Conduct Common Statistical Tests Online

Introduction

Statistics is an inseparable part of biomedical research from the stages of planning to the final publication.[1] For research conducted by an undergraduate or postgraduate medical student, statistics is a fairly new domain to explore. Although a few basic statistical methods are taught in the undergraduate course, their practical application is limited in majority of the institutions. Hence, they seek help from their immediate seniors, mentors, or expert statisticians.[2] Many of the statistical tests can be calculated manually. However, it is time-consuming. The effort is minimized with the use of software packages. Some of these software packages are free and others are paid. Many of the resource-limited settings in developing countries may find difficulty procuring the paid software due to financial constraints. The next option is to use free software packages (e.g., Epi Info) on a personal computer. However, many researchers may not have access to personal computers or have technical difficulty using the software. Hence, we searched for websites that run software on the internet browser and provide free service to the users.

In this article, we aimed to provide a brief technical guide on common statistical tests that can be conducted from any computer connected to the internet.

Selection of Statistical Test

The common statistical test used for numerical data (e.g., the age, height, weight of research participants) is shown in Figure 1 and that for categorical data (e.g., sex [male/female/intersex], presence of disease [yes/no], socioeconomic status [I–V]) is shown in Figure 2.[1,3]

Figure 1.

Example of some common statistical tests for numerical data

Figure 2.

Examples of some common statistical tests for categorical data

Websites for Statistical Tests

Many websites provide multiple statistical tests. Table 1 shows the tests and some of the websites that provide these tests. This would make the readers aware of different websites so that they can make an informed choice for their future statistical tests. Along with the statistical tests listed in [Figures 1 and 2], we included central tendency, frequency distribution and normality test as these are very basic statistics, needed even before the selection of appropriate tests.

Table 1.

Websites to conduct common statistical tests online

Statistics	https://www.statskingdom.com/	https://www.socscistatistics.com/	https://www.graphpad.com/quickcalcs/	https://epitools.ausvet.com.au/	https://astatsa.com/
Central tendency and frequency distribution	√	√	√
Normality test	√	√		√
One-sample t-test	√	√	√	√
One-sample median test	√	√		√
Unpaired t-test	√	√	√	√
Mann-Whitney U test	√	√	√	√
Paired t-test	√	√	√	√
Wilcoxon signed-rank test	√	√		√	√
One-way analysis of variance (ANOVA)	√	√			√
Kruskal-Wallis test	√	√			√
Repeated-measure ANOVA		√
Friedman Test		√			√
Pearson correlation test	√	√			√
Spearman correlation test	√	√			√
Binomial test	√	√
Chi-square test	√	√	√	√
Fisher’s exact test		√	√		√
McNemar test			√	√	√

This list is not a comprehensive list for statistical tests. The range of tests offered by each website may also be missed in this list and websites are dynamic. Readers are encouraged to find more free tools online

Descriptive Statistics

Central tendency and frequency distribution

Central tendency is the most commonly used descriptive statistical test. Invariably, all the research data are expressed as mean, standard deviation, median, interquartile range, mode, and range. Frequency distribution is also used to group the observations into different categories.

Normality test

From Figures 1 and 2, it is obvious how important it is to check the normality of the data set. There is one type of test for normally distributed data and another type of test for not-normally distributed data. Hence, it helps in decision-making about the inferential statistical test to use.[4] If the data are not normally distributed, these are commonly presented as median, quartile, and interquartile range.

Inferential Statistics: Numerical Data

One-sample t-test and median test

When the observations come from a sample and the mean or median of the observations are needed to be compared with a reference value, a one-sample t-test or one-sample median test is used. When the data are normally distributed, the one-sample t-test is used to compare the sample mean with a reference value. When the data are not normally distributed, the one-sample median test is used to compare the sample median with the reference value.

Unpaired t-test and Mann–Whitney U test

When the observations come from two independent samples, either unpaired t-test or Mann–Whitney U test is used to compare the mean or median, respectively. For example, if the mean urticarial activity score is to be compared between male and female research participants, and the data are normally distributed, the unpaired t-test is used. If the data are not normally distributed, the Mann–Whitney U test is used.

Paired t-test and Wilcoxon signed-rank test

When two measurements come from a sample, either paired t-test or Wilcoxon signed-rank test is used. For example, a new treatment regime was applied to a sample and the eosinophil count was measured before and after the treatment. If the data are normally distributed, a paired t-test is used to compare the mean eosinophil count before and after the treatment. If the data are not normally distributed, median eosinophil counts before and after treatments are compared with Wilcoxon signed-rank test.

