Producing anova from already summarized data - r

Question

I have a table that looks like this:
I'm trying to run aov() on the above table, but I'm only able to create a partial output. I'm not sure how to include the standard deviation in the calculation.
Right now I'm concatenating and repeating each group like so:
groups <- c(rep('LHS', 121), rep('HS', 546), rep('Jr', 97), rep('Bachelors', 253), rep('Graduate', 155))
And then doing the same for the means (since I don't have access to the original data sheet):
means <- c(rep(38.67, 121), rep(39.6, 546), rep(41.39, 97), rep(42.55, 253), rep(40.85, 155))
At this point I can create a data fame and then run aov on it:
df <- data.frame(groups, means)
groups.aov <- aov(means ~ groups, data = df)
Unfortunately summary(groups.aov) only gives me a partial result.
Df Sum Sq Mean Sq F value Pr(>F)
groups 4 2004 501 4.247e+27 <2e-16 ***
Residuals 1167 0 0
Any other way I can go, where I can factor in the SD?

Answer 1

We simulate some data so that we know the calculations are correct:
set.seed(100)
df = data.frame(
groups=rep(letters[1:4],times=seq(20,35,by=5)),
value=rnorm(110,rep(1:4,times=seq(20,35,by=5)),1))
We get back something like the table you see above:
library(dplyr)
res <- df %>% group_by(groups) %>% summarize_all(c(mean=mean,sd=sd,n=length))
total <- data.frame(groups="total",mean=mean(df$value),sd=sd(df$value),n=nrow(df))
rbind(res,total)
# A tibble: 5 x 4
groups mean sd n
<fct> <dbl> <dbl> <int>
1 a 0.937 1.14 20
2 b 1.91 0.851 25
3 c 3.01 0.780 30
4 d 4.01 0.741 35
5 total 2.70 1.42 110
We always work with the sum of squares in anova. So from sd back to sum of squares, you usually multiply by n-1, and from there you can derive the F value. The detailed calculations:
# number of groups
ngroups=nrow(res)# number of groups
# total sum of squares
SST = (total$sd^2)*(total$n-1)
#error within groups
SSE = sum((res$sd^2)*(res$n-1))
aovtable = data.frame(
Df = c(ngroups-1,total$n-ngroups-1),
SumSq = c(SST-SSE,SSE)
)
aovtable$MeanSq = aovtable$SumSq / aovtable$Df
aovtable$F = c(aovtable$MeanSq[1]/aovtable$MeanSq[2],NA)
aovtable$p = c(pf(aovtable$F[1],aovtable$Df[1],aovtable$Df[2],lower.tail=FALSE),NA)
And we can compare the two results:
aovtable
Df SumSq MeanSq F p
1 3 140.55970 46.8532330 62.62887 2.705082e-23
2 105 78.55147 0.7481092 NA NA
summary(aov(value~groups,data=df))
Df Sum Sq Mean Sq F value Pr(>F)
groups 3 140.56 46.85 63.23 <2e-16 ***
Residuals 106 78.55 0.74