

ORIGINAL ARTICLE 

Year : 2022  Volume
: 9
 Issue : 1  Page : 6369 

How to conduct inferential statistics online (Part 2): A brief handson guide for biomedical researchers
Shaikat Mondal^{1}, Himel Mondal^{2}, Roopam Panda^{3}
^{1} Department of Physiology, Raiganj Government Medical College and Hospital, Raiganj, India ^{2} Department of Physiology, Fakir Mohan Medical College and Hospital, Balasore, Odisha, India ^{3} Department of Physiology, MKCG Medical College, Berhampur, Odisha, India
Date of Submission  10Dec2021 
Date of Acceptance  17Dec2021 
Date of Web Publication  23Mar2022 
Correspondence Address: Himel Mondal Department of Physiology, Fakir Mohan Medical College and Hospital, Balasore, Odisha India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/ijves.ijves_130_21
Introduction: Researchers from developing countries may not have access to statistical software packages. However, descriptive and inferential statistical tests are to conduct to conclude the study. In a previous article (DOI: 10.4103/ijves.ijves_116_21), we described how to conduct some of the common inferential statistical tests online. This article is the second part of the series. Aim: We aimed to provide the examples of some inferential statistical tests used in clinical studies and provide stepbystep guidelines to conduct those tests online. Methods: We prepared a set of data for each statistical test. These data were used to carry out the test online and the steps are briefly described. The result of the test is presented with screenshots and text to get an idea of how to report the result in a manuscript. Results: We described the process of conduct of the following tests online – Receiver operating characteristics curve analysis, Kaplan − Meier estimate, doseresponse, logistic regression, multiple linear regression, residual analysis, odd ratio, Bland − Altman plot, Cronbach's alpha, Cohen's kappa, and intraclass correlation coefficient. In addition, a method for random allocation of subjects in groups was also described. All the tests were described with example data available in a supplementary file. Conclusion: In this article, some of the inferential statistics used for clinical studies are described with example data and a stepbystep guide. Any clinician from resourcelimited settings may use this guide as a reference for statistical tests. However, the tests described in this article are not a comprehensive list.
Keywords: BlandAltman, Cronbach's alpha, Kaplan − Meier, logistic regression, Odd ratio, relative risk, receiver operating characteristic curve
How to cite this article: Mondal S, Mondal H, Panda R. How to conduct inferential statistics online (Part 2): A brief handson guide for biomedical researchers. Indian J Vasc Endovasc Surg 2022;9:639 
How to cite this URL: Mondal S, Mondal H, Panda R. How to conduct inferential statistics online (Part 2): A brief handson guide for biomedical researchers. Indian J Vasc Endovasc Surg [serial online] 2022 [cited 2022 May 28];9:639. Available from: https://www.indjvascsurg.org/text.asp?2022/9/1/63/340501 
Introduction   
In a previous article titled “How to conduct descriptive statistics online: A brief handson guide for biomedical researchers,” we provided a brief guide on the conduct of some common descriptive statistical tests online.^{[1]} Furthermore, in another article titled “How to conduct inferential statistics online: A brief handson guide for biomedical researchers,” we described some of the common inferential statistical tests.^{[2]} In this final article in the series, we aimed to provide a brief guide on the conduct of some inferential statistics that we did not include in the previous article. These tests are commonly used for clinical studies.
Methods   
Ethics
In this study, we fabricated the data for instructional purposes only. There were no data collected from human subjects. The example study was also created for training purposes. Hence, this study does not require any clearance from the Institutional Ethics Committee.
