There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Selective Laser Melting (SLM) is a particular rapid prototyping, 3D printing, or Additive Manufacturing (AM) technique designed to use high power-density laser to melt and fuse metallic powders. A component is built by selectively melting and fusing powders within and between layers. The SLM technique is also commonly known as direct selective laser sintering, LaserCusing, and direct metal laser sintering, and this technique has been proven to produce near net-shape parts up to 99.9% relative density. This enables the process to build near full density functional parts and has viable economic benefits. Recent developments of fibre optics and high-power laser have also enabled SLM to process different metallic materials, such as copper, aluminium, and tungsten. Similarly, this has also opened up research opportunities in SLM of ceramic and composite materials. The review presents the SLM process and some of the common physical phenomena associated with this AM technology. It then focuses on the following a...

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Review of selective laser melting : materials and applications

Despite its relatively recent emergence over the past few decades, oral health-related quality of life (OHRQoL) has important implications for the clinical practice of dentistry and dental research. OHRQoL is a multidimensional construct that includes a subjective evaluation of the individual's oral health, functional well-being, emotional well-being, expectations and satisfaction with care, and sense of self. It has wide-reaching applications in survey and clinical research. OHRQoL is an integral part of general health and well-being. In fact, it is recognized by the World Health Organization (WHO) as an important segment of the Global Oral Health Program (2003). This paper identifies the what, why, and how of OHRQoL and presents an oral health theoretical model. The relevance of OHRQoL for dental practitioners and patients in community-based dental practices is presented. Implications for health policy and related oral health disparities are also discussed. A supplemental Appendix contains a Medline and ProQuest literature search regarding OHRQoL research from 1990-2010 by discipline and research design (e.g., descriptive, longitudinal, clinical trial, etc.). The search identified 300 articles with a notable surge in OHRQoL research in pediatrics and orthodontics in recent years.

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Oral Health-related Quality of Life: What, Why, How, and Future Implications

https://onlinelibrary.wiley.com/doi/pdf/10.1002/jor.23075

Laser and electron-beam powder-bed additive manufacturing of metallic implants: A review on processes, materials and designs.

Descriptive statistics are an important part of biomedical research which is used to describe the basic features of the data in the study. They provide simple summaries about the sample and the measures. Measures of the central tendency and dispersion are used to describe the quantitative data. For the continuous data, test of the normality is an important step for deciding the measures of central tendency and statistical methods for data analysis. When our data follow normal distribution, parametric tests otherwise nonparametric methods are used to compare the groups. There are different methods used to test the normality of data, including numerical and visual methods, and each method has its own advantages and disadvantages. In the present study, we have discussed the summary measures and methods used to test the normality of the data.

Descriptive statistics and normality tests for statistical data

As discussed in the previous statistical notes, although many statistical methods have been proposed to test normality of data in various ways, there is no current gold standard method. The eyeball test may be useful for medium to large sized (e.g., n > 50) samples, however may not useful for small samples. The formal normality tests including Shapiro-Wilk test and Kolmogorov-Smirnov test may be used from small to medium sized samples (e.g., n < 300), but may be unreliable for large samples. Moreover we may be confused because ‘eyeball test’ and ‘formal normality test’ may show incompatible results for the same data. To resolve the problem, another method of assessing normality using skewness and kurtosis of the distribution may be used, which may be relatively correct in both small samples and large samples. 1) Skewness and kurtosis Skewness is a measure of the asymmetry and kurtosis is a measure of ’peakedness’ of a distribution. Most statistical packages give you values of skewness and kurtosis as well as their standard errors.

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Statistical notes for clinical researchers: assessing normal distribution (2) using skewness and kurtosis

152 This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/ by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Statistical notes for clinical researchers: Chi-squared test and Fisher’s exact test Open lecture on statistics

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Statistical notes for clinical researchers: Chi-squared test and Fisher's exact test

Mean values obtained from different groups with different conditions are frequently compared in clinical studies. For example, two mean bond strengths between tooth surface and resin cement may be compared using the parametric Student's t test when independent groups are subjected to the comparison under the assumptions of normal distribution and equal variances (or standard deviation). In a condition of unequal variances we may apply the Welch's t test as an adaptation of the t test. As the nature and specific shape of distributions are predetermined by the assumption, the t test compares only the locations of the distribution represented by means, which is simple and intuitive. The t statistic is the ratio of mean difference and standard errors of the mean difference.

Even when more than two groups are compared, some researchers erroneously apply the t test by implementing multiple t tests on multiple pairs of means. It is inappropriate because the repetition of the multiple tests may repeatedly add multiple chances of error, which may result in a larger α error level than the pre-set α level. When we try to compare means of three groups, A, B, and C, using the t test, we need to implement 3 pairwise tests, i.e., A vs B, A vs C, and B vs C. Similarly if comparisons are repeated k times in an experiment and the α level 0.05 was set for each comparison, an unacceptably increased total error rate of 1-(0.95)k may be expected for the total comparison procedure in the experiment. For a comparison of more than two group means the one-way analysis of variance (ANOVA) is the appropriate method instead of the t test. As the ANOVA is based on the same assumption with the t test, the interest of ANOVA is on the locations of the distributions represented by means too. Then why is the method comparing several means the 'analysis of variance', rather than 'analysis of means' themselves? It is because that the relative location of the several group means can be more conveniently identified by variance among the group means than comparing many group means directly when number of means are large.

The ANOVA method assesses the relative size of variance among group means (between group variance) compared to the average variance within groups (within group variance). Figure 1 shows two comparative cases which have similar 'between group variances' (the same distance among three group means) but have different 'within group variances'. When the between group variances are the same, mean differences among groups seem more distinct in the distributions with smaller within group variances (a) compared to those with larger within group variances (b). Therefore the ratio of between group variance to within group variance is of the main interest in the ANOVA.



