Selection of Appropriate Statistical Methods for Data Analysis (2024)

Abstract

In biostatistics, for each of the specific situation, statistical methods are available for analysis and interpretation of the data. To select the appropriate statistical method, one need to know the assumption and conditions of the statistical methods, so that proper statistical method can be selected for data analysis. Two main statistical methods are used in data analysis: descriptive statistics, which summarizes data using indexes such as mean and median and another is inferential statistics, which draw conclusions from data using statistical tests such as student's t-test. Selection of appropriate statistical method depends on the following three things: Aim and objective of the study, Type and distribution of the data used, and Nature of the observations (paired/unpaired). All type of statistical methods that are used to compare the means are called parametric while statistical methods used to compare other than means (ex-median/mean ranks/proportions) are called nonparametric methods. In the present article, we have discussed the parametric and non-parametric methods, their assumptions, and how to select appropriate statistical methods for analysis and interpretation of the biomedical data.

Keywords: Diagnostic accuracy, parametric and nonparametric methods, regression analysis, statistical method, survival analysis

Introduction

Selection of appropriate statistical method is very important step in analysis of biomedical data. A wrong selection of the statistical method not only creates some serious problem during the interpretation of the findings but also affects the conclusion of the study. In statistics, for each specific situation, statistical methods are available to analysis and interpretation of the data. To select the appropriate statistical method, one need to know the assumption and conditions of the statistical methods, so that proper statistical method can be selected for data analysis.[1] Other than knowledge of the statistical methods, another very important aspect is nature and type of the data collected and objective of the study because as per objective, corresponding statistical methods are selected which are suitable on given data. Practice of wrong or inappropriate statistical method is a common phenomenon in the published articles in biomedical research. Incorrect statistical methods can be seen in many conditions like use of unpaired t-test on paired data or use of parametric test for the data which does not follow the normal distribution, etc., At present, many statistical software like SPSS, R, Stata, and SAS are available and using these softwares, one can easily perform the statistical analysis but selection of appropriate statistical test is still a difficult task for the biomedical researchers especially those with nonstatistical background.[2] Two main statistical methods are used in data analysis: descriptive statistics, which summarizes data using indexes such as mean, median, standard deviation and another is inferential statistics, which draws conclusions from data using statistical tests such as student's t-test, ANOVA test, etc.[3]

Factors Influencing Selection of Statistical Methods

Selection of appropriate statistical method depends on the following three things: Aim and objective of the study, Type and distribution of the data used, and Nature of the observations (paired/unpaired).

Concept of Parametric and Nonparametric Methods

Inferential statistical methods fall into two possible categorizations: parametric and nonparametric. All type of statistical methods those are used to compare the means are called parametric while statistical methods used to compare other than means (ex-median/mean ranks/proportions) are called nonparametric methods. Parametric tests rely on the assumption that the variable is continuous and follow approximate normally distributed. When data is continuous with non-normal distribution or any other types of data other than continuous variable, nonparametric methods are used. Fortunately, the most frequently used parametric methods have nonparametric counterparts. This can be useful when the assumptions of a parametric test are violated and we can choose the nonparametric alternative as a backup analysis.[3]

Selection between Parametric and Nonparametric Methods

All type of the t-test, F test are considered parametric test. Student's t-test (one sample t-test, independent samples t-test, paired samples t-test) is used to compare the means between two groups while F test (one-way ANOVA, repeated measures ANOVA, etc.) which is the extension of the student's t-test are used to compare the means among three or more groups. Similarly, Pearson correlation coefficient, linear regression is also considered parametric methods, is used to calculate using mean and standard deviation of the data. For above parametric methods, counterpart nonparametric methods are also available. For example, Mann--Whitney U test and Wilcoxon test are used for student's t-test while Kruskal--Wallis H test, median test, and Friedman test are alternative methods of the F test (ANOVA). Similarly, Spearman rank correlation coefficient and log linear regression are used as nonparametric method of the Pearson correlation and linear regression, respectively.[3,5,6,7,8] Parametric and their counterpart nonparametric methods are given in Table 1.

Statistical Methods to Compare the Proportions

The statistical methods used to compare the proportions are considered nonparametric methods and these methods have no alternative parametric methods. Pearson Chi-square test and Fisher exact test is used to compare the proportions between two or more independent groups. To test the change in proportions between two paired groups, McNemar test is used while Cochran Q test is used for the same objective among three or more paired groups. Z test for proportions is used to compare the proportions between two groups for independent as well as dependent groups.[6,7,8] [Table 2].

