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A Guide to Basic Statistics for Educational Research

Donna m. windish.

1 Associate Professor of General Internal Medicine, Department of Internal Medicine, Yale School of Medicine; Director, Resident Research, Yale Primary Care Residency Program, Yale School of Medicine; Program Director, General Internal Medicine Medical Education Fellowship, Yale School of Medicine; Director, Advancement of Clinician-Educator Scholarship (ACES) Faculty Development Program, Department of Internal Medicine, Yale School of Medicine

Associated Data

• Guide to Basic Statistics for Educational Research.mp4
• Educational Examples Worksheet.doc
• Educational Examples Answer Sheet.doc
• Session Evaluation.docx
• Facilitator Guide.docx

All appendices are peer reviewed as integral parts of the Original Publication.

Introduction

Clinician-educators often need to produce scholarship for academic promotion. While some programs exist to help with faculty development skills, few provide adequate statistical training to help educators evaluate their work.

From January 2020 through January 2021, faculty at three academic centers attended one of five in-person or virtual seminars with dedicated statistical training for medical education interventions. These 90-minute seminars included a 45-minute PowerPoint presentation of common statistical tests used for educational interventions followed by small breakout groups to help attendees work on additional practice examples. After each seminar, surveys were distributed in person or virtually to obtain feedback.

Forty-three faculty attended the five seminars, with a range of surgical and nonsurgical specialties represented. Of these attendees, 38 (88%) completed session evaluations. The majority of respondents ( n = 34, 90%) rated the session as extremely useful in helping them know how to use statistics in their scholarly work. Most participants agreed or strongly agreed they had adequate time to practice skills ( n = 30, 79%). Self-rated confidence in using statistics was significantly higher after the session compared to before (3.00 post vs. 1.97 pre, p < .0001). Most participants ( n = 32, 84%) rated the session as excellent and the small-group practice as most useful ( n = 16, 42%), but many ( n = 26, 69%) wanted more skills practice.

This intervention shows that dedicated training on biostatistics used in educational interventions can help clinician-educators improve self-rated confidence and knowledge in choosing statistical tests in educational scholarship.

Educational Objectives

By the end of this activity, learners will be able to:

• 1. Describe the application of the following statistical areas to educational interventions: study designs, variable types, exploratory data analysis, confirmatory (inferential) data analysis, and basic interpretation of results.
• 2. Use a four-step approach to choosing a statistical test for educational cases.

Producing scholarship is often a key determinant to academic advancement for clinician-educators regardless of home institution. 1 – 3 The value of educational scholarship is well recognized and is receiving increased support. 4 To help clinician-educators cultivate faculty development skills, some institutions have established academies of medical educators 5 or education scholarship units. 6 Despite these initiatives, many institutions may not provide adequate statistical or methodological support to help with development and evaluation of educators' work. 3

A recent Association of American Medical Colleges survey showed that a majority of medical schools lack specific biostatistics training. 7 This lack of training can contribute to low statistical knowledge among resident trainees 8 – 11 and subsequently to low statistical literacy among faculty. 11 – 13 A recent scoping review of clinician-educator faculty development programs found that few programs focus on research or scholarship skills. 14 Without statistical knowledge, clinician-educators may be at a disadvantage in publishing their scholarly work and thus potentially miss opportunities to be promoted.

Resources exist that address understanding statistical concepts and evidence-based medicine. The JAMA Guide to Statistics and Medicine contains a series of articles addressing statistical techniques used in clinical research. 15 The goal of the series is to help clinicians understand and learn how to critically appraise the medical literature. One article in the series reviews the reporting guidelines for survey studies. 16 Since survey research is a common tool used in educational interventions, educators might find this particular article helpful in their work. A recent publication in MedEdPORTAL describes a module for teaching students basic biostatistics and evidence-based medicine. 17 The authors of that resource review study design strengths and weaknesses, how to appraise the literature, and how to assess the clinical importance of published studies. Another workshop in MedEdPORTAL contains an interactive review of basic biostatistics and discusses how to apply Bayes' theorem to testing and decision-making. 18 It uses a flipped classroom approach with quizzes to assess knowledge gained. Each of the three publications just described can aid educators in understanding basic statistical concepts, evidence-based medicine, and reading of the literature. None provide a dedicated guide that would aid educators in choosing statistical tests when analyzing their own educational interventions.

