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I have the following data.

Strain  n   mean    variance
A       8     75          18
B       8     70          23
C       8     72          21
D       8     78          20

I want to calculate their ANOVA and LSD grouping in R. I know the simple way of calculating ANOVA and LSD test when value of each sample and each treatment is given. but I am unable to do it when only mean and variance or standard deviation is given.

Mendel
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1 Answers1

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We can find MSE.Strain by using the variances to get the SSE.Strain and then dividing by the strain degrees of freedom. Your strain degrees of freedom are $df = 4(8-1) = 28$ since each variance was computed with 7 degrees of freedom. Therefore, MSE.Strain is given by: $$ MSE.Strain = \frac{7\cdot 18+7\cdot 23+7\cdot 21+7\cdot 20}{28} = 20.5 $$

Then for a $t_{df=28}$-distribution, the 0.05 two-tailed critical value is $t^*_{0.025,df=28}$ = qt(0.975, 28) = 2.048.

The LSD statistic is then: $$ LSD = t^*_{0.025,df=28}\sqrt{MSE.Strain\left(\frac{1}{8}+\frac{1}{8}\right)} = 2.048\sqrt{20.5/4} = 4.64. $$

We would reject the hypotheses that any means differing by more than 4.64 are equal. So we reject B being equal to A or D, and C being equal to D.

kurtosis
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  • I know the manual method. I asked in the question, **I want to calculate their ANOVA and LSD grouping in R** – Mendel Aug 11 '20 at 05:52
  • Ah, sorry for missing that. I'm not sure their is an easy way to do that in $R$. You would essentially be coding the manual method since the methods in $R$ are designed for working with the original dataset. – kurtosis Aug 11 '20 at 07:51