What actually the “P” value tells us in ANOVA table. We normally compare the test statistics with the critical value (F0, obtained from F-table at given d.o.fs) to determine whether the given parameters effects are significant or not.
What used to be done, before computers, was that you would look up a critical value and compare it to your observed F-statistic. That critical value represented the cutoff point for the alpha level of significance, usually 0.05. Well, 0.05 is also the p-value that is associated with a certain F-statistic. When you see a p-value in an ANOVA table what you see is really the area under the F distribution curve that is to the right of your observed F-statistic. It also represents the probability that your observed F-statistic occurs under the assumption that the null hypothesis of your test (in this case, that the means of the factor levels are equal).
The p-value is the area to the right of the F statistic, F0, obtained from ANOVA table. It is the probability of observing a result (Fcritical) as big as the one which is obtained in the experiment (F0), assuming the null hypothesis is true. Low p-values are indications of strong evidence against the null hypothesis. I read in the book that it is common to declare a result as significant if the p-value is less than 0.05 or 0.01.
Hope this helps
This is more of a question than a statement, but I was always taught if you use a P-Value in the ANOVA then you are assuming normality in the data. Correct???
In Analysis of variance test (ANOVA), we have two fundamental assumptions. First that the “means” are normally distributed; secondly the “variances” are equal. So, what I think is that in ANOVA test, we can use both methods, either “F” test or “P” test in oder to see whether the means are significantly different or not. Please correct me if i am wrong!
See this link. It offers one of the best explanations I’ve seen.
P values have 2 specific uses.
1. Normality of Data – a significant P value (P < or = .05) means that the sample data you are testing (either with Normal Probability Plot or Descriptive Stats, using Minitab) is a normal subset of the population data.
2. Hypothesis Testing – a significant P value (P < or = .05) means you would reject your null hypothesis (that there is NO difference between the 2 or more sets of data you are testing).
In Bobby’s reply, paragraph1, is it that P < or = 0.05 implies normal data or
P > or = 0.05 implies normal data?
I agree with 2nd statement, but a P Value in a normality test must be >=.05 to indicate normality.
The P value is the probability of Alpha (or type 1) error, which is the probability that an F value this large could occur by chance and not be due to some assignable cause.
Yes, I will say I placed my sign backwards. Just goes to show that in a few instances inspection may be a value-added step.
Always proofread your email before you hit send.
Thanks Dan and Raja for catching my miscue.
I remember it this way.If the p is low, the null must go.
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