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MATH 2

Competencies
  • General




    General
    • Course Registration Questionnaire
    • Peer Corner Forum
    • Pre-Test Quiz
  • How to create an account and enroll in the course?

     

     

    • MATH 2 Homepage

         


      Welcome to Math 2, the second course in the Mathematics series for the Pre-Health Sciences Training Certificate. This course and the Certificate are designed primarily for learners interested in preparing for and gaining entry for health-related programs, and to help address the prerequisites for the Medical College Admission Test (MCAT). This Math 2 course provides in-depth learning related to general mathematical concepts and techniques used in the bachelor’s-level study of natural, physical, behavioral, and social sciences. Participants will have the opportunity to review and gain mathematical knowledge on how to analyze and manipulate scientific data. The course explores important areas of mathematics such as Statistics, Graphical and Numerical Methods of Describing Data, Probability, Distributions, Estimation, Testing Hypotheses and Regression Analysis that can be applied in the fields of scientific inquiry.

      The Math 2 course is sponsored in part by the International Development Research Centre and by the University of the Incarnate Word School of Osteopathic Medicine. Like all NextGenU.org courses, it is competency-based, using competencies based on the Association of American Medical Colleges’ Medical College Admission Test. It uses learning resources from accredited, academic, professional, and world-class organizations and universities such as Rice University. Volunteer designers for this course include Shaunik Sharma BSc, Tristan Aaron Wild, BMSc (Hons); and the late Mohammad Asadi-Lari, a former MD-PHD Candidate at the University of Toronto. The course was created by Marco Aurelio Hernandez, Ph.D; Alixandria Ali, BSc: and Pablo Baldiviezo, MD. MSc. DiplEd.

      For publications on NextGenU.org’s courses’ efficacy, see NextGenU.org’s publication page.


      52


      There are 8 modules to complete, which provide an introduction to:

      • Module 1: Introduction to Statistics and Research in Health Care.
      • Module 2: Graphical Methods of Describing Data.
      • Module 3: Numerical Methods of Describing Data: Summary Numbers.
      • Module 4: Probability, Random Variables,  and Distributions.
      • Module 5: Sampling Distributions.
      • Module 6: Estimation.
      • Module 7: Testing of Hypotheses.
      • Module 8: Introduction to Linear Regression Analysis.

      The completion time for this course is estimated at 92 hours, 24 comprising hours of learning resources, 48 hours of studying and assimilation of the content, and 20 hours of participating in learning activities and quizzes to assist the learners in synthesizing learning materials. This course is equivalent to 3 credit hours in the U.S. undergraduate/bachelor’s degree system.

      The course requires the completion of all quizzes, discussion forums, and practical activities to receive a course certificate.  

      Practice quizzes are available throughout the course, composed of multiple-choice questions. After you’ve completed each module, quiz, and learning activity, at the end of the course, you’ll have access to a final exam consisting of 25 multiple-choice questions, a final lab activity, and a chance to evaluate this course. 

      Participants have up to three opportunities to take the final exam and achieve the required passing score of >=70%. Once you’ve passed the final exam and completed the evaluations, you will be able to download a certificate of completion from NextGenU.org and our course’s co-sponsoring organizations. 

      We keep all of your personal information confidential, never sell any of your information, and only use anonymized data for research purposes. Also, we are happy to report your testing information and share your work with anyone (your school, employer, etc.) at your request. 

      Engaging with this Course:

      This free course is aimed at students who have graduated from high school and want to prepare to become a health professional and/or pass the MCAT exam. You may also browse this course for free to learn for your personal enrichment; there are no requirements.   

      To obtain a certificate, a learner must first register for the course and then successfully complete:

      • Pre-test
      • All the reading requirements,
      • All quizzes and pass with 70% with unlimited attempts,
      • All practical activities,
      • All discussion forums,
      • The final lab activity,
      • The final exam with a minimum of 70% and a maximum of 3 attempts, and
      • The self and course evaluation forms.

      To obtain credit:

      • Complete all requirements listed above for the certificate, and
      • Your learning institution or workplace should approve the partner-university-sponsored NextGenU.org course for educational credit, as they usually would for their learner taking a course anywhere. 

      NextGenU.org is happy to provide your institution with:

      • A link to and description of the course training, so they can see all of its components, including the co-sponsoring institutions;
      • Your grade on the final exam;
      • Your work products (e.g., discussion forum responses) and any other required or optional shared materials that you produce and authorize to share with them;  
      • Your evaluations -- course, and self-assessments;
      • A copy of your certificate of completion, with the co-sponsoring organizations listed.

