Question

1. The housing for a pregnancy test kit contains a disposable strip with a hole and a reagent that is jetted onto the strip. When the disposable strip is manufactured, the distance between the alignment hole and mark on the strip is measured in order to assure visibility of test results when the strip is assembled in the housing. An experiment is done to determine which of the three measuring instruments: calipers, an optical comparator, or a coordinate measuring machine (CMM), should be used to measure the distance. The experiment is run by having four randomly selected technicians make 3 readings with each of the three measuring instruments in a random order. The values of the absolute difference between the distance reading and the actual distances are given below: Instrument Technician .20 .26 .14 .15 .25 .30 .24 .20 2 35 .19 .21 .28 .50 .14 3 38 .15 54 .17 4 .33.25 .13 .15 .29 .16 Calipers Optical Comparator CMM .14 19 .17 .21 .23.24 .17 .18 21 .25 35 .27 a) Is the design crossed or nested? Is the Instrument Effect fixed or random? Is the Technician effect fixed or random? b) Calculate the ANOVA table and perform the test of significance of effects. What conclusion can you draw? c) Calculate the appropriate variance components.

Answer 1

data

	1	2	3	4
Calipers	0.2	0.24	0.5	0.33
	0.14	0.35	0.38	0.25
	0.15	0.21	0.54	0.29
Optimal Comparator	0.26	0.2	0.14	0.13
	0.25	0.19	0.15	0.15
	0.3	0.28	0.17	0.16
CMM	0.14	0.21	0.17	0.25
	0.19	0.23	0.18	0.35
	0.17	0.24	0.21	0.27

Using Excel

data -> data analysis -> Anova: Two-Factor With Replication

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Instrument	0.0676	2	0.0338	17.8693	0.0000	3.4028
Technician	0.0230	3	0.0077	4.0582	0.0182	3.0088
Interaction	0.1847	6	0.0308	16.2756	0.0000	2.5082
Within	0.0454	24	0.0019
Total	0.3208	35

if p-value < alpha, we reject the null hypothesis

here p-value for all effects (instrument, technician and Interaction) are less than alpha (0.05)

hence we reject the null hypothesis

all effects are significant