Variables
According to the nature of the data, a variable is divided into categorical/qualitative and numerical/quantitative. In addition, according to manipulation, a variable can be divided into dependent and independent variables. A variable that a researcher can manipulate is called the independent variable. It is also called predictor variable or experimental variable. A variable that is observed in an experiment with manipulating another variable (independent variable) is called a dependent variable. It is also called an outcome variable. An example of independent, dependent, and control variables is shown in [Figure 1].^{[3]}
Websites
We listed the websites in [Table 1]. There are some websites that provide multiple tests. However, we tried to include a maximum number of websites.  Table 1: Websites offering free conduct of some inferential statistical tests
Click here to view 
Receiver operating characteristic curve analysis
Example
There were data of atherogenic index of plasma (AIP) and left ventricular ejection fraction (LVEF) of type 2 diabetic patients. The LVEF of each participant was categorized as “within normal limit” and “lower than lower limit.” A statistical test was to conduct to find the AIP as a tool to diagnose subject with low LVEF. Hence, a receiver operating characteristic (ROC) curve analysis was decided that plots the sensitivity (true positive rate) and 1 specificity (false positive rate).^{[4]}
Steps
 Go to https://epitools.ausvet.com.au/roccurves
 You may name the test in “Test name” box; keep the “Data format” as “Stacked” (check the data from supplementary file or example from “Download example data” from website); keep “Confidence interval (CI)” as “0.95;” copy both the columns of data without column headings and paste it in data box (remember to clear the excess row at the end with backspace). Click on the “Submit” button
 You would get the ROC curve with area under the curve along with density curve, frequency distribution, box plot, and other statistical details.
Result
The ROC curve is shown in [Figure 2]a. A carve toward left upper side indicates higher diagnostic capability. The area under the curve was 0.99 which indicates an outstanding diagnostic capability of AIP to detect low LVEF (0 = perfectly inaccurate test, 0.5 = no ability to diagnose patient with or without disease, 0.7 – 0.8 = acceptable, 0.8 – 0.9 = excellent, >0.9 = outstanding, and 1 = perfectly accurate test).^{[5]}  Figure 2: Statistical test result screenshot – (a) Receiver operating characteristic curve analysis, (b) Kaplan–Meier estimate, (c) Dose response and EC_{50}, (d) Logistic regression, (e) Multiple liner regression, (f) Regression residuals analysis, (g) Odds ratio and relative risk, (h) BlandAltman plot, (i) Cronbach's alpha, (j) Cohen's Kappa, (k) Intraclass correlation coefficient, (l) Randomization of subjects. Highresolution figures are available in supplementary file (https://doi.org/10.6084/m9.figshare.17036783)
Click here to view 
Kaplan Meier survival analysis
Example
A new drug was administered to reduce lung fibrosis after suffering from COVID19 in two groups of patients – 16 obese and 16 nonobese (group). They were followed up for months (time) till they were recovered from the fibrosis (event). However, during the course, one person from obese group died due to cardiovascular disease at 9 months and one person did not come for followup after 4 months. One person in nonobese group did not come for followup after 1 month (censored). For Kaplan − Meier Survival Analysis, group, time, event, and censored data are required. According to the nature of the study, the groups may be different. The time may be in days, fortnight, months, or years. The event may be recovery, achievement of certain level of recovery, or death. The censored are the data not available due to any reason.^{[6]}
Steps
 Go to https://www.statskingdom.com/kaplanmeier.html
 Keep chart type as “Confidence interval;” you may name the test; keep “Significance level” as 0.05; keep the data entry option as “Enter raw data directly;” copy the data and paste in the boxes of Time, Event/Censored, and Group column. Click on calculate
 The comparative curve with P value would be shown along with individual curve for obese and nonobese group. Scroll down to get the result of logrank test. Hover, the mouse over the right upper corner of the graph to get a camera icon and click on that to “Download plot as a png”
Result
The Kaplan − Meier curve is shown in [Figure 2]b. The P value was 0.003 that indicates unequal recovery (survival distribution) among obese and nonobese with quick recovery in nonobese group. In the curve, the plus sign indicates censored data and the shade around the line indicates 95% CI.
Dose response and EC_{50}
Example
A new drug was administered in female patients suffering from certain allergic skin disease. The dose of the drug gradually increased to observe the reduction of percentage of eosinophil count from the initial level. A dose response curve was needed to find the halfmaximum effective concentration (EC_{50}) of the drug.^{[7]}
Steps
 Go to https://www.aatbio.com/tools/ec50calculator
 Copy both the column of data including the headings of the column and paste it in “Data Entry” box; click on “Process data”; you may name the axis as “dose” and “response” and set the minimum response to zero and maximum as one with background correction and normalization option ticked. Click on “Calculate EC_{50}”
 The doseresponse curve would be shown with the EC_{50} value. You can right click on the graph to get option to set the minimum and maximum of X and Yaxis. Take a screenshot if the “Download Graph” does not work.
