# How to interpret the P value on the ANOVA

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• #51453

newbie
Participant

How would I practically (or impractically for that matter explain the p value on the ANOVA?  Thanks!

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#178350

Anonymous
Guest

ANOVA tests differences between subgroup averages. The probability the differences you observe occur by chance are given by the p-values.Since there is a tendency among folks to confuse criteria, such as when pressing a glass on to a rash to test for meningitis, it is important to provide a memory hook.The one I use is: “Never p-up, always p-down.”Can anyone in forum come up with an easy memory hook for the meningitis test?

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#178354

Robert Butler
Participant

Another way to say the same thing is that the p-value for the ANOVA is a test of the equality of the various subgroup averages.  If the p-value is significant it is telling you at least one of the subgroup averages is different from the rest.
The question that usually follows this statement is:
How do I tell which average is different?
The answer is you will have to run post-hoc pairwise comparison tests and, because you are repeatedly testing the same group of averages, you will have to invoke one of the adjustment methods such as Bonferonni or Tukey-Kramer to insure you are still testing everything at your chosen level of significance.

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#178355

Sinnicks
Participant

In  Minitab session window we have also kind of graphical presentation on ANOVA results, with 95 % CI limits shown. Am I right that you can also use overlap of  CI limits  (is/is not) to see if there are  significant differences? Ofcourse this is only visual method and if the limits are close to each other you may not be able to tell for sure if there is a difference or not. Or am I missing something?

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#178363

newbie
Participant

Sorry guys, I intended to ask how one interprets and practically explains the R and R sq terms that accompany the ANOVA.  Thanks!

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#178365

Anonymous
Guest

Mark,Why not generate some ‘contrived’ data and try what you suggest.As Robert’s mentioned several times, looking at a graphical representation of data is always a good check. Otherwise there is a risk of misinterpreting the statistic and becoming disorientated. I’m expert at the latter :-)Cheers,
Andy

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#178374

Robert Butler
Participant

https://www.isixsigma.com/forum/showmessage.asp?messageID=89209
and the thread, of which this post is the first, covers the rest.
https://www.isixsigma.com/forum/showmessage.asp?messageID=39974

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#178375

Jered Horn
Participant

I think the S, “R-Sq”, and “R-Sq (adj)” below the ANOVA table is something new in Minitab 15???
S is the pooled estimate for the standard deviation and is the square root of the average of the variances for the individual observations.
R-Sq is actually what I’ve always called the epsilon square or 100 x SS factor/SS total.
R-Sq (adj) is what they are calling “R-Sq”, adjusted for the degrees of freedom.
So, in general, R-Sq is the percentage of the variation explained by the factors you are analyzing in the ANOVA.  The rest would be due to what is called “error”.
Hope that helps.

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#178387

newbie
Participant

Super!  Thanks Doc.

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#178393

newbie
Participant

Ok, so I am a bit confused.  I understand the previous thread in regression, since we have a response and at least one predictor, but an ANOVA (one way)  uses a single factor with multiple levels, so what are we considering the response and what are we considering the predictor?
Example:  There are 4 machines and I would like to run a test of means on cycle time to determine if a true difference exists.  I run the ANOVA (one way) and I get a p value of 0.000.  So I know with a high degree of confience that at least one cycle time is statistically different.  Now I look at the Rsq value of 4.5%.  The model (what) explains only 4.5% of the variability in (what)?  If the respsonse is cycle time, what is the predictor or factor?  The “levels”?
Sorry for being so slow on this…..Thanks again!

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#178405

Jered Horn
Participant

In your example, the factor is “machine”.  Response is “cycle time”.
The interpretation of the result…The p-value of 0.000 means there is a significant difference in the mean cycle time generated by at least one of the four machines.  R-Sq of 4.5% means 4.5% of the variation in cycle time can be explained by the differences in your four machines.  Or…you have a lot of error – within group variation.  It appears that a factor other than “Machine” is causing all that variation.
With the data you have…do a test for equal variances, then a box plot.  What do you see?

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#178407

newbie
Participant

Ok, so this is going back to the “signal to noise” ratio, right?  Whereby we compare the “within group” variation to the “between group” variation with the resulting ratio being the Rsq?  Hence, a small error term relative to the overall variability (1-SSerror / SStotal) would result in a high Rsq, while a poorly predicting model (ie high SSerror) would give me a poor Rsq. Am I tracking?

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