Rugosity
AI
1 Synopsis
There were 64 acrylate plates, made from 4 different mateial (16 each). Half of them were polished with a micromotor and the other half with a horizontal motor. For each on them we measured and averaged 3 rugosity values before and after polishing. We found that after polishing, both motors reduced the rugosity with an overall averge of 0.32 (p<0.001), with no statistically signficant difference between motors.
2 Methods
Because the values were right-skewed, we applied two different transformations to all average rugosity values. The base 2 log transformation maps differences as ratios (for example a plate with rugosity 3 is twice as rugous as a plate with rugosity 2). The inverse transformation maps each rugosity value to its coresponding ‘smoothness’.
We applied a repeated-measurements ANOVA model amd used least-square means to calcluate p-values for post-hoc comparrisons between the two types of motors, separately at both time points.
With both raw and transformed data, I performed the same analisys procedures. All statistical methods applied were robust to asymetrical distributions and yielded very similar results.
All analyses were performed using R 3.6.0. The code is availabe online at … .
3 Results
The measurements that were averaged to obtain the initial and final rugosity values had high intraclass correlation coefficients (initial: ICC3=0.677, p<0.001, final: ICC3=0.657, p<0.001).
Summary statistics for all transformations are calculated in tables below.
Regardless of motor, we noticed a statistically signifficant reduction in average rugosity of 0.318 (0.242 to 0.394, p<0.001). Before polishing, average rugosity values ranged from 0.53 to 3.73, with an averge (SD) of 1.17 (0.63) and no significant difference between plates that would be polished with the respective motors (p=0.787, post-hoc comparison of least-squares means). After polishing, average rugosity values ranged from 0.39 to 2.61, with an averge (SD) of 0.85 (0.43) and no significant difference between plates that would be polished with the respective motors (p=0.732, post-hoc comparison of least-squares means).
The intercept row is shown only for completness but it will not take part in any dicussion. The 3 models performed similarly. No sphericity correction was necessary for any of the models. The main result from this table is that there is a significant difference in rugosity after treatment but both motors ere similar. The interaction is not sigificat, therefore motors were similar at both measurements.
Interpret Eta² as for R². A rule of thumb (Cohen):
0.01 -> small; 0.06 -> medium; >0.14 -> large;
Table 1: Two Repeated measures ANOVA models: linear, with raw data and log, with log-transformed data.
Transformation: | None (Raw rugosity): | Log base 2: | Inv ('Smoothness'): | ||||||
Effect | F (DF) | Partial Eta² | p-value | F (DF) | Partial Eta² | p-value | F (DF) | Partial Eta² | p-value |
(Intercept) | F(1, 56) = 482.16 | 0.90 | <0.001 | F(1, 56) = 9.64 | 0.15 | 0.003 | F(1, 56) = 1 121.16 | 0.95 | <0.001 |
Motor | F(1, 56) = 0.21 | <0.01 | 0.650 | F(1, 56) = 0.08 | <0.01 | 0.773 | F(1, 56) = 1.10 | 0.02 | 0.299 |
Material | F(3, 56) = 19.81 | 0.51 | <0.001 | F(3, 56) = 24.87 | 0.57 | <0.001 | F(3, 56) = 21.12 | 0.53 | <0.001 |
Measurement | F(1, 56) = 96.03 | 0.63 | <0.001 | F(1, 56) = 162.75 | 0.74 | <0.001 | F(1, 56) = 160.53 | 0.74 | <0.001 |
Motor:Material | F(3, 56) = 3.18 | 0.15 | 0.031 | F(3, 56) = 5.66 | 0.23 | 0.002 | F(3, 56) = 6.99 | 0.27 | <0.001 |
Motor:Measurement | F(1, 56) = 0.02 | <0.01 | 0.879 | F(1, 56) = 0.77 | 0.01 | 0.385 | F(1, 56) = 4.12 | 0.07 | 0.047 |
Material:Measurement | F(3, 56) = 8.76 | 0.32 | <0.001 | F(3, 56) = 4.75 | 0.20 | 0.005 | F(3, 56) = 6.45 | 0.26 | <0.001 |
Motor:Material:Measurement | F(3, 56) = 1.44 | 0.07 | 0.240 | F(3, 56) = 3.05 | 0.14 | 0.036 | F(3, 56) = 4.59 | 0.20 | 0.006 |
The next tables are just different arrangemements of the same averages. We provided
- regular means (with SDs) best used in combination with untransformed data models,
- geometric means (with geometric SDs) best used in combination with log-transformed data models,
- regular means (with SDs) for inverted data (smoothness) models,
- medians (with ranges) for completness; no nonparametric model was computed.