Result
The doseresponse curve is shown in [Figure 2]c. The EC_{50} of the fictitious drug in reduction of eosinophil count was 45.91. There is an option to calculate the X value from Y value or vice versa from the regression equation of the calculation.
Binary logistic regression
Example
According to different level of body fat percentage and age (independent variables), the depression (dependent variable) was tabulated with “presence of depression” and “absence of depression” (dichotomous). As the dependent variable was categorical with dichotomous distribution, a binomial logistic regression was conducted to ascertain the effects of age and body fat on the likelihood that research participants have depression.^{[8]}
Steps
 Go to https://www.statskingdom.com/420logistic_regression.html
 Copy the age column data without heading and paste it in X1, body fat in X2, and Depression in Y (0). Click on the “Calculate” button
 The result will be shown as per newton's method with goodness of fit, Nagelkerke R^{2} and coefficient table containing significance for each of the independent variables.
Result
The result is shown in [Figure 2]d. The logistic regression model was statistically significant, χ^{2} (2) = 36.5, P < 0.0001. The regression model explained 73% (Nagelkerke R^{2}) of the variance in depression. However, age (P = 0.86) and body fat (P = 0.86) as independent variable were not significant predictor of depression.
Multiple linear regressions
Example
There were age, height, weight, and body fat (independent variables) and resting respiratory exchange ratio (RER) (dependent variable) data of 20 research participants. Multiple linear regressing was selected to check if these independent variables are significant predictor of the resting RER.^{[9]}
Steps
 Go to https://www.statskingdom.com/410multi_linear_regression.html
 Insert one more column as we had four columns. Name the column heading as “age,” “height,” “weight” and “body fat” in X variables and “resting RER” as Y variable. Copy the respective column of data and paste it without column heading. Click on “Calculate” button
 Result would be shown with overall regression and individual variables along with correlation and ANOVA details. You can take screenshots of the result page for further use.
Result
The result is shown in [Figure 2]e. The multiple linear regression model was statistically significant, F (1, 18) = 27.13, P < 0.0001. However, individually only the body fat significantly predicted (P < 0.001) the resting RER. The age (P = 0.97), height (P = 0.73), and weight (P = 0.77) were not significant predictor of resting RER.
Regression residuals analysis
Example
A study was conducted to find a way to calculate arm span of persons from the height. This would help to get arm span of person with amputated upper limbs. The height was taken as an independent variable and arm span was taken as a dependent variable. Suppose, calculated regression equation was: Arm span = 28.691 + 0.8092 × Height. With this equation, from each height, we can calculate the predicted arm span. Then each residual (i.e., observed arm span – predicted arm span) is calculated and plotted against predicted value. The regression residuals plot would give us an idea about the goodness of fit of a regression model visually.^{[10]}
Steps
 Go to https://mathcracker.com/regressionresidualscalculator
 Copy height data without column heading and paste it in “Independent variable X sample data;” copy arm span data without column heading and paste it in “Dependent variable Y sample data;” name the variables. Click on “CALCULATE”
 Scroll down to get the regression equation and plot. Take a screenshot of the plot.
Result
The plot is shown in [Figure 2]f. The residuals indicate how far the prediction differs from the observed value. Hence, researchers would like to get residuals as low as possible where the points stay near the 0 line.
Relative risk and odds ratio
Example
An effect of a new drug on coronary artery disease (CAD) was to assess. A group of patients having risk of CAD were assigned in either in placebo group or drug group. At the end of two years, patients suffered from CAD were tabulated in 2 × 2 contingency table to calculate the relative risk and odds ratio (OR).^{[11]}
Steps
 Go to https://www.socscistatistics.com/biostatistics/default2.aspx
 Input the data in the groups where “Group 1” is placebo group (or exposed to risk) and “Group 2” is drug group (or unexposed to risk). Fill the “Bad outcome” (Presence of CAD) and “Good outcome” (Absence of CAD). Click on the “calculate” button
 The result would be shown both for relative risk and OR with details of the calculation. The result is also shown if group is interchanged.
