In the context of a Two Factor ANOVA, should you proceed to an analysis of the main effects? Justify your answer. If you should, please indicate all the relevant null hypotheses and your conclusions.
In the context of a Two Factor ANOVA, should you proceed to an analysis of the main effects? Justify your answer. If you should, please indicate all the relevant null hypotheses and your conclusions.
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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In the context of a Two Factor ANOVA, should you proceed to an analysis of the main effects? Justify your answer. If you should, please indicate all the relevant null hypotheses and your conclusions.
Transcribed Image Text:### Line Graph Analysis
#### Graph Description
The graph displays two lines, labeled D and E, that represent different sets of data across three categories: A, B, and C.
- **Line D (Blue):**
- Category A: Value 6
- Category B: Value 7
- Category C: Value 7
- **Line E (Orange):**
- Category A: Value 2
- Category B: Value 3
- Category C: Value 4
Both lines show an increasing trend, with Line D having consistently higher values than Line E across all categories.
### ANOVA Table
The table presents the results of an ANOVA (Analysis of Variance) test, detailing the different sources of variance, their sum of squares (SS), degrees of freedom (df), mean square (MS), F-statistic (F), p-value, and critical F-value (F crit).
#### ANOVA Table Explanation
- **Sources of Variation:**
- **Sample:**
- SS = 72
- df = 1
- MS = 72
- F = 76.23529
- p-value = 1.52E-06
- F crit = 4.747225
- **Columns:**
- SS = 16.77778
- df = 2
- MS = 8.388889
- F = 8.882353
- p-value = 0.004294
- F crit = 3.885294
- **Interaction:**
- SS = 4.333333
- df = 2
- MS = 2.166667
- F = 2.294118
- p-value = 0.143313
- F crit = 3.885294
- **Within (Error):**
- SS = 11.33333
- df = 12
- MS = 0.944444
- **Total:**
- SS = 104.4444
- df = 17
This ANOVA analysis aids in understanding whether there are any statistically significant differences between the means of the different groups (Sample, Columns, Interaction) in the dataset.
- The p-values indicate the probability of observing the data given
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