Interpret repeated measures ANOVA results in R

Question

I developed many model on groups of data I applied repeated measures anova to check the significant difference. Then I applied pairwise.t.test using Bonferroni correction.

I got this result from the anova test:

    Error: data
               Df    Sum Sq   Mean Sq F value Pr(>F)
    Residuals  9 6.533e-05 7.259e-06               

   Error: data:model
              Df    Sum Sq   Mean Sq F value Pr(>F)    
   model      15 0.0007337 4.892e-05    25.4 <2e-16 ***
   Residuals 135 0.0002600 1.930e-06                   
   ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

What am not sure about it is how to interpret this result, I understand that there is a significant difference because there is ***, but:

1. what does the F-value mean? what should I compare it to?
2. should I compare the pr to p-value(0.05)? the pr is 2e-16 which is too small number so what this means?

3. after applying the pairwise.t.test, this is the result:

        m1      m10     m11     m12     m13     m14     m15     m16     m2      m3      m4     
    m10 1.00000 -       -       -       -       -       -       -       -       -       -      
    m11 1.00000 1.00000 -       -       -       -       -       -       -       -       -      
    m12 1.00000 1.00000 1.00000 -       -       -       -       -       -       -       -      
    m13 0.00011 2.7e-07 6.1e-06 0.01300 -       -       -       -       -       -       -      
    m14 0.00167 5.9e-06 0.00011 0.12148 1.00000 -       -       -       -       -       -      
    m15 1.3e-10 1.0e-13 3.9e-12 6.4e-08 0.98736 0.14375 -       -       -       -       -      
    m16 4.0e-08 4.2e-11 1.4e-09 1.2e-05 1.00000 1.00000 1.00000 -       -       -       -      
    m2  1.00000 0.34365 1.00000 1.00000 0.12397 0.86949 1.6e-06 0.00022 -       -       -      
    m3  1.00000 1.00000 1.00000 1.00000 1.3e-05 0.00022 9.3e-12 3.2e-09 1.00000 -       -      
    m4  1.00000 1.00000 1.00000 1.00000 0.02063 0.18257 1.2e-07 2.2e-05 1.00000 1.00000 -      
    m5  0.14672 1.00000 1.00000 0.00211 4.1e-12 1.4e-10 < 2e-16 3.0e-16 0.00014 0.64775 0.00127
    m6  1.00000 1.00000 1.00000 1.00000 0.01057 0.10112 4.8e-08 9.4e-06 1.00000 1.00000 1.00000
    m7  0.59267 1.00000 1.00000 0.01218 5.0e-11 1.6e-09 < 2e-16 4.1e-15 0.00097 1.00000 0.00759
    m8  1.00000 1.00000 1.00000 1.00000 1.3e-06 2.6e-05 6.1e-13 2.4e-10 0.87263 1.00000 1.00000
    m9  1.00000 1.00000 1.00000 1.00000 1.8e-07 4.2e-06 6.5e-14 2.8e-11 0.27244 1.00000 1.00000
   

Does this mean that only p-values under (0.05) in this table indicate there are significant difference? so there is no significant difference between m1 and m10 because the p-value is 1, but there is a significant difference between m12 and m13 because the p-value is 0.01300?

Answer 1

I realised no one has answered you... i have been there lol !SO you have a few questions, can i suggest you take a look at some youtube videos and also buy some stats in R books, i promise you it will be worth it.

1. The F-value column is the test statistic from the F test. This is the mean square of each independent variable divided by the mean square of the residuals. The larger the F value, the more likely it is that the variation caused by the independent variable is real and not due to chance.

2. Kannan described this best: Pr(>F) is the same as P value – This is the p-value associated with the F statistic of a given effect and test statistic. The null hypothesis that a given predictor has no effect on either of the outcomes is evaluated with regard to this p-value. For a given alpha level, if the p-value is less than alpha, the null hypothesis is rejected.

So your P value in decimal notation would be 0.00000000000000002....So it is under the pvalue 0.05, inferring statistical significance. However, as this is very small it may be worth running some checks to ensure all is as it should be. You havent shared your script or some data, so i cant really comment.

hope this helps