Figure 1

Distributions with the same between group variance. (a) smaller variance within groups; (b) larger variance within groups.



Table 1 displays an artificial data of bond strength according to different resin types and Table 2 shows the result of the one-way ANOVA. The 'SSB' represents the sum of squares between groups which is the variation of group means from the total grand mean, and the mean of squares between groups (MSB) is subsequently obtained by dividing SSB with degrees of freedom. The 'SSW' represents sum of squares within groups which is the sum of squared deviations from the group means and individual observations because the equal variances in all the groups were already assumed. The mean of square within groups (MSW) is subsequently obtained by dividing SSW with degrees of freedom, in the same way. The ratio of MSB and MSW determines the degree of how relatively greater the difference is between group means (between group variance) compared to within group variance. If the ratio is greater than expected by chance we may think not all the group means are the same which means that at least one mean is substantially different. As the result is interpreted about the whole set of groups, it is called as a global or overall test. The ratio of MSB and MSW is known to follow the F distribution. Therefore, to get a statistical conclusion we may compare the F value calculated from the observed data with the critical value at an α error level of 0.05 in the F table.



Table 1

Measurements of bonding strength according to three different types of resin (artificial data)





Table 2

One-way ANOVA table









Larger F value implies that means of the groups are greatly different from each other compared to the variation of the individual observations in each groups. Larger F value than the critical value supports that the differences between group means are larger than what would be expected by chance. In this example the critical F value is 3.23 in the F table when the degrees of freedom of numerator and denominator are 2 and 42 respectively at the α error level 0.05. As the observed F value 8.4 is larger than the critical value, the result in Table 2 may be interpreted as statistically significant difference among the means of the groups at the α error level 0.05. The result suggests to rejection of the null hypothesis that all the group means are the same, and coincidently supports that at least one group mean differs from other group means.

If any significant difference is detected by the 'overall F test' above, we need to examine what specific pair of group means shows difference and what pairs do not. While many different kinds of post-hoc multiple comparison procedures have been proposed, the choice needs to be made according to the specific research question. One basic method is implementing multiple pairwise t tests using the common variance as MSW and appropriately adjusting α error level to get the optimal α error level for the whole experiment. For example, the Bonferroni correction is a simple method that adjusts comparisonwise type α error level as the usual experiment-wise α error level divided by the number of comparisons, e.g., 0.05/k. However, caution is needed because in some situations the Bonferroni correction may be substantially conservative that actual experiment-wise α error level applied may be lower than 0.05. Tukey's HSD, Schaffe method, and Duncan multiple range test are more frequently preferred methods for the multiple comparison procedures. Table 3 displays the analysis results by both the ANOVA and multiple comparison procedure. We usually need to report the p-value of overall F test and the result of the post-hoc multiple comparison. Table 3 shows that 'C' resin has the highest bond strength and 'A' resin shows the lowest.



Table 3

Comparative mean bond strength according to different types of resin (display of ANOVA results)



The comparison of more than two group means by ANOVA using the SPSS statistical package (SPSS Inc., Chicago, Il) according to the following procedures:

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Analysis of variance (ANOVA) comparing means of more than two groups.

PURPOSE. This study aimed to identify the effects of the sintering conditions of dental zirconia on the grain size and translucency. MATERIALS AND METHODS. Ten specimens of each of two commercial brands of zirconia (Lava and KaVo) were made and sintered under five different conditions. Microwave sintering (MS) and conventional sintering (CS) methods were used to fabricate zirconia specimens. The dwelling time was 20 minutes for MS and 20 minutes, 2, 10, and 40 hours for CS. The density and the grain size of the sintered zirconia blocks were measured. Total transmission measurements were taken using a spectrophotometer. Twoway analysis of variance model was used for the analysis and performed at a type-one error rate of 0.05. RESULTS. There was no significant difference in density between brands and sintering conditions. The mean grain size increased according to sintering conditions as follows: MS-20 min, CS-20 min, CS-2 hr, CS-10 hr, and CS-40 hr for both brands. The mean grain size ranged from 347-1,512 nm for Lava and 373-1,481 nm for KaVo. The mean light transmittance values of Lava and KaVo were 28.39-34.48% and 28.09-30.50%, respectively. CONCLUSION. Different sintering conditions resulted in differences in grain size and light transmittance. To obtain more translucent dental zirconia restorations, shorter sintering times should be considered. [J Adv

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Effects of the sintering conditions of dental zirconia ceramics on the grain size and translucency

Various parametric tests make assumptions of the normal distribution, including t-test, analysis of variance (ANOVA), correlation, and regression. Different from some researcher’s understanding, tests of normality are not for the normality of observed data but for normality of the population distribution of a random characteristic; e.g. assuming normality for the population distribution of the characteristic is reasonable when referring to the observed sample data. Actual distribution of the characteristic in a random sample chosen from a population with normal distribution doesn’t appear normal, especially when the sample size is small (Figure 1). Distributions of larger samples tend to resemble the distribution of the characteristic in the population better by taking on a bell-shaped curve when the values of a characteristic in the population are plotted against their frequency. Open lecture on statistics

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Hae Young Kim

Papers

Statistical notes for clinical researchers: assessing normal distribution (2) using skewness and kurtosis

Statistical notes for clinical researchers: Chi-squared test and Fisher's exact test

Analysis of variance (ANOVA) comparing means of more than two groups.

Effects of the sintering conditions of dental zirconia ceramics on the grain size and translucency

Statistical notes for clinical researchers: assessing normal distribution (1).