The first one emphasizes the differences of the motors separately for both initial (baseline) and final measurements. The second one emphasized the differences from baseline to final measurements separately for both motors. P-values were computed using post-hoc tests on least-square estimated marginal means.
Table 2: Average rugosity values for each type of motors, at both initial and final measurements. We privided regular means and SDs (with p-values from the raw data model), geometric means and SDs (with p-values from the log-transfomed data model) and medians with ranges.
Motor | Mean (SD) | Geometric mean | Smoothness | Median (Range) |
Material: Castapress | ||||
Measurement: Initial | ||||
micromotor | 2.07 (0.91) | 1.93 (1.46) | 0.55 (0.17) | 1.68 (1.37, 3.73) |
horizontal motor | 1.76 (0.57) | 1.68 (1.38) | 0.62 (0.20) | 1.69 (1.00, 2.76) |
p-value: | 0.067 | 0.135 | 0.343 | |
Measurement: Final | ||||
micromotor | 1.50 (0.71) | 1.38 (1.53) | 0.78 (0.28) | 1.13 (0.89, 2.61) |
horizontal motor | 1.14 (0.28) | 1.11 (1.29) | 0.93 (0.23) | 1.12 (0.75, 1.62) |
p-value: | 0.117 | 0.341 | 0.629 | |
Material: Rapid Simpl | ||||
Measurement: Initial | ||||
micromotor | 1.01 (0.46) | 0.92 (1.56) | 1.17 (0.47) | 0.86 (0.56, 1.75) |
horizontal motor | 0.80 (0.25) | 0.77 (1.32) | 1.34 (0.33) | 0.69 (0.57, 1.32) |
p-value: | 0.371 | 0.171 | 0.130 | |
Measurement: Final | ||||
micromotor | 0.82 (0.32) | 0.77 (1.46) | 1.38 (0.49) | 0.80 (0.51, 1.44) |
horizontal motor | 0.65 (0.15) | 0.63 (1.24) | 1.61 (0.32) | 0.60 (0.50, 0.95) |
p-value: | 0.292 | 0.217 | 0.296 | |
Material: Superacryl Plus | ||||
Measurement: Initial | ||||
micromotor | 0.99 (0.20) | 0.97 (1.23) | 1.05 (0.21) | 0.98 (0.74, 1.29) |
horizontal motor | 0.82 (0.20) | 0.80 (1.26) | 1.28 (0.28) | 0.78 (0.63, 1.16) |
p-value: | 0.808 | 0.532 | 0.268 | |
Measurement: Final | ||||
micromotor | 0.58 (0.11) | 0.57 (1.21) | 1.79 (0.34) | 0.55 (0.44, 0.76) |
horizontal motor | 0.63 (0.07) | 0.62 (1.11) | 1.61 (0.18) | 0.64 (0.52, 0.73) |
p-value: | 0.394 | 0.189 | 0.148 | |
Material: VillacrylH | ||||
Measurement: Initial | ||||
micromotor | 0.69 (0.10) | 0.69 (1.17) | 1.47 (0.23) | 0.68 (0.53, 0.82) |
horizontal motor | 1.19 (0.38) | 1.14 (1.37) | 0.92 (0.28) | 1.13 (0.78, 1.75) |
p-value: | 0.082 | 0.001 | <0.001 | |
Measurement: Final | ||||
micromotor | 0.57 (0.14) | 0.55 (1.28) | 1.86 (0.45) | 0.53 (0.39, 0.78) |
horizontal motor | 0.91 (0.17) | 0.90 (1.20) | 1.13 (0.20) | 0.88 (0.74, 1.14) |
p-value: | 0.013 | <0.001 | <0.001 | |
P-values are computed from the raw data model for the means and from log-transformed data model for the geometric means. | ||||
The only material for which we found significant differences between motors was VillacrylIH. With the raw data model, the difference of 0.5 was not significant (p = 0.082) at the initial measurement but the difference of 0.34 was statistically significant (p=0.013). However, with the other models (log-trasformed and inverse), at both time points, the motors were statistially different (all p <0.001).
