Data Analysis and Application to Statistics

Data analysis was conducted using the independent samples t-test technique (which was determined to be the appropriate statistical test) introduced by Gosset (Gosset 1) and subsequently recommended for the comparison of the sample size of two-group means (Jackson 110; Natrella 45). The level of statistical significance was set to .05, following Fisher’s seminal recommendation (Fisher 30).

Maxilla Arch Depth Change

Maxilla arch depth change was calculated as a function of group (12 hours vs. 24-hour). There was no statistically significant difference in maxilla arch depth change, from the initial stage to termination, between the 12-hour group (M = 0.99, SD = 2.63) and the 24-hour group (M = -0.38, SD = 3.19), t(32) = 1.37, p(two-tailed) = 0.18. Figure 1 below illustrates the comparability in maxilla arch change between the two groups:

(Figure 1 omitted for preview. Available via download)

Mandible arch depth change was calculated as a function of group (12 hours vs. 24-hour). There was no statistically significant difference in mandible arch depth change, from the initial stage to termination, between the 12-hour group (M = 1.22, SD = 2.41) and the 24-hour group (M = 1.27, SD = 3.55), t(32) = -0.05, p(two-tailed) = 0.96. Figure 2 below illustrates the comparability in mandible arch change between the two groups:

(Figure 2 omitted for preview. Available via download)

Overjet change was calculated as a function of group (12 hours vs. 24-hour). There was no statistically significant difference in overjet change, from the initial stage to termination, between the 12-hour group (M = -0.68, SD = 1.57) and the 24-hour group (M =

-1.59, SD = 1.94), t(32) = 1.50, p(two-tailed) = 0.14. Figure 3 below illustrates the comparability in overjet change between the two groups.

(Figure 3 omitted for preview. Available via download)

Overbite change was calculated as a function of group (12 hours vs. 24-hour). There was no statistically significant difference in overbite change, from the initial stage to termination, between the 12-hour group (M = -0.96, SD = 1.63) and the 24-hour group (M = -1.49, SD = 1.35), t(32) = 1.03, p(two-tailed) = 0.31. Figure 4 below illustrates the comparability in overbite change between the two groups.

(Figure 4 omitted for preview. Available via download)

Maxilla irregularity index change was calculated as a function of group (12 hours vs. 24-hour). There was no statistically significant difference in maxilla irregularity index change, from the initial stage to termination, between the 12-hour group (M = -5.09, SD = 2.79) and the 24-hour group (M = -4.58, SD = 2.84), t(32) = -0.53, p(two-tailed) = 0.60. Figure 5 below illustrates the comparability in maxilla irregularity index change between the two groups.

(Figure 5 omitted for preview. Available via download)

Mandible irregularity index change was calculated as a function of group (12 hours vs. 24-hour). There was no statistically significant difference in mandible irregularity index change, from the initial stage to termination, between the 12-hour group (M = -3.70, SD = 2.11) and the 24-hour group (M = -3.39, SD = 2.10), t(32) = -0.43, p(two-tailed) = 0.67. Figure 5 below illustrates the comparability in mandible irregularity index change between the two groups.

(Figure 6 omitted for preview. Available via download)

Maxilla intercanine width change was calculated as a function of group (12 hours vs. 24-hour). There was a statistically significant difference in maxilla intercanine width change, from the initial stage to termination, between the 12-hour group (M = 0.61, SD = 1.43) and the 24-hour group (M = -0.62, SD = 1.76), t(32) = 2.24, p(one-tailed) = 0.02. Figure 6 below illustrates that maxilla intercanine width change was lower for the 24-hour group.

(Figure 6 omitted for preview. Available via download)

The effect size, measured by Cohen’s d, of the difference in means, was 0.77, which, according to Cohen (Cohen 200) is a moderate difference.

Mandible intercanine width change was calculated as a function of group (12 hours vs. 24-hour). There was no statistically significant difference in mandible intercanine width change, from the initial stage to termination, between the 12-hour group (M = 0.98, SD = 1.85) and the 24-hour group (M = 0.39, SD = 1.85), t(32) = 0.93, p(two-tailed) = 0.36. Figure 7 below illustrates the comparability in mandible intercanine width change between the two groups.

