Three Factor Data Analysis

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MTH 547 – FA 2017 Test 3 Take-Home Problem General Instructions: You should create appropriate graphs to evaluate all assumptions and provide a visual comparison of the treatment effects. Since the computer is doing the computations, it is important that you clearly interpret all results in the context of the problem. Don’t just say the F test is significant. Explain what that means in terms of the treatments being studied. 1) Assemblers in an electronics firm will attach 12 components to a newly developed “board” that will be used in automatic control equipment in manufacturing plants. An operations analyst was interested in the impact of three factors on the mean time to complete an assembly. The factors were gender (1=male, 2=female), three specific sequences for installing the 12 components (1, 2, 3), and the experience of the assembler (1: under 18 months, 2:18 months or more). 15 assemblers of each combination of gender and experience were randomly assigned to use one of the sequences with 5 assigned to each sequence. After an appropriate learning period each of the 60 assemblers was timed and the results are in “Take home data.csv”. Identify the type of design used and conduct a complete analysis. What would you recommend to the analyst about minimizing assembly time. Time Gender 1250 1175 1236 1239 1193 1021 1099 1069 996 1070 1319 1251 1241 1295 1265 1119 1110 1123 1097 1163 1217 1190 1201 1232 1251 1033 1067 1057 1077 1022 1066 1076 1004 1002 1034 864 848 881 892 868 1105 1043 1051 1128 1060 927 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Sequence Experience rep 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 1 2 2 2 2 2 2 2 2 2 2 3 1 3 1 3 1 3 1 3 1 3 2 3 2 3 2 3 2 3 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 1 2 2 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 944 957 897 933 1021 1020 1035 1000 1026 841 865 817 911 868 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 2 2 2 2 1 1 1 1 1 2 2 2 2 2 2 3 4 5 1 2 3 4 5 1 2 3 4 5
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Tags: statistics programmig SAS resolution design and analysis of experiments Factorial design

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Nov 07,2017
Three-factor Data Analysis (Multiple Factor ANOVA)
The type of design to be used is the multiple factor ANOVA where there are three factors
gender, experience, and sequence. Gender, experience, and age are categorical variables.
Gender is denoted by 1 and 2 indicating males and females respectively. Sequence are
categories are 1,2, and 3.Experience of the assembler are categorised as 1 who have
experience under 18 months and 2 whose experience are more than or equal to 18 months.
For multiple factor ANOVA, the significance level is assumed at 0.05.
Assumption of Anova
In order to test the normality assumption of ANOVA, quantile plot of residual vs. normal
quantiles was drawn. The graph is drawn below which shows that the distribution lie close to
the normal ,and hence normal distribution can be assumed.
Quantile plot

Residual Analysis

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Residual Vs Experience

Residual vs Sequen...