Question

Results from an experiment involving a storage battery used in the launching mechanism of a shoulder-fired ground-to-air missile are presented in the table below. Three material types can be used to make the battery plates. The objective is to design a battery that is relatively unaffected by the ambient temperature. The output response from the battery is effective life in hours. Three operating temperature levels are selected, and an experiment with four replicates per combination is run. Material A 70 Temperature Low Medium High 130 155 34 40 20 74 180 80 75 82 58 150 188 136 122 25 159 126 106 115 58 45 138 110 174 120 96 104 168 160 150 139 82 B 70 С 60 The dataset can be downloaded from Blackboard under “BatteryLife.csv". i. Visualise the data using an appropriate plot. Briefly argue why your plot provides a good visual summary of the data. ii. Fit a two-way ANOVA model with interactions to the dataset, and summarise the main findings from your analysis. iii. Using appropriate residual diagnostic plots, or otherwise, critically assess the validity of the assumptions behind the ANOVA method on these data.

Answer 1

(i) The graph is:

Graph 200 180 160 140 120 100 80 60 40 20 0 А В с Low Medium High

The graph clearly displays both the categories of the data.

(ii) There is a significant main effect of Material. (p < .05)

There is a significant main effect of Temperature. (p < .05)

There is an interaction effect. (p < .05)

Source	SS	df	MS	F	p-value
Material	10,902.06	2	5,451.028	8.60	.0013
Temperature	41,527.06	2	20,763.528	32.74	6.04E-08
Interaction	10,200.44	4	2,550.111	4.02	.0110
Error	17,120.75	27	634.102
Total	79,750.31	35

(iii) The plot is:

Residual Plots for C3 Normal Probability Plot Versus Fits 99 50 90 25 Percent 50 -25 10 -50 1 -50 -25 25 50 50 75 150 0 Residual 100 125 Fitted Value Histogram Versus Order 12 50 9 25 Frequency -25 -50 0 -60 -30 30 60 1 5 30 35 0 Residual 10 15 20 25 Observation Order

The assumptions are met.

Material	Temperature
A	Low	130
A	Low	74
A	Low	155
A	Low	180
B	Low	150
B	Low	188
B	Low	159
B	Low	156
C	Low	138
C	Low	110
C	Low	168
C	Low	160
A	Medium	34
A	Medium	80
A	Medium	40
A	Medium	75
B	Medium	136
B	Medium	122
B	Medium	106
B	Medium	115
C	Medium	174
C	Medium	150
C	Medium	120
C	Medium	139
A	High	20
A	High	82
A	High	70
A	High	58
B	High	25
B	High	58
B	High	70
B	High	45
C	High	96
C	High	104
C	High	82
C	High	60