3 0 0 0 0 In the study, the percentage of total variability explained by the independent variable is approximately: 95 49 Ⓒ51
3 0 0 0 0 In the study, the percentage of total variability explained by the independent variable is approximately: 95 49 Ⓒ51
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![## Analysis of Variance (ANOVA) in Independent-Measures Experiment
**Table: Raw Data from an Independent-Measures Experiment Comparing Three Different Treatment Conditions.**
| Treatment 1 | Treatment 2 | Treatment 3 |
|-------------|-------------|-------------|
| 0 | 1 | 3 |
| 1 | 4 | 3 |
| 0 | 1 | 4 |
| 3 | 2 | 5 |
| **X̄ = 1** | **X̄ = 2** | **X̄ = 3.75** |
### Evaluating the Effect of the Independent Variable
To evaluate the effect of the independent variable, researchers conducted an independent-measures one-way ANOVA. They computed:
- Sum of squares between groups (SSB) = 15.5
- Sum of squares within groups (SSW) = 14.75
### Calculating the Percentage of Total Variability Explained
In the study, the percentage of total variability explained by the independent variable is approximately:
- ○ 0
- ○ 95
- ○ 49
- ● 51
### Methodology for Calculating Explained Variability
To find the percentage of total variability explained by the independent variable, we use the following formula:
Percentage of Total Variability Explained = (SSB / SST) * 100
Where:
- SST (Total Sum of Squares) = SSB + SSW
- SST = 15.5 + 14.75 = 30.25
Now, calculating the percentage:
\[ \text{Percentage} = \left( \frac{15.5}{30.25} \right) \times 100 \approx 51.24\% \]
Thus, approximately 51% of the total variability is explained by the independent variable in this study.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf10b40a-fae6-4e8b-9b89-0711a68556bc%2F682f6be9-939e-4b67-9987-49d94692bf82%2Fu5nxdvd_processed.png&w=3840&q=75)
Transcribed Image Text:## Analysis of Variance (ANOVA) in Independent-Measures Experiment
**Table: Raw Data from an Independent-Measures Experiment Comparing Three Different Treatment Conditions.**
| Treatment 1 | Treatment 2 | Treatment 3 |
|-------------|-------------|-------------|
| 0 | 1 | 3 |
| 1 | 4 | 3 |
| 0 | 1 | 4 |
| 3 | 2 | 5 |
| **X̄ = 1** | **X̄ = 2** | **X̄ = 3.75** |
### Evaluating the Effect of the Independent Variable
To evaluate the effect of the independent variable, researchers conducted an independent-measures one-way ANOVA. They computed:
- Sum of squares between groups (SSB) = 15.5
- Sum of squares within groups (SSW) = 14.75
### Calculating the Percentage of Total Variability Explained
In the study, the percentage of total variability explained by the independent variable is approximately:
- ○ 0
- ○ 95
- ○ 49
- ● 51
### Methodology for Calculating Explained Variability
To find the percentage of total variability explained by the independent variable, we use the following formula:
Percentage of Total Variability Explained = (SSB / SST) * 100
Where:
- SST (Total Sum of Squares) = SSB + SSW
- SST = 15.5 + 14.75 = 30.25
Now, calculating the percentage:
\[ \text{Percentage} = \left( \frac{15.5}{30.25} \right) \times 100 \approx 51.24\% \]
Thus, approximately 51% of the total variability is explained by the independent variable in this study.
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