      To obtain a degree, NextGenU.org co-sponsors degree programs with institutional partners. To obtain a full degree co-sponsored with NextGenU.org, registrants must be enrolled in a degree program as a student of a NextGenU.org institutional partner. If you think your institution might be interested in offering a degree with NextGenU.org, contact us.

      We hope you will find this a rewarding learning experience, and we count on your assessment and feedback to help us improve this training for future students.

      Here are the next steps to take the course and earn a certificate:

      • Complete the registration form.
      • Take the pre-test.
      • Begin the course with Module 1:Introduction to Statistics and Research in Health Care. In each lesson, read the description, complete all required readings and any required activity, as well as take the corresponding quizzes.

      • Module 1: Introduction to Statistics and Research in Health Care

        Competency covered in this module: 

        • MCAT: Identify the Role of theory, past findings, and observations in scientific questioning.
        • MCAT: Reason about ethical issues in scientific research.
        • Miami-Dade: Demonstrate an understanding of descriptive statistics by contrasting between the levels of data.
        • MCAT: Distinguish between samples and populations.
        • Miami-Dade: Demonstrate an understanding of descriptive statistics by contrasting between the levels of data.
        • MCAT: Reason about random and systematic error.
        • MCAT: Reason about the appropriateness, precision, and accuracy of tools used to conduct research in the natural sciences.
        • MCAT: Reason about the appropriateness, reliability, and validity of tools used to conduct research.
        • Miami-Dade: Demonstrate an understanding of descriptive statistics by: designing and formulating sources of decision-making data.
        • MCAT: Identify the relationships among the variables in a study (e.g., independent versus dependent variables; control and confounding variables)
        • MCAT: Identify testable research questions and hypotheses.
        • MCAT: Reason about the features of research studies that suggest associations between variables or causal relationships between them (e.g., temporality, random assignment)
        • Miami-Dade: Demonstrate an understanding of descriptive statistics by: designing and formulating sources of decision-making data.
        • Module 1: Lesson 1: Research, The Scientific Method, and the Role of Statistics in the Health Care Field

          Student Learning Outcomes:
          Upon completion of this lesson, you will be able to:
          • Explain the role of theory, past findings and observations in scientific research.
          • Discuss the steps of the scientific method as necessary for scientific research.
          • Discuss the role and Identify instances of statistics being used in our daily lives and the in world around us.
          • Explain the important role of ethics in research.
          Approximate time required for the readings for this lesson (at 144 words/minute): 3 hours and 36 minutes.

          Click here to start this lesson

          2 URLs, 1 Forum
          • Required Learning Resources and Activities
          • Fundamentals of The Scientific Approach URL

            Read from Pages 3-6: Defining Science to Pages 3-18: Common Sense and Science. (30 minutes)

            University of Central Arkansas - 2013

          • What is Ethics in Research and Why is it Important? URL

            Read the entire page. (22 minutes)

            US Government; National Institute of Environmental Health Sciences - 2021

          • Discussion Forum 1

            In this activity, you will discuss the issue of the indispensable use of statistics, despite it being an imperfect science and measure. 

            Step 1. Review

            Review the learning resources for this lesson before answering the question.

            Step 2. Analyze

            Analyze and discuss the question below.

            52

            Step 3. Respond

            Respond to the case problem by writing a 300-500-word discussion post with the following inclusions.

            Step 4. Share

            To share your work, click on the “Add a new discussion topic” button under this post and paste your work in the “Message” box. Make sure to reference others’ intellectual property when necessary. All references should follow 7th Edition APA formatting. For further instructions, see the resource on the Himmelfarb Health Sciences Library: APA citation resource (N.B. references are excluded from word counts).

            Step 5: Interact

            To complete the activity, you will need to reply to at least two posts made by your peers in a respectful and professional manner. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If a peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “Post to the forum.”

        • Module 1: Lesson 2: Data, Variables, Populations, Samples, and Measurement 

          Student Learning Outcomes:
          Upon completion of this lesson, you will be able to:
          • Given a research situation, identify and classify the variables and data generated.
          • Identify populations, samples, and frames in given statistical studies.
          • Classify given measurements according to levels.
          • Distinguish between the two categories of measurement error.
          • Distinguish between accuracy and precision in measurements.
          • Determine the level of accuracy and precision of measurements.
          • Explain Validity and Reliability and their importance in research.
          • Identify situations of reliability and validity in given measurement.
          Approximate time required for the readings for this lesson (at 144 words/minute): 3 hours and 10 minutes.