Other Statistical Methods

Intraclass correlation coefficient is calculated when both pre-post data are in continuous scale. Unweighted and weighted Kappa statistics are used to test the absolute agreement between two methods measured on the same subjects (pre-post) for nominal and ordinal data, respectively. There are some methods those are either semiparametric or nonparametric and these methods, counterpart parametric methods, are not available. Methods are logistic regression analysis, survival analysis, and receiver operating characteristics curve.[9] Logistic regression analysis is used to predict the categorical outcome variable using independent variable(s). Survival analysis is used to calculate the survival time/survival probability, comparison of the survival time between the groups (Kaplan--Meier method) as well as to identify the predictors of the survival time of the subjects/patients (Cox regression analysis). Receiver operating characteristics (ROC) curve is used to calculate area under curve (AUC) and cutoff values for given continuous variable with corresponding diagnostic accuracy using categorical outcome variable. Diagnostic accuracy of the test method is calculated as compared with another method (usually as compared with gold standard method). Sensitivity (proportion of the detected disease cases from the actual disease cases), specificity (proportion of the detected non-disease subjects from the actual non-disease subjects), overall accuracy (proportion of agreement between test and gold standard methods to correctly detect the disease and non-disease subjects) are the key measures used to assess the diagnostic accuracy of the test method. Other measures like false negative rate (1-sensitivity), false-positive rate (1-specificity), likelihood ratio positive (sensitivity/false-positive rate), likelihood ratio negative (false-negative rate/Specificity), positive predictive value (proportion of correctly detected disease cases by the test variable out of total detected disease cases by the itself), and negative predictive value (proportion of correctly detected non-disease subjects by test variable out of total non-disease subjects detected by the itself) are also used to calculate the diagnostic accuracy of the test method.[3,6,10] [Table 3].

Advantage and Disadvantages of Nonparametric Methods over Parametric Methods and Sample Size Issues

Parametric methods are stronger test to detect the difference between the groups as compared with its counterpart nonparametric methods, although due to some strict assumptions, including normality of the data and sample size, we cannot use parametric test in every situation and resultant its alternative nonparametric methods are used. As mean is used to compare parametric method, which is severally affected by the outliers while in nonparametric method, median/mean rank is our representative measures which do not affect from the outliers.[11]

In parametric methods like student's t-test and ANOVA test, significance level is calculated using mean and standard deviation, and to calculate standard deviation in each group, at least two observations are required. If every group did not have at least two observations, its alternative nonparametric method to be selected works through comparisons of the mean ranks of the data.

For small sample size (average ≤15 observations per group), normality testing methods are less sensitive about non-normality and there is chance to detect normality despite having non-normal data. It is recommended that when sample size is small, only on highly normally distributed data, parametric method should be used otherwise corresponding nonparametric methods should be preferred. Similarly on sufficient or large sample size (average >15 observations per group), most of the statistical methods are highly sensitive about non-normality and there is chance to wrongly detect non-normality, despite having normal data. It is recommended that when sample size is sufficient, only on highly non-normal data, nonparametric method should be used otherwise corresponding parametric methods should be preferred.[12]

Impact of Wrong Selection of the Statistical Methods

As for each and every situation, there are specific statistical methods. Failing to select appropriate statistical method, our significance level as well as their conclusion is affected.[13] For example in a study, systolic blood pressure (mean ± SD) of the control (126.45 ± 8.85, n₁=20) and treatment (121.85 ± 5.96, n₂=20) group was compared using Independent samples t-test (correct practice). Result showed that mean difference between two groups was statistically insignificant (P = 0.061) while on the same data, paired samples t-test (incorrect practice) indicated that mean difference was statistically significant (P = 0.011). Due to incorrect practice, we detected the statistically significant difference between the groups although actually difference did not exist.

Conclusions

Selection of the appropriate statistical methods is very important for the quality research. It is important that a researcher knows the basic concepts of the statistical methods used to conduct research study that produce a valid and reliable results. There are various statistical methods that can be used in different situations. Each test makes particular assumptions about the data. These assumptions should be taken into consideration when deciding which the most appropriate test is. Wrong or inappropriate use of statistical methods may lead to defective conclusions, finally would harm the evidence-based practices. Hence, an adequate knowledge of statistics and the appropriate use of statistical tests are important for improving and producing quality biomedical research. However, it is extremely difficult for a biomedical researchers or academician to learn the entire statistical methods. Therefore, at least basic knowledge is very important so that appropriate selection of the statistical methods can decide as well as correct/incorrect practices can be recognized in the published research. There are many softwares available online as well as offline for analyzing the data, although it is fact that which set of statistical tests are appropriate for the given data and study objective is still very difficult for the researchers to understand. Therefore, since planning of the study to data collection, analysis and finally in the review process, proper consultation from statistical experts may be an alternative option and can reduce the burden from the clinicians to go in depth of statistics which required lots of time and effort and ultimately affect their clinical works. These practices not only ensure the correct and appropriate use of the biostatistical methods in the research but also ensure the highest quality of statistical reporting in the research and journals.[14]

Acknowledgements

Authors would like to express their deep and sincere gratitude to Dr. Prabhat Tiwari, Professor, Department of Anaesthesiology, Sanjay Gandhi Postgraduate Institute of Medical Sciences, Lucknow, for his encouragement to write this article. His critical reviews and suggestions were very useful for improvement in the article.

References