First, an exploratory and descriptive study of 8 quantitative variables was carried out at 3 different times: (a) control measurement: n=74, (b) measurement of patients at the beginning of treatment: n=98 and (c) measurement of the same patients during treatment: n=98.
The variables were tested for normal statistical distribution using skewness and Kurtosis indices as well as the Kolmogorov–Smirnov (KS) goodness-of-fit test. Additionally, a normal Q-Q plot was used as a visual indicator of fit.
The results of this exploration are summarized in Table 1. The following observations were made:
- In the control measurement, almost all variables collected on the number of particles of different sizes are normally distributed (p>.05 in the KS test). Likewise, the relative humidity tends towards normality. Only two variables – particles>10µ and ambient temperature – have significant deviations (p<.01) although their Q-Q plots reveal that they are quite small in distance to the normal model.
- During the initial measurement of the patient group, some asymmetries were seen in the particle size; nevertheless, the deviations according to the KS goodness-of-fit test, although significant (p<.05), are slight and therefore tolerable. Only for the 2.5-micron particle size variable, the deviation is highly significant (p<.01), and the Q-Q graph confirms this lack of statistical normality.
- In the measurements taken during orthodontic treatment, in most of the variables, deviations do not reach statistical significance (p>.05) in the KS test, which allows us to accept their normality. Only for relative humidity, a significant deviation (p<.01), confirmed by its Q-Q graph, prevents us from accepting that it follows the Gaussian normal model.
Therefore, most of the variables obtained are normally distributed or clearly tend to statistical normality. Owing to this statistical normality, parametric tests were chosen.
Second, we proceeded to carry out a study using classical descriptive statistics for this whole set of variables (see table 2).
Owing to the tendency of most of the variables towards normality, parametric tests – 1-factor ANOVA – were used, except in the assumptions of non-normality, where the results provided by the parametric tests were checked against their non-parametric alternative – the Mann–Whitey or Wilcoxon test. Statistical significance was present in all the results.
Table 3 shows the comparison of the variables studied at the control time with those studied at the "start of treatment" time. The main findings were that the number of particles, of any size, is much higher in the initial situation than in the control group (p<.001). There were also significant differences (p<.01) in both the ambient temperature and relative humidity, which increased with respect to the control measurement.
It has been found (table 4) that there are highly significant differences (p<.001) in the number of particles, of any of the sizes, which are equivalent to effect size again very large and higher than the previous ones (50.0%-57.6%). Since the average values are clearly higher in the end-of-treatment situation, it can be stated that there is a very strong statistical evidence to affirm that at the end of the treatment the number of particles of any size is much higher with respect to the control measurement. At the same time, it is observed that there is also an increase in temperature (p<.001; large effect: 17.5%), as well as a significant (p<.05 effect3,7%) but smaller incerease in RH.
Finally, when comparing the average values of the measurements taken at the end of the session with those at the beginning (table 5), highly significant differences (p<.001) are still found in all the variables, with the values always being higher at the end; except in HR where they are equal or lower. The effect size expressing the magnitude of the changes is much higher in the smallest particles variable (56.8%) compared to the effects of the rest of the variables (<30%) although always being large or very large effects (between 17.7% and 29.1%). Consequently, we have very solid statistical evidence to be able to affirm that the number of particles increases at the end of the session with respect to the beginning; especially of the smallest ones (<0.3µ). Likewise, we have sufficient evidence to affirm that the temperature increases (p<.001; effect of 28.8%) and that the RH. is reduced (p<.001 and effect of 26.7%).
If we compare the time of treatment with the control (Table 6), we find highly significant differences (p<.001) in the number of particles, of any size, that are equivalent to the effect size, again very large and higher than the previous ones. Therefore, we can state that during the treatment, the number of particles of any size is much higher than that during the control measurement. Temperature increased greatly from the time of control to the time of treatment and relative humidity increased at a lower rate than that existed before.
On comparing the baseline group and the treatment group, we found that particles of all sizes increase significantly while relative humidity remains the same or decreases and the temperature increases. The variations among the smallest particles (0.3 micron) are especially significant. (Graph 1)
To test the correlation between relative humidity and particle size, statistical modelling with General Model Regression Equations was used. The degree of fit of the data to predictive models was checked with the following relationships: linear, quadratic, cubic, logarithmic, inverse, potential and exponential.
Table 6 contains the results of the prediction of the number of particles of different sizes measured in the AR situation from the current relative humidity value in the room. These results, first of all, constitute a significantly strong statistical proof of the direct relationship between relative humidity and the number of particles, i.e., the higher the relative humidity in a room, the more the number of particles. This relationship is not linear but potentially of the type Y=Xb±ε. In the models presented, the degree of adjustment of this type of mathematical model to the empirical data collected in the initial measurement situation appears significant (always above 97% and even above 99%). From particle size of 5 microns onwards, the smaller the particle size, the better the fit, with best fit at the smallest particle size of 0.3 and 0.5 micron. The potential coefficients (b) of these models decrease in value as the particle size increases, while the margin of error increases.
The results of the same study carried out with the variables collected from BR are presented in table 7. As can be seen, despite the significant variations between the two measurement situations, the results are comparable. In other words, a potentially direct relationship between the relative humidity of the room and the number of particles observed is maintained. Both values of the coefficients and the standard errors of each of the models are comparable to those obtained in AR.
Having shown that there is an increase in the number of particles during the treatment with respect to the number that existed during initial measurement, we proceeded to determine the relationship between relative humidity and this trend. To this end, a variable was generated that expresses the magnitude of the difference in the values of the change in the number of particles of each size. Subsequently, the relationship of these differential variables with relative humidity, both in AR and BR, was studied. The best fitting model is the linear model, with direct correlation, i.e., a higher value of relative humidity corresponds to a greater differential increase (BR-AR) between the number of particles. The fits of these models are significantly lower than those found in the previous models but still maintain their high significance, especially for smaller particle sizes.