In 2006, Windish and Diener-West developed a guide to help clinician-educators understand and choose statistical tests. 19 Since then, little has been published that provides specific training on statistics for educational interventions with detailed examples. The resource presented here is a unique contribution to the literature aimed at building knowledge of biostatistics using educational examples that clinician-educators will find germane to their educational scholarship. The resource includes an instructional video identical to content presented in faculty development seminars across multiple institutions taught to medical educators. It also provides active learning opportunities through additional educational examples to practice and apply what has been learned from the video. This resource can be used as a seminar at other institutions in addition to serving as an everlasting resource for individuals when conducting educational research.

Five faculty development seminars were offered at three different schools of medicine from January 2020 through January 2021. Seminars were either in person or virtual via Zoom, with a range of six to 12 participants, and lasted 90 minutes. Each seminar was led by the author and included a 45-minute PowerPoint presentation that reviewed study designs, variable types, exploratory data analysis, confirmatory data analysis, basic interpretation of results, and a four-step approach to choosing a statistical test. 19 Statistical content was determined based on the low literacy regarding these concepts seen in prior studies of residents and educators. 8 – 13 A video of the PowerPoint presentation contained in this seminar is available in Appendix A . All figures in the presentation were created by the author using Stata statistical software version 14.2 (StataCorp) from fabricated data for illustrative purposes only. The photographs in the apple-pie analogy for regression analysis are author owned. In each seminar, statistical concepts were introduced and interwoven throughout the presentation using an example of an educational intervention aimed at improving second-year medical students' counseling skills, confidence in medical interviewing, professionalism skills, and pass rate. This example was designed to address how to evaluate a curriculum using different evaluation strategies, including the broad categories of assessing knowledge, attitudes, and skills. Statistical concepts included continuous, ordinal, and dichotomous outcome variables, parametric tests, nonparametric tests, and paired analyses.

After the PowerPoint presentation, faculty divided into smaller groups of two to five people who worked together for 20 minutes on additional practice examples provided on worksheets ( Appendix B ). This small-group practice allowed participants to apply the statistical knowledge learned in the presentation. All figures in the worksheets were created by the author from manufactured data and used for illustrative purposes. Half of the small groups completed questions from case 1, and the other half completed questions from case 2. Case 1 addressed the following statistical concepts: Student t test, correlation, and multiple logistic regression. Case 2 had participants work through examples that used a paired t test and analysis of variance. The last 15 minutes of the seminar featured a debrief of the practice examples with answers provided in the larger group ( Appendix C ).

Seminars were held at the Yale School of Medicine, the Washington University School of Medicine in St. Louis, and the University of Wisconsin School of Medicine and Public Health. The two sessions held at Yale were hosted by the Department of Medicine and were open to all faculty in the department, with one in-person session and one virtual session. The two in-person sessions held at the Washington University in St. Louis were hosted by the Academy of Educators and were open to all faculty in any discipline throughout the university. One seminar was hosted virtually for the University of Wisconsin and was open to educators in graduate and undergraduate medical education.

At the end of each seminar, faculty were asked to complete a session evaluation ( Appendix D ). Questions asked participants to rate the following:

• 1. The usefulness of the session in helping know them how to use statistics in their current scholarly work (5-point scale: 1 = extremely useful, 5 = extremely useless ),
• 2. The adequacy of the faculty facilitator (5-point scale: 1 = extremely adequate, 5 = extremely inadequate ),
• 3. The adequacy of time to practice skills (5-point scale: 1 = strongly disagree, 5 = strongly agree ),
• 4. Their confidence in using statistics before and after the seminar (4-point scale: 1 = very unconfident, 4 = very confident ), and
• 5. The overall session (5-point scale: 1 = poor, 5 = excellent ).

Open-ended questions were also asked to elucidate the most useful part of the session and recommendations for change. A paired t test was used to compare self-rated confidence before and after the session.

Appendix E is a facilitator guide providing a step-by-step approach to replicating the previously described seminar. It features information on how to develop a successful session, including what to do prior to the session, how to use the video in Appendix A , how to execute the small-group breakout session, and how to review the answers to the small-group work. The video can be stopped at various times to discuss each area covered. Educational and statistical topics with corresponding video start times are as follows:

• • Start time: 0:03:02—educational example question 1: counseling skills.
• • Start time: 0:03:25—study designs.
• • Start time: 0:04:43—paired data versus unpaired data.
• • Start time: 0:07:40—types of outcome research variables.
• • Start time: 0:11:31—exploratory data analysis.
• • Start time: 0:14:27—parametric tests.
• • Start time: 0:16:06—nonparametric tests.
• • Start time: 0:17:55—confirmatory data analysis.
• • Start time: 0:18:46—regression analysis.
• • Start time: 0:25:34—hypothesis testing.
• • Start time: 0:29:30—educational example question 2: confidence in skills.
• • Start time: 0:32:33—educational example question 3: professionalism skills.
• • Start time: 0:35:25—educational example question 4: pass rate.
• • Start time: 0:36:01—dichotomous outcomes.

