STATZIKI

Input

Treatment1 Treatment2 Treatment3 Treatment4 Treatment5

24 28 37 30 37 44 31 35 42 47 52 35 46 43 57 34 58 46 52 38

Summary

Sum y1^2	14161
Sum y2^2	21609
Sum y3^2	30976
Sum y4^2	32400
Sum y5^2	37636
Sum all	816
Sum yij^2	35020

Formulas and Output

\[SStreatment = \sum \frac{y_{i}^2}{n_{i}} - \frac{y^2}{N}= \frac{ 14161 }{ 4 } + \frac{ 21609 }{ 4 } + \frac{ 30976 }{ 4 } + ... - \frac{ 816^2 }{ 20 } = 902.7\] \[SSE = SST-SStreatment = 1727.2 - 902.7 = 824.5\] \[SST = \sum\sum y_{ij}^2-\frac{y^2}{N} = 35020 - \frac{ 816^2 }{ 20 } = 1727.2\] \[MSR = \frac{ SStreatment }{ k-1 } = \frac{ 902.7 }{ 4 } = 225.675\] \[MSE = \frac{ SSE }{ N-k } = \frac{ 824.5 }{ 15 } = 54.9667\] \[Fvalue = \frac{ MSR }{ MSE } = \frac{ 225.675 }{ 54.9667 }\]

Source of variation

Source of Variation	Degree of Freedom	Sum of Square	Mean Sum of Squares	F-test	p-value
Treatment	4	902.7	225.675	4.1057	0.0192
Error	15	824.5	54.9667	-	-
Total	19	1727.2	-	-	-

Example

Typical textbook problem that requires a one-way ANOVA

Pfizer wants to investigate the bioactivity of a new drug on four different levels of dosage.
They tested the drug on each level four times on different observations and collected the following data:
Dosage 20g = [24 28 37 30]
Dosage 30g = [37 44 31 35]
Dosage 40g = [42 47 52 35]
Dosage 50g = [46 43 57 34]
a) Is there evidence that dosage levels affects bioactivity? Use a=0.01.
b) Analyse the residuals to check model adequacy (Is the variance on the residuals constant)
Using this calculator you can find the answer to the questions above
on any one-way ANOVA dataset and the method used to find them.