# ANOVA Output Questions

I've been looking at the ANOVA output, and even with the help pages, I'm still a bit confused. (I probably would not be confused if I knew more about statistics.) I have four questions about the output for the full-factorial ANOVA, with 3 factors (with 2 levels each):

1) Does the "Prob." column refer to a probability that the computed F value is correct, or to a probability that the null-hypothesis was wrong, or something else?

2) How do I interpret the F value in the "overall test of model" section? I guess there are two sub-questions here:
a) How to I convert the F-value into a statement about whether the treatments had a statistically significant impact on the measured value (i.e. do I need to refer to an F-table, or is there something in the program that does that)?
Since I am doing a test with 3 factors, what does the overall test mean?

3) In the section "Test of effects...", do I understand correctly that those F-values tell me about the signiifance of the individual factors and their interactions?

4) The "Df" column in my "Test of effects..." section is all ones, although I have up to 15 data values in each cell. Does the Df in this case equal #levels-1, instead of N-1?

--Paul

• Hello Paul

1) The probability value refers to the likelihood that there areno differences amongst the various groups of data e.g. a low P value (< 0.05, the scientifically-accepted level of probability) indicates that there is less than a 1/20 chance of there being no differences, so there is a high chance that there are differences.

2) The overall F and P values indicate whether there is any difference in any groups for any factor - if P is non-significant, then there aren't any differences at all. statistiXL compares the F value with the theoretical F distribution (taking into account the two degrees of freedom) to calculate the exact P corresponding to this F - it "looks up" the F table for you.

3) Yes - these F values tell you about each particular factor, or interaction of factors.

4) Yes - the DF value is the number of levels - 1.

I hope this helps you interpret the output of statistiXL for ANOVA tests.

Phil Withers

• That was very helpful. Thank you.
--Paul