          Click here to start this lesson

          7 URLs, 1 Quiz
          • Required Learning Resources and Activities
          • Data and Variables URL

            Watch the entire video. (19 minutes)

            2022

          • Definitions, Uses, Data Types, and Levels of Measurement URL

            Click on and Read the "Types of Data" section. (10 minutes)

            Andrews College - 2019

          • 1.2 Samples & Populations URL

            Read entire page. (2 minutes)

            Penn State Eberly College of Science - 2022

          • Levels of Measurement URL

            Read the Entire Page: Levels of Measurement, and try the set of six questions at the bottom of the page. (10 minutes)

            Rice University - 2021

          • Notes on Measurement Error URL

            Read from beginning up to the end of section titled 'We Can Not Avoid Them'. (6 minutes)

            University of Oregon - 2017

          • Practices of Science: Precision vs. Accuracy URL

            Read entire page. (6 minutes)

            University of Hawaii - 2022

          • Reliability and Validity of Measurement URL

            Read entire page. (13 minutes)

            Washington State University - 2022

          • Quiz: Module1: Lessons 1 & 2

            To access the quiz, click on the name of the quiz provided above. On the following screen, click the "Preview quiz now" button to respond to the questions.

        • Module 1: Lesson 3: Research Design and Data Collection

          Student Learning Outcomes:
          Upon completion of this lesson, you will be able to:
          • Describe and identify the various sources of data.
          • Describe some methods and tools of data collection.
          • Identify research variables and Describe the relationship between them.
          • Generate testable research questions from an idea.
          Approximate time required for the readings for this lesson (at 144 words/minute): 1 hour and 51 minutes.

          Click here to start this lesson

          4 URLs
          • Required Learning Resources and Activities
          • Data Sources URL

            Read entire page. (3 minutes)

            Australian Bureau of Statistics - 2022

          • Data Collection Methods URL

            Read entire page. (10 minutes)

            Australian Bureau of Statistics - 2022

          • Variables in Research URL

            Read Entire page. (10 minutes)

            Samarpan Institute of Nursing Sciences - 2013

          • Generating Good Research Questions URL

            Read entire page and watch included video. (14 minutes)

            Research Methods in Psychology - 2015

        • Module 1: Lesson 4: Randomization and Sampling

          Student Learning Outcomes:
          Upon completion of this lesson, you will be able to:
          • Discuss the importance of and identify instances of Random Selection and Random Assignment in Research.
          • Determine the sampling method that will best generate samples for a given situation in research.
          • Explain the generation of a stratified, a cluster, a systematic, or any other types of sampling discussed in the text.
          Approximate time required for the readings for this lesson (at 144 words/minute): 3 hours and 55 minutes.

          Click here to start this lesson

          3 URLs, 1 Forum, 2 Quizzes
          • Required Learning Resources and Activities
          • Elements of Research URL

            Read entire page. (2 minutes)

            San Diego State University - 2021

          • Elements of Research URL

            Read entire page. (2 minutes)

            San Diego State University - 2021

          • Chapter 7: Sampling Techniques URL

            Read up to the end of page 14. (30 minutes)

            University of Central Arkansas - 2013

          • Practical Activity 1 Forum

            Student Learning outcome (Module 1 Lesson 4): Discuss the importance of and identify instances of Random Selection and Random Assignment in Research. 

            Step 1. Review

            Review the learning resources for this lesson before studying the case problem.

            Step 2. Analyze

            Analyze the case problem below.

            A new drug is introduced. How should an experiment be designed to test its effectiveness? The primary method is comparison. The drug is given to subjects in a treatment group, but other subjects are used as controls ‒ they aren’t treated. The treatment and control groups should be as similar as possible ‒ except for the treatment. Then the responses of the two groups are compared. Subjects should be assigned to the groups at random. A randomized controlled assignment is when an impartial chance procedure is used to assign the subjects to treatment or control. This method provides the best assurance of validity and reliability. However, randomized controlled experiments are hard to do. As a result, doctors often use other designs which are not as good. For example, a new treatment can be tried out on one group of patients, who are compared to “historical controls:” patients treated the old way in the past. Usually, using historical controls, assignment to the groups is not randomized, resulting in a poorly-designed experiment. The problem is that the treatment and historical groups may differ in important ways besides the treatment.

            Coronary bypass surgery is a widely used ‒ and very expensive ‒ operation for coronary artery disease. Chalmers and associates identified 29 trials of this surgery (first line of the table below). There were 8 randomized controlled trials, and 7 were quite pessimistic about the value of the operation. By comparison, there were 21 trials with historical controls, and 16 were positive. Three other therapies were evaluated: 5-FU, used in chemotherapy for colon cancer; BCG, used to treat melanoma; and DES, used to prevent miscarriage. The data are given below.