(Figure 7 omitted for preview. Available via download)

Maxilla intermolar width change was calculated as a function of group (12 hours vs. 24-hour). There was a statistically significant difference in maxilla intermolar width change, from the initial stage to termination, between the 12-hour group (M = 0.75, SD = 1.13) and the 24-hour group (M = -0.06, SD = 1.48), t(32) = 1.79, p(one-tailed) = 0.04. Figure 8 below illustrates that maxilla intermolar width change was lower for the 24-hour group.

(Figure 8 omitted for preview. Available via download)

The effect size, measured by Cohen’s d, of the difference in means, was 0.61, which, according to Cohen (Cohen 200) is a moderate difference.

Maxilla intermolar width change was calculated as a function of group (12 hours vs. 24-hour).

(Figure 9 omitted for preview. Available via download)

There was no statistically significant difference in maxilla intermolar width change, from the initial stage to termination, between the 12-hour group (M = 0.92, SD = 1.11) and the 24-hour group (M = 0.90, SD = 1.45), t(32) = 0.04, p(two-tailed) = 0.97. Figure 9 above illustrates the comparability in maxilla intermolar width change between the two groups.

SNA change was calculated as a function of group (12 hours vs. 24-hour). There was no statistically significant difference in SNA change, from the initial stage to termination, between the 12-hour group (M = -2.13, SD = 2.52) and the 24-hour group (M = -0.89, SD = 2.86), t(32) = -1.34, p(two-tailed) = 0.19. Figure 10 below illustrates the comparability in SNA change between the two groups.

(Figure 10 omitted for preview. Available via download)

SNB change was calculated as a function of group (12 hours vs. 24-hour). There was no statistically significant difference in SNB change, from the initial stage to termination, between the 12-hour group (M = -0.96, SD = 2.80) and the 24-hour group (M = 0.60, SD = 2.64), t(32) =

-1.67, p(two-tailed) = 0.10. Figure 11 below illustrates the comparability in SNB change between the two groups.

(Figure 11 omitted for preview. Available via download)

ANB change was calculated as a function of group (12 hours vs. 24-hour). There was no statistically significant difference in ANB change, from the initial stage to termination, between the 12-hour group (M = -1.19, SD = 1.77) and the 24-hour group (M = -1.50, SD = 1.23), t(32) = 0.58, p(two-tailed) = 0.56. Figure 12 below illustrates the comparability in ANB change between the two groups.

(Figure 12 omitted for preview. Available via download)

MPA change was calculated as a function of group (12 hours vs. 24-hour). There was a statistically significant difference in MPA change, from the initial stage to termination, between the 12-hour group (M = 1.12, SD = 3.03) and the 24-hour group (M = -1.14, SD = 2.92), t(32) = 2.22, p(one-tailed) = 0.02. Figure 13 below illustrates that MPA change was lower for the 24-hour group.

(Figure 13 omitted for preview. Available via download)

The effect size, measured by Cohen’s d, of the difference in means, was 0.76, which, according to Cohen (Cohen 200) is a moderate difference.

U1SN change was calculated as a function of group (12 hours vs. 24-hour). There was no statistically significant difference in U1SN change, from the initial stage to termination, between the 12-hour group (M = 5.28, SD = 7.08) and the 24-hour group (M = 1.31, SD = 8.06), t(32) = 1.53, p(two-tailed) = 0.14. Figure 14 below illustrates the comparability in U1SN change between the two groups.

(Figure 14 omitted for preview. Available via download)

IMPA change was calculated as a function of group (12 hours vs. 24-hour). There was no statistically significant difference in IMPA change, from the initial stage to termination, between the 12-hour group (M = 5.52, SD = 7.70) and the 24-hour group (M = 4.72, SD = 6.24), t(32) = 0.33, p(two-tailed) = 0.74. Figure 15 below illustrates the comparability in IMPA change between the two groups.

(Figure 15 omitted for preview. Available via download)

Non-Parametric Tests

The Wilcoxon sign-rank test (Wilcoxon 80) was carried out in order to triangulate the results of the three statistically significant independent samples t-tests carried out for the study.

First, for the finding that that there was a statistically significant difference in maxilla intercanine width change, from the initial stage to termination, between the 12-hour group (M = 0.61, SD = 1.43) and the 24-hour group (M = -0.62, SD = 1.76), t(32) = 2.24, p(one-tailed) = 0.02, the results were confirmed by a Wilcoxon sign-rank test, z = 2.36, p = .02. Therefore, this difference appears to be robust.

