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.

**Answer**

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.

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