusion that the population has changed when in fact it has not. H0 is true, but in your observation you have found it to be false. In your case this means that you say mean(A)NOT=mean(B), although it is.
Type II error: A conclusion that the population has not changed when in fact it has. H0 is false, but in your observation you have found it to be true. In your case this means that you say mean(A)=mean(B), although it is not true.
U test only the Type I error. Alfa is the probability of Type I error.
U fail to reject H0 Hypothesis if p>alfa, but you reject H0, if p<alfa.
I hope this is enough, if not pls contact me.
brg,
doma0December 28, 2005 at 11:01 am #131651doma,
I understand you do not test the alternate hypothesis. My mistake in the posting. All we are trying to do is to see if statistically, there is enough evidence to reject or fail to reject the null hypothesis.
My question is more to do with the p value. How do you interpret the numeric pvalue?0December 28, 2005 at 12:07 pm #131652Again, alfa is the probability of Type I error. U fail to reject H0 Hypothesis if p>alfa, but you reject H0, if p<alfa. I guess this should Let me give an example: H0 – the coin is fair. Observe 40 heads, 60 tails. p is the probabiliy of observing at least 40 heads (60 tails) from a fair coin.
0December 28, 2005 at 12:20 pm #131653understood. Thanks for the explanation
neo0December 28, 2005 at 12:39 pm #131654p can be considered as probability of obtaining the test results assuming Ho is true. when you do the Hyp test between means ( Mean A= Mean B ) and if p=0.02, it means that there is 0.02 probability of obtaining the result Mean A= Mean B. if our probability from the test is 0.05 then we still have a risk of accepting Ho when it is not true.
hope this helps0December 28, 2005 at 1:38 pm #131656Hi !!
The explainations given by all of you are great. Its
just a matter of how one understands it. Let me try
to make it little simple (for a practitioner):
0 Null hypothesis is status quo, that is, true till proven wrong
1 Whatever you’re trying to prove is HA (Opposite of Ho), i.e., prove if there is a difference between means, medians, variance etc.
2 You are not making conclusions about the samples but about the populations. In simple words you are trying to look at the kids (samples) and find out if they belong to same parent (population) or not. Therefore we always compare samples not the statistic (mean, median, std dev).
3 (1P) is the confidence in accepting HA (in statistical world you never accept anything in hypothesis testing, you always reject or fail to reject the null hypothesis but for practioners above statement is simpler.)
4 in most commercial processes 95% or more confidence is good enough to accept the HA
5 So when you are testing means of two samples then alternate hypothesis is mean(A) is not equal to mean(B). If you get a pvalue of 0.02 then you are (10.02 = 0.98) 98% confident that mean(A) is not equal to mean(B) so go for it.Let me know you need more info.Regards,
AG0December 29, 2005 at 7:39 am #131672Another contribution to the mistery of p.
At Hypothesis Testing U try to prove, that H0 is not true. With the typical given alfa=0.05 this means that u have 0.95 probability that its not true and 0.05 that it is true. So the smaller U set the alfa value the greater the probability that U accept a H0 Hypothesis. This is why U only achieve significant result if U can prove that H0 is not true. So this means that U have to make the test in a way that U come out with significant results.
Another thing is that p gives U the value where Ure about to accept the H0 Hypothesis. If this level is smaller than the alfa then U reject H0, if higher then U accept H0.
I hope this is clear.
This leads to the following contribution in your case. U should have H0 as mean(A)NOT=mean(B). So if this passes You can be pretty sure that U were right, otherwise the result will not be significant.0December 29, 2005 at 3:49 pm #131687The pvalue is the least Alpha (prob of making type I error) that is acceptable.
Hope this helps.0December 29, 2005 at 4:59 pm #131689Why you don’t try to run your test using Zvalues [or any other distribution, of course] ? After that you can convert Zvalue in pvalue, and compare it with alpha, so all could be more clear, I think [please, don’t forget if it is for one tail or two tails].
Rgs, Peppe0December 29, 2005 at 8:18 pm #131701
Ken FeldmanParticipant@Darth Include @Darth in your post and this person will
be notified via email.Not very helpful since the pvalue is the actual calculated probability of a type 1 error whereas the experimenter selects the alpha error that is acceptable.
0December 30, 2005 at 1:29 am #131707Doma,
If not mistaken, we cannot set any hypothesis we like in minitab. We cannot set not equal null hypothesis….
Please advise what to do in that case0December 30, 2005 at 2:13 am #131708
Ken FeldmanParticipant@Darth Include @Darth in your post and this person will
be notified via email.Mini lets you select; less than, greater than or not equal to for alternative hypothesis. For example, in a 2 sample t test look under “Options/Alternative”. The null will either be zero (default) or some number other than zero. That number serves the same purpose as “not equal” but must be specified.
0December 30, 2005 at 2:48 am #131709Darth,
Sorry, I don’t really understand what you meant. Do you mean we can set the null hypothesis as a “not equal” statement, and set alternative hypothesis as “equal” statement? How can we set this in Minitab?
Please advise
CG0December 30, 2005 at 7:27 am #131715That should be right, though I do not know the Hypothesis tools of Minitab. But there are plenty of possibilities of different Hypothesis testing (should be even in Minitab), so U should be able the test what U want as well.
In case of Minitab, I’m affraid I cannot help, because I use company sw. sorry. But as far as I know there are plenty of minitab gurus at this forum.
brg0 
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