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.


The F-test is essentially a ratio of standard deviations. Every factor has only one observation in your sample data. Your standard deviation is zero. You get a test-statistic of zero because one cannot compare variances in your sample because there is no variance in your sample.

There is variance across factors but not within a factor.

Source : Link , Question Author : B. Davis , Answer Author : Hans Roggeman

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