In total, 43 faculty attended the five sessions, with a range of surgical and nonsurgical specialties represented, including general surgery, orthopedics, radiology, internal medicine, nephrology, pulmonology, cardiology, geriatrics, gastroenterology, ophthalmology, pediatrics, physical therapy, genomics, psychiatry, pathology, and dermatology. Of the 43 faculty, 38 (88%) completed session evaluations. Most respondents ( n = 34, 90%) rated the session as extremely useful in helping them know how to use statistics in their current scholarly work. All 38 respondents (100%) rated the facilitator as extremely adequate at teaching the statistical concepts. Most participants agreed or strongly agreed that they had adequate time to practice skills in the small-group breakout session ( n = 30, 79%). Self-rated confidence in using statistics was significantly higher after the session compared to before (3.00 post vs. 1.97 pre, p < .0001). Most participants ( n = 32, 84%) rated the session as excellent, with the remainder rating it as very good ( n = 6, 16%).

All respondents provided at least one comment on the most useful part of the session. The majority of comments listed the small-group practice as most useful ( n = 16, 42% of all comments), followed by the usefulness of the flowcharts to determine which statistical test to use ( n = 14, 36%). Other faculty felt the session helped demystify statistics ( n = 7, 18%) or found the descriptions of when to use statistical tests most useful ( n = 2, 5%).

Thirty-two faculty (84%) provided recommendations for change. Having more examples ( n = 12, 38%) and more time for practice ( n = 10, 31%) were the top two recommendations. Remaining suggestions for change included providing an opportunity for hands-on practice with statistical software ( n = 4, 12%) and having a specific slide that included a link to the Windish and Diener-West reference 19 ( n = 3, 9%).

This educational seminar shows that dedicated training on statistics using educational interventions can provide guidance to clinician-educators in conducting and analyzing their work. The seminars were well received by faculty across a spectrum of specialties, disciplines, and institutions, with universal agreement regarding the sessions' usefulness in helping participants in their educational scholarly work. The versatility of the seminars was also demonstrated as they were done both in person and virtually.

In thinking about lessons learned, I realize that although the educational examples worksheet ( Appendix B ) allows participants to practice with additional examples, some faculty may wish to practice and obtain feedback using their own scholarship or might want a review of how to employ statistical software. I initially contemplated having such activities as part of the seminar but feel that participants need time to digest the material and think about how to apply what they have learned to their own work. Consequently, to help solidify the concepts, in the future I will be offering an optional follow-up 90-minute session a few weeks after each seminar. One goal of this additional session will be to provide feedback to any participant who wants to demonstrate how they have used the statistical approach taught with their own educational scholarship. Faculty will be asked to use the last page of the educational examples worksheet to guide them in their own initiatives and in presenting their thought process. Another goal of this follow-up session will be to review how to utilize SPSS and Microsoft Excel for statistical analyses using participant data. I have chosen these two platforms as they contain easy-to-use analytic software. If faculty do not have their own data to analyze, I will provide a small sample educational database for them to work through.

Certain limitations to this method of training should be considered. First, the detailed video may not answer all questions that viewers have on statistics despite multiple examples and practice. While the video is comprehensive and covers many statistical tests that clinician-educators can use, it does not cover all possible statistical tests, qualitative assessment, curriculum development, or how to choose evaluation instruments. Some of these limitations can be offset by using Appendix 1 in the Windish and Diener-West article 19 and textbooks that address curriculum development 20 and educational research. 21 In addition, some of the original wording of the evaluation tool may not have captured all participants' opinions. Thus, changes to the session evaluation ( Appendix D ) have been made. Question 2 now reads, “How would you rate the Statistics facilitator in presenting the content materials covered?” Question 4 now asks, “Was there a part of the Statistics session that was most useful for you? If so, please describe what and why.” This is in place of asking what part of the seminar the participant felt was most useful. Questions 6 and 7, which rate participant confidence, now contain a neutral category to be consistent with other questions featuring 5-point Likert-scale responses. Finally, given the immediate-post design of the session evaluation, it is unclear if the seminars foster actual long-term improvement in subsequent clinician-educator work.

