An overview of statistics for dental research: Prosthodontic perspective

Clinicians often lack knowledge in statistical analysis; however, his/her inputs form a major role in enhancing the quality of research, especially in identifying relevant statistics for the obtained data based on the research objective. The statistician’s expertise in dental research will be limited due to their lack of understanding of clinical and nonclinical trials. An inapposite communication of our requirement and the statistician’s underexposure to our subject will result in skewed results. This editorial intends to provide an overview of statistics for different situations in dental research for the clinicians to have a basic knowledge in statistics for designing their research framework. The basis to perform statistical analysis depends on the research hypothesis, type of data, number of variables, and the test of normality.

A hypothesis is stated as either a null (there is no difference between cause and effect) or an alternate (there exists a difference between cause and effect) hypothesis that plays a vital role in suggesting the P value to choose the correct statistical method as discussed in our previous editorial.

The data collected by conducting research are categorized as, namely, qualitative (nominal or ordinal) and quantitative (interval or ratio).[1]

• Nominal data are categorical and qualitative, which are based on factors such as gender (male/female) and habits (smoking/nonsmoking), and they do not provide any quantitative value

• Ordinal data are also categorical; however, they are in between quantitative and qualitative data (e.g., ranking/grading based on education level and economic status). It could be confused with ratio data

• Interval data are the numerical type that has precise and continuous data (e.g., peri-implant bone loss/resonance frequency analysis (RFA) values at various stages of osseointegration). They can have negative data or positive data but lack a true zero

• Ratio is also numerical data, which ranks data and is continuous (e.g., total number of implant failures). They have a true zero value (e.g., the number of participants presented with crestal bone loss up to 1.5 mm is the representation of ratio data; while measuring a crestal bone loss to find the average bone loss is the representation of an interval data). Unlike the qualitative (nominal and ordinal) data, both the quantitative (interval and ratio) data have equal intervals.

The number of variables in the study also plays a role in the type of statistical analysis. A study with a single variable is the evaluation of therapy at a single point of time, where only one type of data (e.g., measuring crestal bone loss) is collected from several participants. A study with two or more variables can be either a comparison of pre- and postoperative data of therapy or assessing a postoperative effect based on age, sex, and economic level. In the former, there are two variables of pre- and postoperative effect, whereas the latter compares one variable (therapeutic effect) with several variables such as age and sex. With multiple variables, the researcher should know whether the data collected for each variable will be qualitative or quantitative. Even if the data are quantitative, the test of normality suggests the requirement of parametric or nonparametric statistical analysis.

The test of normality is commonly performed by methods such as the Shapiro–Wilk test for a study with small sample size and the Kolmogorov–Smirnov test for a study with a larger sample size. If there is no significant difference (P > 0.05) in either of the above tests, indicate that the data are normally distributed and require a parametric test.[2] However, normality tests such as D’Agostino’s K-squared test, Jarque–Bera test, Anderson–Darling test, Cramér–von Mises criterion, Lilliefors test, and Pearson’s Chi-squared test are available for precise interpretation.

Research may require multiple statistical tests to interpret the obtained data. We would like to make the readers understand better with examples to know the type of statistical analysis of different research objectives [Table 1]. Although this editorial stated with several examples of quantitative data, the analysis should be further confirmed by the test of normality and Shapiro–Wilk/Kolmogorov–Smirnov test, and if P > 0.05, a nonparametric analysis has to be conducted even for a quantitative data.

Table 1.