One-way analysis of variance (ANOVA) and Kruskal–Wallis test

When the observations come from > two samples, the one-way analysis of variance (ANOVA) or Kruskal–Wallis test is used. For example, if the urticarial activity scores among males, females, and the intersex group is to be compared and the data are normally distributed, one-way ANOVA is used to compare the mean. If the data are not normally distributed, the Kruskal–Wallis test is used to compare the median.

If there is a significant difference, it is established that there is a difference among the mean or median of the three groups. However, which pair (e.g., male–female, male–intersex, female–intersex) significantly differ is not revealed from the ANOVA or Kruskal–Wallis test. To know this, a post-hoc test is to be carried out. For ANOVA, Tukey’s honestly significant difference (Tukey’s HSD) is used and for Kruskal–Wallis test, Dunn’s test is used. If Dunn’s test is not available online, a pair-wise Mann–Whitney U test with Bonferroni correction (a = 0.05 will be divided by the number of groups; corrected a = 0.05/3 = 0.0166) can be used to compare between the pairs (e.g., male–female, male–intersex, female–intersex).[5]

Repeated-measure ANOVA and Friedman test

When the observations come from one sample with more than two measurements, repeated-measure ANOVA or Friedman test is used. For example, after the application of a new drug regimen, the eosinophil count was measured after 1^st week, 2^nd week, and 3^rd week of treatment. If the data are normally distributed, repeated-measure ANOVA is used to compare the mean. If the data are not normally distributed, the Friedman test is used to compare the median.

If there is a significant difference, a post hoc test is to be run. For ANOVA, paired t-test with Bonferroni correction is carried out to compare the mean. For the Friedman test, a multiple pair-wise Wilcoxon signed-rank test with Bonferroni correction is used to compare the median.

Pearson’s correlation test and Spearman’s correlation test

When the relationship between two groups needs to be tested, Pearson’s correlation test or Spearman’s correlation test is used. For example, if the relationship between the urticarial activity score and Pittsburgh sleep quality index score is to be tested and if the data are normally distributed, Pearson’s correlation is used and if not normally distributed, Spearman’s correlation test is used. The correlation coefficient spans between –1 and +1.

Inferential Statistics: Categorical Data

Binomial test

When there is one variable with a dichotomous outcome, a binomial test is used. For example, outcome of a treatment regimen as a variable with a dichotomous outcome—success or failure.

Chi-square test and Fisher’s exact test

When there are ≥ two variables and ≥ two samples, the Chi-square test is used. For example, if there were two samples—smoker and non-smoker and two variables—having oral carcinoma and not having carcinoma, a 2 × 2 contingency table can be created to conduct the Chi-square test to find any relationship between smoking and oral cancer. When there are more than 2 columns and rows (e.g., a 4 × 4 contingency table), the Chi-square test should be coupled with a post-hoc 2 × 2 Chi-square test with Bonferroni correction of alpha. If the frequency is less than five, Fisher’s exact test is used instead of the Chi-square test.

McNemar test

When there is one sample and two variables or two matched samples and one variable, the McNemar test is used. For example, a new drug was applied to a sample and two variables were measured—decrease in itching (yes/no) and decrease in eosinophil count (yes/no), then a 2 × 2 contingency table was created with the number of four types of patients—decreased itching + decreased eosinophil, decreased itching + not decreased eosinophil, not decreased itching + decreased eosinophil, not decreased itching + not decreased eosinophil. The result would show if there is a difference in the proportion of participants with decreased itching and eosinophil count after the treatment.[6]

Discussion

We presume that this article would help us to know the basics of biomedical statistics and get an idea of the websites where these tests can be carried out with limited resources.

Although we have listed some of the available websites for the statistical tests, this may not be the comprehensive list. In addition, the descriptive statistics were not described in detail. It can be found in the article contributed by Kaliyadan and Kulkarni.[7] Furthermore, in many cases, multiple tests are available for analyzing the same set of data. For example, there are several tests for checking the normality of data.[8] Similarly, there may be other websites that offer the same test. We presume that researchers would find the best suitable websites for their statistical tests.

This article was written with the sole purpose of training novice researchers. We do not claim it to be a complete guide for inferential statistics. However, we presume that the glimpse of common statistical tests with examples would enhance the learning of the physicians cum researchers.

Conclusion

We briefly described how common statistical tests used in biomedical researches can be conducted online, without installing any dedicated software. However, minimum cost involving access to a computer with an internet connection is a prerequisite. Novice researchers in resource-limited settings may carry out these statistical tests. The application of statistical tests for analyzing clinical data is evolving. Hence, researchers are suggested to update themselves continually.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.