The video and educational examples provided here can be used as a lasting reference for dedicated teaching and practice of evaluating educational initiatives. This resource can be used by institutions that need ways to help their faculty in their educational scholarship pursuits or by individuals who need a guide in analyzing their work. With more faculty reviewing these materials and using them in their educational work, more long-term outcomes can be assessed.

Disclosures

None to report.

Funding/Support

Ethical approval.

Reported as not applicable.

Free exercises

The exercises section provides free PDF downloads of over 20 exercises related to the statistical procedures covered in the book. The typical exercise describes an investigation, provides excerpts from the Results section of the resulting fictitious article, and then asks questions about those results. The exercises can be used as in-class discussion activities, homework assignments, and source material for exam questions.

Traditional practices versus best practices

Advanced Statistics in Research illustrates popular practices : the established conventions that researchers have traditionally followed when writing up their results. It also illustrates best practices : the newer conventions that are currently recommended by the Publication Manual of the American Psychological Association , the APA's Task Force on Statistical Inference , and other authoritative sources. Readers will learn how to report significance tests and will see how researchers now supplement significance tests with confidence intervals, effect size, and replication statistics. A Reference section with over 200 entries is included for those who want to learn more.

Advanced Statistics in Research may be used as a stand-alone reference for researchers or as a textbook for graduate students or upper-level undergraduates.

Chapter 1: What this Book will Do Chapter 2: Basic Concepts in Research and Statistics Chapter 3: Central Tendency, Variability, and Descriptive Statistics Chapter 4: z  Scores and Area Under the Normal Curve Chapter 5: The Big-Three Results in Research Articles Chapter 6: Bivariate Correlation Chapter 7: Bivariate Regression Chapter 8: Partial Correlation and Statistical Control Chapter 9: Multiple Regression I: Basic Concepts Chapter 10: Multiple Regression II: Advanced Concepts Chapter 11: Discriminant Analysis Chapter 12: Logistic Regression Chapter 13: MANOVA and ANOVA Chapter 14: Analysis of Covariance (ANCOVA) Chapter 15: Exploratory Factor Analysis Chapter 16: SEM I: Path Analysis with Manifest Variables Chapter 17: SEM II: Confirmatory Factor Analysis Chpater 18: SEM III: Path Analysis with Latent Factors Chapter 19: Meta-Analysis Chapter 20: Learning More about Statistics Appendix A: Questionnaire on Eating and Exercising Appendix B: Basics of APA Format                   (and How this Book Sometimes Deviates) References Index

Title: Advanced Statistics in Research: Reading, Understanding and Writing Up Data Analysis Results Author: Larry Hatcher Paperback: 644 pages Publisher: Shadow Finch Media LLC (January 7, 2013) Language: English ISBN-10: 0985867000 ISBN-13: 978-0985867003 Product Dimensions: 10 x 7 x 1.5 inches Shipping Weight: 3 pounds

If you feel this book merits a review, please take a moment to write a review.

Advanced Statistics: Reading, Understanding and Writing Up Data Analysis Results

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Statistics Questions

Statistics questions based on CBSE syllabus and NCERT guidelines are provided here for students. These questions cover the syllabus of Statistics concept for Class 9, 10 and 11. Practising these problems will help students to score better on this topic. Also, it will help them to participate in competitive exams. Also, find probability questions here at BYJU’S.

Definition : Statistics is a branch of mathematics concerned with collecting meaningful data or information.

Also, read: Statistics

Questions on Statistics with Answers

1. Give any two examples of collecting data from day-to-day life.

A. Increase in population of our country in the last two decades.

B. Number of tables and chairs in a classroom

2. If marks obtained by students in a class test is given as per below:

55 36 95 73 60 42 25 78 75 62

Then arrange the marks from lowest to highest.

Solution: We need to arrange the marks obtained by each student in ascending order:

25 36 42 55 60 62 73 75 78 95

3. Check the following frequency distribution table, consisting of weights of 38 students of a class:

(i) What is class-interval for classes 31 – 35?

(ii) How many students are there in the range of 41-45 kgs?

(i) Class interval = Upper class limit – lower class limit

(ii) For the 41-45 range, there are 14 students.

4. A family with a monthly income of ` 20,000 had planned the following expenditures per month under various heads:

Draw a bar graph for the data above.

5. In a city, the weekly observations made in a study on the cost of the living index are given in the following table:

Draw a frequency polygon for the data above.