Figure 2: Average rugosity distributions, at both measurements, with both motors (white diamonds: geometric means, black diamonds: regular means).
The basic box-plots show only the medians (vertical lines), IQR (boxes), outlier-free range and eventual outliers. Additionally, I added white diamonds for geometric means and black diamonds for regular means. The chart shows that both motors dicrease rugosity by the same amount.
3.1 Only VillacrylIH
Table 1: Two Repeated measures ANOVA models: linear, with raw data and log, with log-transformed data.
Transformation: | None (Raw rugosity): | Log base 2: | Inv ('Smoothness'): | ||||||
Effect | F (DF) | Partial Eta² | p-value | F (DF) | Partial Eta² | p-value | F (DF) | Partial Eta² | p-value |
(Intercept) | F(1, 14) = 262.10 | 0.95 | <0.001 | F(1, 14) = 18.19 | 0.57 | <0.001 | F(1, 14) = 345.26 | 0.96 | <0.001 |
Motor | F(1, 14) = 16.34 | 0.54 | 0.001 | F(1, 14) = 19.87 | 0.59 | <0.001 | F(1, 14) = 19.73 | 0.58 | <0.001 |
Measurement | F(1, 14) = 24.06 | 0.63 | <0.001 | F(1, 14) = 39.59 | 0.74 | <0.001 | F(1, 14) = 34.51 | 0.71 | <0.001 |
Motor:Measurement | F(1, 14) = 3.37 | 0.19 | 0.088 | F(1, 14) = 0.06 | <0.01 | 0.807 | F(1, 14) = 3.02 | 0.18 | 0.104 |
Table 3: Average rugosity values for each type of motors, at both initial and final measurements. We privided regular means and SDs (with p-values from the raw data model), geometric means and SDs (with p-values from the log-transfomed data model) and medians with ranges.
Motor | Measurement | Mean (SD) | Geometric mean | Smoothness | Median (Range) |
micromotor | 0.63 (0.14) | 0.62 (1.26) | 1.67 (0.40) | 0.65 (0.39, 0.82) | |
Final | 0.57 (0.14) | 0.55 (1.28) | 1.86 (0.45) | 0.53 (0.39, 0.78) | |
Initial | 0.69 (0.10) | 0.69 (1.17) | 1.47 (0.23) | 0.68 (0.53, 0.82) | |
p-value: | 0.048 | <0.001 | <0.001 | ||
horizontal motor | 1.05 (0.32) | 1.01 (1.32) | 1.02 (0.26) | 0.98 (0.74, 1.75) | |
Final | 0.91 (0.17) | 0.90 (1.20) | 1.13 (0.20) | 0.88 (0.74, 1.14) | |
Initial | 1.19 (0.38) | 1.14 (1.37) | 0.92 (0.28) | 1.13 (0.78, 1.75) | |
p-value: | <0.001 | <0.001 | 0.011 | ||
P-values are computed from the raw data model for the means and from log-transformed data model for the geometric means. | |||||
4 Refs
- R Core Team (2019). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.