Result
The result is shown in [Figure 2]g. Patients receiving placebo has (RR = 1.65; 95% CI: 0.9187 to 2.9547) 1.65 times higher risk of developing CAD in comparison to patients treated with the drug. For every 1.85 (OR = 1.85; 95% CI: 0.9060 to 3.7751) persons suffered from CAD in placebo group, 1 person would suffer from CAD in drug group.^{[11]}
As the primary website from where we calculated RR and OD, does not provide 95% CI, alternative websites were used  https://www.medcalc.org/calc/relative_risk.php and https://www.scistat.com/statisticaltests/odds_ratio.php for 95% CI of RR and OR, respectively.
BlandAltman plot
Example
A sample of diabetic people was taken to compare the blood sugar level measured by laboratory method and a new glucose monitor (i.e., glucometer). The agreement between the two methods may be tested by correlation coefficient. However, correlation does not study the difference between the two variables. For clinical applicability of the glucometer, the difference between the blood glucose reading from a glucometer and that acquired from a laboratory should not differ substantially. Hence, in this case, Bland − Altman plot is one of the important analysis.^{[12]}
Steps
 Go to https://huygens.science.uva.nl/BAplotteR
 Click on the bullet of “Paste data” and paste the copied two columns of data with column heading in the box; click on the “Submit data” and keep “Delimeter” as “Tab (from Excel)”; Select the “Measurement 1” as “Laboratory” and “Measurement 2” as “Glucometer” and optionally, units as “mg/dl”; Click on the “Plot” tab
 The plot would be shown. Click on the “Download pngfile” to save the image. Click on the “Data Summary” tab to get the analysis details (difference, upper limit and lower limit of agreement, intercept and slope) with a QQ plot.
Result
The plot is shown in [Figure 2]h. It is a plot of differences between laboratory glucose and glucometer glucose versus the mean of the two measurements. The middle dotted line is the mean and upper and lower dotted line is + 1.96 and − 1.96 standard deviation, respectively. The result showed that the difference was 9.07, upper limit of agreement was 35.43, lower limit of agreement was − 17.30, and intercept at 14.06. Majority of the differences were within the upper and lower limits.
Cronbach's alpha
Example
A new questionnaire was developed for the assessment of preoperative stress before exploratory laparotomy. The questionnaire was composed of six items (questions) with 5point Likert type response options. The questionnaire was distributed among 31 patients and their responses were used to find the internal consistency of the questionnaire (how well the questionnaire measure what it supposed to measure by finding correlations between different items).^{[13]}
Steps
 Go to http://www.wessa.net/rwasp_cronbach.wasp
 Copy all columns of data and paste it in the box below “Data X”; name the columns as Q1 to Q6. Click on the “Compute” button
 The overall Cronbach's alpha with alpha if any item deleted is shown. This is important to decide which question to exclude to increase the internal consistency of the scale (questionnaire). A screenshot may be captured for keeping record of the result.
Result
The Cronbach's alpha was 0.8972 [Figure 2]i. It indicates a good level of internal consistency (<0.5 = unacceptable, 5 to < 0.6 = poor, 6 to < 0.7 = questionable, 7 to < 0.8 = acceptable, 0.8 to < 0.9 = Good, and > 0.9 = excellent).^{[14]}
Cohen's Kappa
Example
A lowcost smartphone adapter was developed to capture the photomicrographs. Histopathological slides of 20 patients were captured with the help of the adapter and sent to two pathologists to diagnose the case from the photomicrograph. The degree of agreement between the observers was to test by Cohen's Kappa. A table was prepared with the following categories – both observer diagnosed, first observer diagnosed and second observer did not diagnose, first observer did not diagnose and second observer diagnosed, and both observer did not diagnose.^{[15]}
Steps
 Go to https://www.graphpad.com/quickcalcs/kappa1.cfm
 Keep the categories as “2 categories”; fill the table with the following data AA = 13, AB = 1, BA = 0, BB = 6. Click on the “Calculate now”
 The Kappa would be shown with 95% CI. A list containing interpretation would also be shown. A screenshot of the result may be captured for further use.
