Dear RG Researchers,
When we apply the null hyposthesis to test the relationship, for two data set , we compare the F-statistic with the critical value (P-value) and upon this comparison we reject the null hypotheis (means there is relationship between the two data set (F>P-value)) or we accept it (F
We can never prove that a hypothesis is true because there are so many other factors that might be involved. Instead, we can only minimize the likelihood that the results is due to chance alone. Selecting a p value such as .05 determines how strongly you will rule out chance. Based on this logic, you can reject a hypothesis whenever the results could have been to chance. However, a failure to reject (i.e., significant results) does not allow you to "affirm" the hypothesis -- it only allows you say that the results are unlikely to be due to chance.
You don't compare an F-value to a P-value. You compare the (observed) F-value to the critical F-value. The critical F-value is a value for which Pr(F > Fcrit | H0) = alpha, with alpha being the level of significance (the "size" of the test). If F > Fcrit you know that this probability is smaller than alpha, in which case you reject H0.
Today, we don't need to use tables with Fcrit and can calculate Pr(F>Fobs | H0) directly. This is the p-value, and we can compare this p-value to alpha and reject H0 if p < alpha.
We NEVER accept H0. Failure to reject H0 means that we don't have enough data to interpret the statistic w.r.t. H0.
The reason behind this procedure is to dare an interpretation of a statistic calculated from the data (e.g. a mean difference, or the slope o a regression line, or an odds ratio, etc.) only if the data provides enough information about this statistic. The statistical significance is a proxy for this amount of information.
You are correct @Jochen Wilhelm, but he is asking that at what level will F-Stat be at a particular P-value to determine when to reject or accept hypothesis.
So the larger the F-stat the smaller the P-value to the alpha. Therefor you may have to not reject the null hypothesis. Vise versa. This shows that critical value is larger than the calculated value and therefore 0< .05.
You may also want to read https://www.statisticshowto.com/probability-and-statistics/f-statistic-value-test/#:~:text=The%20F%20value%20in%20one,one%20that%20was%20actually%20observed%2C
Dear all,
Thank you so much all for sharing your knowledge.
However, I am not accepting when we reject or we accept, I am asking the reasons (statistical reasons) behind this comparison from which we decide.
I appreciate all your answers
Are you not satisfied with the statistucal reasons behind this procedure I gave? And if so: why?
Dear Prof. Jochen Wilhelm,
My answer was not about satisfied or not and I am trying to understand your answer. However, I re-asked my questions just to be more clear for the others.
I will ask you again if I do not understand or for more understanding
Thank you so much sir
Prof Wilhelm Is trying to teach some statistics. The questioner is comparing a statistic(F) to a a probability (p=value) ie this does not make sense eg does your fish taste red? it makes no sense. Wilhelm wants the questioner to figure out why it makes no sense and then see what should be done. This is called discovery learning .I believe. D. Booth
You don't compare the p-value and F statistic but you can use both as part of your conclusion. The F statistic can be compared to the F critical value, If the F statistic is > than F critical value then you reject the Ho. However, even if the Fstat is > than the Fcrit, but the P value is non significant basing on the alpha level used, we still fail to reject the null hypothesis for group differences.
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