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hypothesis testing confusion

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  • #41834

    Neo
    Participant

    while testing hypothesis’, if the p-value 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 p-value 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
    neo

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    #131640

    pise
    Participant

    Hypothesis 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.
     

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    #131641

    Ram
    Participant

    Raj,
    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?
     
    Ram

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    #131643

    AVY
    Participant

    Hi  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 p-value 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.
    AVY

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    #131650

    domanoid
    Participant

    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,
    doma

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    #131651

    Neo
    Participant

    doma,
    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 p-value?

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    #131652

    doma
    Participant

    Again, 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.

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    #131653

    Neo
    Participant

    understood. Thanks for the explanation
    neo

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    #131654

    pise
    Participant

    p 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 helps

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    #131656

    AG
    Participant

    Hi !!
    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- (1-P) 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 p-value of 0.02 then you are (1-0.02 = 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,
    AG

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    #131672

    doma
    Participant

    Another 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 it’s 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 U’re 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.

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    #131687

    Jawad
    Participant

    The p-value is the least Alpha (prob of making type I error) that is acceptable.
    Hope this helps.

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    #131689

    Peppe
    Participant

    Why 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, Peppe

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    #131701

    Darth
    Participant

    Not very helpful since the p-value is the actual calculated probability of a type 1 error whereas the experimenter selects the alpha error that is acceptable.

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    #131707

    CG
    Participant

    Doma,
    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 case

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    #131708

    Darth
    Participant

    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.

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    #131709

    CG
    Participant

    Darth,
    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
    CG

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    #131715

    doma
    Participant

    That 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.
    brg

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