Statistical tool for data analysis

Number of variables	Type of data in one variable	Type of data in the second variable	Parametric or nonparametric	Statistical analysis
Single variable	Quantitative	-	Parametric	t-test for single mean
Single variable	Qualitative	-	Nonparametric	Chi-square test for goodness of fit
Two variables	Nominal (two groups)	Quantitative	Parametric	Independent sample t-test
Two variables	Nominal (two groups)	Ordinal/quantitative	Nonparametric	Mann–Whitney U-test
Two variables with equal samples	Quantitative	Quantitative	Parametric	Paired sample t-test
Two variables with equal samples	Ordinal/quantitative	Ordinal/quantitative	Nonparametric	Wilcoxon signed-rank test
Multiple variables	Nominal (>2 groups)	Quantitative	Parametric	ANOVA
Multiple variables	Nominal (>2 groups)	Ordinal/quantitative	Nonparametric	Kruskal–Wallis test
Two variables for correlation	Quantitative	Quantitative	Parametric	Pearson correlation coefficient
Two variables for correlation	Quantitative	Qualitative	Nonparametric	Spearman rank correlation
Two variables for association	Qualitative	Qualitative	Nonparametric	Chi-square test

• A research objective with a single variable; recording the RFA values for evaluating the implant stability of several participants during placement to obtain a mean will be considered continuous quantitative data of a single variable. This methodology would require a t-test of a single mean for a parametric analysis

• A research objective with a single variable, but the samples are categorized based on RFA values, such as 1–10 implant stability quotient (ISQ) value as Grade I and 1–20 ISQ value as Grade II, the data obtained are ordinal (qualitative) data (the difference between two grading may not be equal and hence cannot be considered ratio [quantitative] data. The participant with a score of 10 in Grade I and the participant with a score of 11 in Grade II have a difference of only 1 score, whereas within the grade will present with a difference of 9. There is no equal difference between the participants between and within grading and hence will be considered qualitative data.). This objective is also a single-variable study, but with qualitative data that require the Chi-square test for nonparametric analysis

• A research objective with two variables; to find the relation/association between the intercanthal distance and intercanine distance, a correlation analysis should be performed and not a t-test. In this objective, the intercanthal distance (quantitative) and intercanine distance (quantitative) are two independent variables, and the values obtained will be continuous quantitative data, requiring a parametric analysis like Pearson correlation analysis. A similar research objective wherein to find the relationship between the different maxillomandibular relationships (qualitative) and the intercanine distance (quantitative), a combination of qualitative (Class I, II, and III maxillomandibular relations depicting ordinal data) and quantitative (measurement depicting continuous data) data will be obtained. Hence, a nonparametric test like the Spearman rank correlation test will be used. When both variables are qualitative, as in establishing an association between the gender (male/female) and jaw positions (Class I, II, and III), a nonparametric analysis like the Chi-square test of independence should be performed

• A research objective with two variables; evaluating the mean bone loss (quantitative) in the anterior edentulous space based on sex (qualitative), one variable is nominal (male/female), and the second variable is continuous (crestal bone loss in the anterior edentulous space). These two variables are independent of each other, and hence, an unpaired (independent) sample t-test is performed if the data are normally distributed. If the data are not normally distributed, it becomes nonparametric, and a Mann–Whitney U-test should be done

• A research objective with two variables that are dependent on each other would be similar to the pre- and postoperative assessment of crestal bone loss. Both variables of quantitative and are dependent of each other. This should be evaluated by the paired (dependent) t-test for parametric analysis if normality is even, while a Wilcoxon signed-rank test should be used for nonparametric analysis if the normality is unevenly distributed. An example of qualitative dependent variables is the assessment of economic wellness before and after prosthetic rehabilitation

• A research objective may require a comparison within and outside a variable. For example, the assessment of crestal bone loss between different categories of diabetes and within each category of diabetics at different time periods requires the one-way ANOVA for parametric and the Kruskal–Wallis for nonparametric analysis.

These are a few examples of the most common statistical analysis that can be correlated to their own research as shown in Table 1.[3,4] There are more number of statistical methods for systematic reviews and survival analyses. The editorial aimed at enumerating the type of statistical analysis for commonly used research objectives in prosthodontics that could be useful for upcoming researchers. Statistics is a vast subject, and it is mandatory that the researcher undertakes basic training in statistics to coordinate with the statistician for effective interpretation of obtained data.