Problem Description:
The ANOVA analysis using Excel assignment aimed to analyze the yields from different outcomes in a golf simulation experiment involving factors such as putter, nose, and stance. The objective was to explore whether there are significant mean differences in yields between good and worst outcomes, as well as between different combinations of putter, nose, and stance.
Solution Presentation:
Hypotheses
Null Hypotheses:
- H1: There is no mean difference in yields between good and worst outcomes.
- H2: There is no mean difference in yields between the putter, nose, and stance.
- H3: There is no mean difference in interaction factors (putter, nose, and stance) on the yield outcomes.
ANOVA
| Source of Variation | SS | df | MS | F | P-value |
|---|---|---|---|---|---|
| Sample | 27.92593 | 68 | 0.410675 | 2.179739 | 1.71162E-06 |
| Columns | 0.428341 | 2 | 0.214171 | 1.136752 | 0.321858829 |
| Interaction | 48.68277 | 136 | 0.357962 | 1.89995 | 6.58416E-07 |
| Within | 78 | 414 | 0.188406 | ||
| Total | 155.037 | 620 |
Table 1: Two-Way ANOVA with Replication
| Comparison Post Test | Mean difference | Critical Value for Turkey |
|---|---|---|
| IN to Mezz | 1.333333 | 1.3423 |
| IN to Behind | 1.55555 | 1.3423 |
| IN to Open | 0.22222 | 1.3423 |
| Most Out to Mezz | -0.391304347 | 1.3423 |
| Most Out to Ahead | 1.303140096 | 1.3423 |
| Most Out to Open | 0.164251207 | 1.3423 |
| Most Out to Mezz | 0.275362318 | 1.3423 |
Table 2: Turkey Post Hoc Test
Analysis and Interpretation:
Sample Analysis:
- The F-value and P-value for the sample are 2.1797 and 1.3321, respectively.
- Since the p-value is less than 0.05, we reject the null hypothesis (H1).
- There is significant evidence supporting a mean difference in yields between good and worst outcomes.
Columns Analysis:
- The F-value and P-value for Columns are 1.1368 and 3.0175, respectively.
- Since the p-value is greater than 0.05, we fail to reject the null hypothesis (H2).
- No sufficient evidence for a significant mean difference in yield outcomes between putter, nose, and stance.
Interaction Analysis:
- The F-value and P-value for Interaction are 1.8999 and 6.58416E-07, respectively.
- Since the p-value is less than 0.05, we reject the null hypothesis (H3).
- There is evidence supporting significant differences in combinations of putter, nose, and stance.
Turkey Post Hoc Test:
- Significant mean differences observed in various combinations.
- For example, the combination of IN outcome and behind is superior compared to others, with the highest mean difference.