# Warning (in R): “ANOVA F-tests on an essentially perfect fit are unreliable”

I have the data:

numbers <- c(0.176, 0.005, 0.022, 0.016, 0.036, 0.095, 0.069 )
Inds <- as.factor(c("P06", "P07", "P08", "P09", "P10", "P12", "P13") )


and am trying to test for differences in numbers as a function of Inds. The numbers are proportions of an events success for each individual. With Inds specified as a factor, I am trying conduct an ANOVA using aov() (below)

anova(aov(numbers ~ Inds))


which results in the warning (below)

Analysis of Variance Table
Response: numbers
Df   Sum Sq   Mean Sq F value Pr(>F)
Inds       6 0.021743 0.0036238
Residuals  0 0.000000
Warning message:
In anova.lm(aov(numbers ~ Inds)) :
ANOVA F-tests on an essentially perfect fit are unreliable


Any suggestions (changes in code or theoretical mistakes) would be appreciated.

• This is really a statistical question rather than a programming question. If you want to do an ANOVA you need more than one observation per group. You can test equality of proportions with a single observation per group (e.g. with a binomial GLM or with a Pearson X^2 contingency table analysis), but you will need to have the total number of individuals per group, not just the proportions. – Ben Bolker Jan 15 '14 at 23:52
• This question appears to be off-topic because it is about statistics – John Jan 15 '14 at 23:53
• The other point to consider is that using proportions as a continuous variable obscures the underlying data which of necessity are counts. (So still evidence that you DO need statistical help.) – DWin Jan 16 '14 at 1:51
• the F-test is essentially a ratio of standard deviations. Every factor has only one observation. Your standard deviation is zero. You get a test-statistic of infinity making it ridiculous to compare variances because there is no variance in your sample. – Hans Roggeman Jan 16 '14 at 2:08
• I first read the title as implying that R can't be trusted here. But R's reaction to the command is undoubtedly reasonable. If anything it understates that the user asked a question that can't be answered. Otherwise put, the warning is a warning to the user, not a warning about R. – Nick Cox Jan 16 '14 at 12:03