Question

Four laboratories are being used to perform chemical analysis. Samples of the same material are sent to the laboratories for analysis as part of the study to determine whether or not they give, on average, the same results. Assume the distributions of results for the laboratories are of the same shape but not normal. The analytical results of the sample material are as follows:

A	B	C	D
97	62.7	55.9	60.7
61.4	64.5	56.1	60.3
60.9	63.1	57.3	61.4
59.1	59.2	55.2	60.9
58.2	60.3	58.1	62.3

Test if the laboratories give the same results on average. Use a = 0.005.

Answer 1

For the given data using Anova single factor in Excel we get output as

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
A	5	336.6	67.32	276.977
B	5	309.8	61.96	4.668
C	5	282.6	56.52	1.352
D	5	305.6	61.12	0.592
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	294.086	3	98.02867	1.382686	0.284066	6.303385
Within Groups	1134.356	16	70.89725
Total	1428.442	19