Week 10 Assignment MBA503

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Stony Brook University *

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503

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Statistics

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Jan 9, 2024

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Week 10 Assignment Exercise 1 Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 5 61.5 12.3 2.475 Column 2 5 69.8 13.96 4.313 Column 3 5 47.9 9.58 7.027 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 48.8973 3 2 24.44867 5.309157 0.022301 3.885294 Within Groups 55.26 12 4.605 Total 104.157 3 14 The p-value is .022301 which is less than .05 so we accept the null hypothesis. There is no significant difference between the mean scrap rates among the different production process. Looking at the box plot, the scrap rates from Plant C has a greater range of scrap per thousand units. Plant B has the highest scrap rates out of all the plants. Plant A has the most uneven distribution. Plant C has a noticeable outlier. Exercise 2

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Accounting 7 19.84 2.834285714 0.255295238 Finance 7 21.17 3.024285714 0.031528571 Human Resources 7 22.69 3.241428571 0.094680952 Marketing 7 23.6 3.371428571 0.066280952 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 1.181157143 3 0.393719048 3.517030893 0.03039 3.008787 Within Groups 2.686714286 24 0.111946429 Total 3.867871429 27 Based on the GPA dataset, the p-value is less than .05, therefore it is significant. The F crit is less than the F value too so there is a difference. Post-Hoc(Tukey) Column A Colum n B Mean Dif n(colum n A) n(Colum n B) SE Crit. Value Tcal Tcal v. Crit.Valu e ACC FIN 0.19 7 7 0.12646 1 3.901 1.50244 1 accept FIN HR 0.21714285 7 7 7 0.12646 1 3.901 1.71707 6 accept HR MRK 0.13 7 7 0.12646 1 3.901 1.02798 6 accept MRK ACC 0.53714285 7 7 7 0.12646 1 3.901 4.24750 3 reject MRK FIN 0.34714285 7 7 7 0.12646 1 3.901 2.74506 2 accept ACC HR 0.40714285 7 7 7 0.12646 1 3.901 3.21951 7 accept We reject the null hypothesis for all the groups except Marketing versus Accounting. Exercise 3 In a two-way ANOVA, you typically test three null hypotheses: a. Null Hypothesis for Main Effect of Factor A(Gender): This tests if there is a significant difference in the means of the dependent variable among the levels of Factor A, while ignoring Factor B. In this case the rows are the gender. There is no significant difference since the p-value is greater than 0.05.

Anova: Two-Factor Without Replication SUMMARY Count Sum Average Variance Female 3 9.59 3.19666667 0.54123333 Female 3 9 3 0.6481 Female 3 9.17 3.05666667 0.18503333 Female 3 9.36 3.12 0.0513 Female 3 9.76 3.25333333 0.10363333 Female 3 8.35 2.78333333 0.04973333 Female 3 9.74 3.24666667 0.13623333 Male 3 10.24 3.41333333 0.04813333 Male 3 9.43 3.14333333 0.26333333 Male 3 8.95 2.98333333 0.00563333 Male 3 9.8 3.26666667 0.11213333 Male 3 9.78 3.26 0.0793 Male 3 9.37 3.12333333 0.04813333 Male 3 9.25 3.08333333 0.04083333 Accounting 14 40.35 2.88214286 0.10917198 Finance 14 44.77 3.19785714 0.07758736 Human Resources 14 46.67 3.33357143 0.12613242 ANOVA Source of Variation SS df MS F P-value F crit Rows 0.94417381 13 0.07262875 0.6045771 0.82831614 2.11916569 Columns 1.502114286 2 0.75105714 6.25195832 0.00606862 3.36901636 Error 3.123419048 26 0.1201315 Total 5.569707143 41 b. Null Hypothesis for Main Effect of Factor B: This tests if there is a significant difference in the means of the dependent variable among the levels of Factor B, while ignoring Factor A. In this case the columns are the majors. There is a significant difference since the p-value is lesser than 0.05. Anova: Two-Factor Without Replication SUMMARY Count Sum Average Variance Female 3 9.59 3.19666667 0.54123333 Female 3 9 3 0.6481 Female 3 9.17 3.05666667 0.18503333 Female 3 9.36 3.12 0.0513 Female 3 9.76 3.25333333 0.10363333 Female 3 8.35 2.78333333 0.04973333 Female 3 9.74 3.24666667 0.13623333 Male 3 10.24 3.41333333 0.04813333 Male 3 9.43 3.14333333 0.26333333 Male 3 8.95 2.98333333 0.00563333 Male 3 9.8 3.26666667 0.11213333 Male 3 9.78 3.26 0.0793 Male 3 9.37 3.12333333 0.04813333 Male 3 9.25 3.08333333 0.04083333 Accounting 14 40.35 2.88214286 0.10917198 Finance 14 44.77 3.19785714 0.07758736 Human Resources 14 46.67 3.33357143 0.12613242 ANOVA Source of Variation SS df MS F P-value F crit Rows 0.94417381 13 0.07262875 0.6045771 0.82831614 2.11916569 Columns 1.502114286 2 0.75105714 6.25195832 0.00606862 3.36901636 Error 3.123419048 26 0.1201315 Total 5.569707143 41 c. Null Hypothesis for Interaction Effect: This tests if there is an interaction effect between Factor A and Factor B. In this case the gender does not affect the majors since the p-value is less than 0.05 and the F-crit is less than the F-value.

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Anova: Two-Factor With Replication SUMMARY Accounting Finance Human Resou Total Female Count 7 7 7 21 Sum 19.18 21.17 24.62 64.97 Average 2.74 3.024285714 3.51714286 3.09380952 Variance 0.157866667 0.031528571 0.10492381 0.19652476 Male Count 7 7 7 21 Sum 21.17 23.6 22.05 66.82 Average 3.024285714 3.371428571 3.15 3.18190476 Variance 0.031528571 0.066280952 0.08973333 0.07788619 Total Count 14 14 14 Sum 40.35 44.77 46.67 Average 2.882142857 3.197857143 3.33357143 Variance 0.109171978 0.077587363 0.12613242 ANOVA Source of Variation SS df MS F P-value F crit Sample 0.081488095 1 0.0814881 1.01466534 0.32051064 4.11316528 Columns 1.502114286 2 0.75105714 9.35193841 0.00053594 3.25944631 Interaction 1.094933333 2 0.54746667 6.81689083 0.0030864 3.25944631 Within 2.891171429 36 0.08031032 Total 5.569707143 41

Week 10 Assignment MBA503

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