oftware was used to conduct a one-way ANOVA to determine if the means are equal using a = 0.10. ummary Statistics: Mean Standard Deviation Sample Size Work Study 13.0633 Co-op 14.3633 Internship 15.231 0.5005 2.2051 0.6029 15 24 10
oftware was used to conduct a one-way ANOVA to determine if the means are equal using a = 0.10. ummary Statistics: Mean Standard Deviation Sample Size Work Study 13.0633 Co-op 14.3633 Internship 15.231 0.5005 2.2051 0.6029 15 24 10
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**One-Way ANOVA Analysis Summary**
A software tool was used to perform a one-way ANOVA analysis to determine if there are significant differences in means with a significance level of \( \alpha = 0.10 \).
**Summary Statistics:**
| | Mean | Standard Deviation | Sample Size |
|-------------|---------|--------------------|-------------|
| Work Study | 13.0633 | 0.5005 | 15 |
| Co-op | 14.3633 | 2.2051 | 24 |
| Internship | 15.231 | 0.6029 | 10 |
**ANOVA Table:**
| Source | SS | df | MS | F | P-value |
|----------|----------|----|---------|--------|---------|
| Between | 30.4877 | 2 | 15.2439 | 5.9117 | 0.005189|
| Within | 118.6151 | 46 | 2.5786 | | |
| Total | 149.1028 | 48 | | | |
The between-group variation is assessed using an ANOVA F-test, which shows a P-value of 0.005189, indicating a significant difference between the group means.
**Bonferroni Test:**
A Bonferroni test was conducted to determine which specific means are significantly different. Results of this post-hoc test follow, with a requirement to round to three decimal places.
| Comparison | Test Statistic | Adjusted P-value | Statistically Significant Difference? |
|--------------------------|----------------|------------------|---------------------------------------|
| Work Study vs. Co-op | -2.237 | 0.031 | Yes |
| Work Study vs. Internship| 14.3633 | 0 | Yes |
| Co-op vs. Internship | 15.231 | 0.233 | No |
**Hints for Bonferroni Test:**
- Retain the assumption of equal variances, as the test follows an ANOVA.
- Use Bonferroni’s adjustment to control the type I error rate.
The Bonferroni test results suggest statistically significant differences between "Work Study vs. Co-op" and "Work Study vs. Internship,"
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