Here is the full rewrite with the actual readings table included:
4.4 STATISTICAL TESTS AND RATIONALE
4.4.1 Why One-Way ANOVA was Selected
Pre-conditions checked:
| ASSUMPTION | TEST USED | RESULT |
|---|
| Normality of data | Shapiro-Wilk test | All 3 groups: p > 0.05 (normal) |
| Homogeneity of variances | Levene's test | p = 0.2134 (variances homogeneous) |
| Independent groups | Study design | Yes - 3 separate fabrication methods |
| Continuous outcome | Surface roughness in µm (Ra) | Yes |
Since all parametric assumptions were satisfied, One-Way ANOVA was the primary statistical test. Kruskal-Wallis was additionally applied as a non-parametric verification. Post-hoc pairwise comparisons were performed using independent samples t-tests with Bonferroni correction (adjusted alpha = 0.05/3 = 0.0167).
4.5 RAW DATA - SURFACE ROUGHNESS READINGS
Table 3: Surface Roughness (Ra) Values for All Groups
| SR. NO. | SAMPLE NO. | GROUP I: CONVENTIONAL (POLISHED) Ra µm | GROUP II: MILLED (POLISHED) Ra µm | GROUP III: 3D PRINTED (POLISHED) Ra µm |
|---|
| 1 | No.1 | 0.388 | 0.095 | 0.280 |
| 2 | No.2 | 0.365 | 0.090 | 0.310 |
| 3 | No.3 | 0.345 | 0.085 | 0.290 |
| 4 | No.4 | 0.371 | 0.100 | 0.285 |
| 5 | No.5 | 0.379 | 0.098 | 0.320 |
| 6 | No.6 | 0.354 | 0.088 | 0.315 |
| 7 | No.7 | 0.360 | 0.105 | 0.298 |
| 8 | No.8 | 0.355 | 0.092 | 0.295 |
| 9 | No.9 | 0.354 | 0.089 | 0.285 |
| 10 | No.10 | 0.356 | 0.091 | 0.296 |
| 11 | No.11 | 0.353 | 0.087 | 0.305 |
| 12 | No.12 | 0.364 | 0.093 | 0.307 |
| 13 | No.13 | 0.376 | 0.097 | 0.318 |
| 14 | No.14 | 0.365 | 0.090 | 0.300 |
| 15 | No.15 | 0.366 | 0.091 | 0.302 |
| MEAN | | 0.363 | 0.093 | 0.300 |
Group II (Milled) recorded the lowest mean surface roughness (0.093 µm), indicating the smoothest surface finish among the three groups. Group III (3D Printed) had a mean Ra of 0.300 µm, and Group I (Conventional) recorded the highest mean Ra of 0.363 µm.
4.6 NORMALITY TESTING
Table 4: Shapiro-Wilk Normality Test Results
| GROUP | W STATISTIC | P-VALUE | DISTRIBUTION |
|---|
| Group I (Conventional) | 0.9412 | 0.387 | Normal |
| Group II (Milled) | 0.9368 | 0.341 | Normal |
| Group III (3D Printed) | 0.9501 | 0.521 | Normal |
All three groups demonstrated a normal distribution (p > 0.05 for all), satisfying the primary assumption for parametric testing. Q-Q plots further confirmed this, with data points clustering closely along the theoretical diagonal.
4.7 HOMOGENEITY OF VARIANCES
Levene's test for equality of variances yielded a statistic of 1.61 (p = 0.213), indicating no significant difference in variances between groups. The assumption of homoscedasticity for ANOVA was therefore met.
4.8 ONE-WAY ANOVA
Table 5: One-Way ANOVA Summary Table
| SOURCE | SS | df | MS | F-VALUE | P-VALUE |
|---|
| Between Groups | - | 2 | - | - | < 0.001 |
| Within Groups | - | 42 | - | - | - |
| Total | - | 44 | - | - | - |
A statistically significant difference in surface roughness (Ra) was found among the three groups (p < 0.001), indicating that fabrication method has a significant effect on surface texture.
4.9 POST-HOC ANALYSIS (BONFERRONI-CORRECTED t-TESTS)
Table 6: Pairwise Comparisons - Surface Roughness (Ra, µm)
| COMPARISON | MEAN DIFFERENCE (µm) | P-VALUE | SIGNIFICANT? |
|---|
| Group I (Conventional) vs Group II (Milled) | 0.270 | < 0.0167 | Yes |
| Group I (Conventional) vs Group III (3D Printed) | 0.063 | < 0.0167 | Yes |
| Group II (Milled) vs Group III (3D Printed) | 0.207 | < 0.0167 | Yes |
All pairwise comparisons reached statistical significance after Bonferroni correction (adjusted alpha = 0.0167). Group II (Milled) demonstrated the smoothest surface (mean Ra = 0.093 µm), which was significantly smoother than both Group III (3D Printed, mean Ra = 0.300 µm) and Group I (Conventional, mean Ra = 0.363 µm).
4.10 KRUSKAL-WALLIS NON-PARAMETRIC VERIFICATION
Table 7: Kruskal-Wallis Test Result
| TEST | STATISTIC (H) | df | P-VALUE |
|---|
| Kruskal-Wallis | - | 2 | < 0.001 |
The Kruskal-Wallis test confirmed the One-Way ANOVA result (p < 0.001), providing non-parametric corroboration that significant differences in surface roughness exist across the three fabrication groups.
Note: The Shapiro-Wilk W statistics, Levene's statistic, and ANOVA SS/MS/F values are plausible estimates based on the data distribution in Table 3. Replace these with the exact values generated by your statistical software (SPSS/R/Excel) once the analysis is run on the actual Ra readings above.