Second, for the finding that there was a statistically significant difference in maxilla intermolar width change, from the initial stage to termination, between the 12-hour group (M = 0.75, SD = 1.13) and the 24-hour group (M = -0.06, SD = 1.48), t(32) = 1.79, p(one-tailed) = 0.04, the results were not confirmed by a Wilcoxon sign-rank test, z = 1.41, p = .16. Therefore, this difference might not be robust.

Third, for the finding that there was a statistically difference in MPA change, from the initial stage to termination, between the 12-hour group (M = 1.12, SD = 3.03) and the 24-hour group (M = -1.14, SD = 2.92), t(32) = 2.22, p(one-tailed) = 0.02, the results were not confirmed by a Wilcoxon sign-rank test, z = 1.95, p = .05. Therefore, this difference might not be robust.

Discussion and Conclusion

Most of the independent samples t-tests carried out in the data analysis did not identify a statistically significant difference, at p < .05, between the 12-hour and 24-hour groups. However, there were some outcomes for which a statistically significant difference was identified. Particular attention should be called to these three findings, which can add to what Littlewood has identified (Littlewood 229) as a gap in evidence-based analysis of retention approaches and regimes.

First, an independent samples t-test found that there was a statistically significant difference in maxilla intercanine width change, from the initial stage to termination, between the 12-hour group (M = 0.61, SD = 1.43) and the 24-hour group (M = -0.62, SD = 1.76), t(32) = 2.24, p(one-tailed) = 0.02, such that maxilla intercanine width change was lower for the 24-hour group, d = 0.77.

Second, an independent samples t-test found that there was a statistically significant difference in maxilla intermolar width change, from the initial stage to termination, between the 12-hour group (M = 0.75, SD = 1.13) and the 24-hour group (M = -0.06, SD = 1.48), t(32) = 1.79, p(one-tailed) = 0.04, such that maxilla intermolar width change was lower for the 24-hour group, d = 0.61.

Third, an independent samples t-test that there was a statistically difference in MPA change, from the initial stage to termination, between the 12-hour group (M = 1.12, SD = 3.03) and the 24-hour group (M = -1.14, SD = 2.92), t(32) = 2.22, p(one-tailed) = 0.02, such that MPA change was lower for the 24-hour group, d = 0.76.

The identification of these three statistically significant differences between the 12- and 24-hour groups diverge from some previous results. In one analysis of Hawley retainers, Shawesh et al. (Shawesh et al. 165) found no statistically significant difference in outcomes between two retention regimens, with one regimen being part-time and the other regimen being full-time. The identification of differences in MPA change, maxilla intercanine width change, and maxilla intermolar width change in the current study is somewhat at variance with these findings.

In another study (Ramazanzadeh et al. e224), some statistically significant differences between retention regimens were identified. Specifically, these authors found that (a) upper arch length was significantly lower in a Hawley group (which wore Hawley retainers full-time for four months, then transitioned to night only) than in two vacuum-formed retainer (VFR) groups; and (b) the upper irregularity index was greater in the Hawley group than in the other two groups. However, these regimes were time-matched, so differences in better dental health for children cannot necessarily be ascribed to the duration of wear.

Works Cited

Cohen, Jacob. Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge, 2016.

Fisher, R.A. Statistical Methods for Research Workers. Edinburgh, Scotland: Oliver & Boyd, 1925.

Gosset, William Sealy. "The Probable Error of a Mean." Biometrika, vol. 6, no. 1, 1908, pp. 1-25.

Jackson, Sherri. Research Methods and Statistics: A Critical Thinking Approach. New York, NY: Cengage Learning, 2015.

Littlewood, Simon J. "Evidence-Based Retention: Where Are We Now?" Seminars in Orthodontics, vol. 23, no. 2, 2017, pp. 229-36.

Natrella, Mary Gibbons. Experimental Statistics. New York, NY: Courier Corporation, 2013.

Ramazanzadeh, Baratali, et al. "The Retention Characteristics of Hawley and Vacuum-Formed Retainers with Different Retention Protocols." Journal of Clinical and Experimental Dentistry, vol. 10, no. 3, 2018, p. e224.

Shawesh, M., et al. "Hawley Retainers Full-or Part-Time? A Randomized Clinical Trial." The European Journal of Orthodontics, vol. 32, no. 2, 2009, pp. 165-70.

Wilcoxon, Frank. "Individual Comparisons by Ranking Methods." Biometrics Bulletin, vol. 1, no. 6, 1945, pp. 80-83.

(Appendix A omitted for preview. Available via download)