Result
Calculated Cohen's Kappa was 0.886 (95% CI: 0.671 to 1) [Figure 2]j. This indicates almost a perfect agreement between two observers (≤0 = no agreement, 0.01–0.20 = none to slight, 0.21–0.40 = fair, 0.41–0.60 = moderate, 0.61–0.80 = substantial, ≥0.81 = almost perfect agreement).^{[15]} Hence, photomicrograph captured with the help of the new adapter may be used for the remote diagnosis with nearly perfect interrater agreement.
Intraclass correlation coefficient
Example
Systolic blood pressure of 22 research participants where measured by two observers with a new aneroid sphygmomanometer with both odd and even marking on the gauge. The consistency of measurements was to check by intraclass correlation coefficient (ICC).^{[16]}
Steps
 Go to http://vassarstats.net/icc.html
 Copy both column of the data without the column headings and paste it in the box designated as “Data Entry:” Click on the “Calculate” button
 The result would be shown with ANOVA summary. The result page screenshot may be taken for further use.
Result
The result screenshot is shown in [Figure 2]k. The ICC was 0.97 and it indicates an excellent interrater agreement in the measurement of systolic blood pressure by two raters (i.e., measurers or observers or operators) (<0.5 = poor, 0.5 – 0.75 = moderate, 0.76 – 0.9 = good, and >0.90 = excellent reliability). There are several models of ICC as described by Koo et al.^{[17]} The website we used to calculate ICC allows a measurement by two raters or two measurements by a single rater. We could not find online calculator for other models.
Random assignment of subjects
Example
A sample of 60 subjects needs a simple random allocation of 20 subjects in placebo group, treatment Group 1, and treatment Group 2.^{[18]}
Steps
 Go to https://www.graphpad.com/quickcalcs/randomize1.cfm
 Assign “20”; subject to each of “3” groups; repeat “1” times. Click on “Do it!”
 The result would be shown. This can be copied and pasted in any spreadsheet. A screenshot may also be taken.
Result
Truncated list of allocation is shown in [Figure 2]l. The groups are indicated as A, B, and C.
Results   
A total of 11 statistical tests  receiver operating characteristics curve analysis, Kaplan − Meier estimate, dose response, logistic regression, multiple liner regression, residual analysis, OR and Relative risk, Bland − Altman plot, Cronbach's alpha, Cohen's Kappa, ICC were described with successful conduct in the public domain websites. In addition, a method of random allocation of subjects was also described as it is important for clinical studies. The websites are listed in [Table 1] for quick access.
The screenshots of the result page are presented in [Figure 2]. Highresolution images along with example can be downloaded from Figshare (https://doi.org/10.6084/m9.figshare. 17036783).
Discussion   
This was the second article of a series that discussed inferential statistics that can be conducted online.^{[2]} Another article was about the conduct of descriptive statistics including visualization of data.^{[1]} Among the inferential tests, some tests and graphing method were missed in the previous article. Hence, this article was prepared. We successfully conducted the tests online without registering for any account in the websites. This gives freedom to users to conduct test without hassle of opening and confirming account.
Although we included many of the tests, we do not claim it to be comprehensive. Many of the tests are also not available online. In addition, some have limitations. For example, there are several models of ICC.^{[17]} However, online conduct allows only two of the models. Hence, this guide should be considered as an introductory basic guide for researchers from the settings where access to statistical software package is limited.^{[18],[19]}
Conclusion   
We discussed with example data how to run some of the inferential statistical tests that were not available in the previous article in this series.^{[2]} All the tests described in this article can be conducted online without installing any software in computers. The steps were explained briefly for each website. Researchers from resourcelimited settings can conduct the tests without buying costly statistical software package.
Supplementary file
Supplementary file with the data, web links, and result is found from the following link: https://doi.org/10.6084/m9.figshare. 17036783.
Acknowledgment
We would like to thank Sarika Mondal and Ahana Aarshi for allowing their precious time during preparation of this article.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2]
[Table 1]