Solution: Class- mark = (Upper class limit-lower class limit)/2 = (150 + 140)/2 = 290/2 = 145

Thus we can create a new table with class-mark.

Now with these class marks we can plot the frequency polygon as shown below.

6. Consider a small unit of a factory where there are 5 employees : a supervisor and four labourers. The workers earn a salary of Rs. 5,000 per month each while the supervisor gets Rs. 15,000 per month. Calculate the mean, median and mode of the salaries.

Mean = (5000 + 5000 + 5000 + 5000 + 15000)/5 = 35000/5 = 7000

So, the mean salary is Rs. 7000 per month

To obtain the median, let us arrange the salaries in ascending order:

5000, 5000, 5000, 5000, 15000

Median = (n+1)/2 = (5+1)/2 = 6/2 = 3rd observation

Median = Rs. 5000/-

Mode = Number of times an observation is repeated = Rs.5000/-

7. The distribution in the table below shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean number of wickets using the correct method. What does the mean signify?

Solution: Here, the class size varies, and the class marks (x i ) are large. Apply the step deviation method for a = 200 and h = 20.

So, ʉ = -106/45

x̄ = 200+20(-106/45) = 200 – 47.11 = 152.89

Hence, on an average, the number of wickets taken by these 45 bowlers in one-day cricket is 152.89.

8. A survey conducted on 20 houses in an area by a group of people resulted in the subsequent frequency table for the number of family members in a house:

Find the mode of this data.

Solution: Here the maximum class frequency = 8,

Class corresponding to this frequency = 3 – 5.

So, the modal class = 3 – 5.

Modal class = 3 – 5, lower limit (l) of modal class = 3, class size (h) = 2

Frequency (f 1 ) of the modal class = 8

Frequency (f 0 ) of class preceding the modal class = 7,

Frequency (f 2 ) of class succeeding the modal class = 2.

Now, let us put these values in the formula :

Therefore, the mode of the data above is 3.286.

9. A survey regarding the heights (in cm) of 51 girls of Class X of a school was conducted and the following data were obtained:

Find the median height.

Solution: Observe the below table:

n/2 = 51/2 = 25.5

This observation lies in the class 145 – 150.

l (the lower limit) = 145,

cf (the cumulative frequency of the class preceding 145 – 150) = 11

f (the frequency of the median class 145 – 150) = 18,

h (the class size) = 5

Using the formula,

So, the median height of the girls is 149.03 cm.

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M. Ed. Question Papers

2.1.1: educational studies, 2021 , 2022, 2.1.2: historical, political and economical perspectives of education, 2.1.3: psychology of learning and development, 2.1.4: pre-service and in-service teacher education, 2020 , 2021 , 2022, 2.1.5: communication and expository writing, 2019, 2020, 2021, 2022, 2.1.6: self development through yoga education, 2.2.1: philosophical perspective of education, 2020 , 2021, 2022, 2.2.2: sociological perspectives of education, 2020, 2021, 2022, 2.2.3: introduction to research methodology, 2.2.4: inclusive education and gender issues in education, 2.2.5: curriculum studies, 2.2.6: internship in teacher education institutions, 2.3.1a: specialization courses in elementary or secondary education, 2.3.1b: specialization courses in elementary or secondary education, 2.3.1c: specialization courses in elementary or secondary education, 2.3.2: advanced research methods (including statistical techniques), 2.3.3: intership, 2.3.4: ict in education, 2.3.5: dissertation related work, 2.3.6: academic writing, 2.4.5 dissertation, 2.4.1: perspectives and issues and research in teacher education, 2.4.2 or 2.4.3 or 2.4.4: specialization (any one), 2.4.3 a: educational planning in the context of secondary education, 2.4.3 b: educational administration in the context of secondary education, 2.4.3 c: educational management and school leadership in the context of secondary education, 2.4.3 e or 2.4.3 s : educational planning, educational administration and management, leadership in the context of elementary education or secondary education, 2.4.4 or 2.4.4 s : educational technology and ict in elementary / secondary education.

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Here you can download sample paper for Maharshi Dayanand University, Rohtak M.Ed., MDU M.Ed. last year papers, MDU M.Ed. previous year papers in pdf file. You can also get latest MDU M.Ed. 2018 updates. Get all state wise papers form here. If no previous year papers found then for reference purpose we are giving you sample papers for M.Ed. .Also get Haryana Papers . For your exams we are providing Following are links to download these paper in pdf file.

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