            Table 1: A study of studies. Four therapies were evaluated by randomized controlled trials and by trials using historical controls. Conclusions of trials are summarized as positive about the value of the therapy (+) or negative (-).

            355

            Why are the randomized controlled studies less enthusiastic, and the less well-designed studies more enthusiastic about the value of the surgery? 

            Look at it in view of the data in the table below.

            Table 2: Randomized controlled experiments vs. studies with historical controls: three-year survival rates for surgery patients and patients used as controls in trials of coronary bypass surgery.

            6422

            Step 3. Respond

            Respond to the case problem by answering the question: Why are the randomized controlled studies less enthusiastic and the less well-designed studies more enthusiastic about the value of the surgery? 

            Step 4. Share

            To share your work, access to the first post below and click on the “Reply” button under this post and paste your work into the “Message” box. Make sure to reference others’ intellectual property when necessary. All references should follow 7th Edition APA formatting. For further instructions, see the resource on the Himmelfarb Health Sciences Library: APA citation resource (N.B. references are excluded from word counts).

            Step 5: Interact

            To complete the activity, you will need to reply to at least two posts by your peers respectfully and professionally. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If a peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “post to the forum.”

          • Quiz: Module1: Lessons 3 & 4

            To access the quiz, click on the name of the quiz provided above. On the following screen, click the "Preview quiz now" button to respond to the questions.

          • Quiz: Module 1

            To access the quiz, click on the name of the quiz provided above. On the following screen, click the "Preview quiz now" button to respond to the questions.

        • Module 2: Graphical Methods of Describing Data

          Competency covered in this module: 
          • MCAT: Use, analyze, and interpret data n figures, graphs, and tables.
          • MCAT: Evaluate whether representations make sense for particular observations and data.
          • Module 2: Lesson 1: Displaying Univariate Data

            Student Learning Outcomes:
            Upon completion of this lesson, you will be able to:
            • Determine the appropriateness of, Create, and Interpret Graphical Representations of Univariate Data with: Pie Charts, Dot Plots, Stem-and-leaf Plots, and Frequency tables.
            Approximate time required for the readings for this lesson (at 144 words/minute): 2 hours and 59 minutes.

            Click here to start this lesson

            8 URLs
            • Required Learning Resources and Activities
            • Graphing Qualititative Variables URL

              Read entire page. (7 minutes)

              Rice University - 2021

            • Graphing Qualititative Variables - Graphic Distribution (Video) URL

              Watch the entire video. (7 minutes)

              Rice University - 2021

            • Dot Plots URL

              Read the entire page. (3 minutes)

              Rice University - 2021

            • Stem and Leaf Displays URL

              Read entire page. (9 minutes)

              Rice University - 2021

            • Graphing Distributions - Stem and Leaf Displays (Video) URL

              Watch entire video. (9 minutes)

              Rice University - 2021

            • Histograms URL

              Read the entire page. (7 minutes)

              Rice University - 2021

            • Graphing Distributions - Histograms (Video) URL

              Watch the entire video. (6 minutes)

              Rice University - 2021

            • Creating a Frequency Table and its Graphs URL

              Watch entire video. (41 minutes)

              2022

          • Module 2: Lesson 2: Displaying Bivariate Data

            Student Learning Outcomes:
            Upon completion of this lesson, you will be able to:
            • Determine the appropriateness of, Create, and Interpret Graphical Representations of Bivariate Data with:: Scatterplots, Line Graphs, and Runs (Time Series) Plots.
            Approximate time required for the readings for this lesson (at 144 words/minute): 1 hour and 18 minutes.

            Click here to start this lesson

            5 URLs
            • Required Learning Resources and Activities
            • Scatter Plot URL

              Read entire page. (6 minutes)

              Statistics Canada, Government of Canada - 2021

            • Line Graphs URL

              Read entire page. (4 minutes)

              Rice University - 2021

            • Graphing Distributions - Line Graphs (Video) URL

              Watch entire video. (5 minutes)

              Rice University - 2021

            • Run charts URL

              Read entire page. (4 minutes)

              Clinical Excellence Commission, Govt. of Australia - 2022

            • Graphing of Bivariate Data 1 URL

              Watch entire Video. (21 minutes)

              2022

          • Module 2: Lesson 3: Communicating and Interpreting the Results of Graphical Statistical Analysis

            Student Learning Outcomes:
            Upon completion of this lesson, you will be able to:
            • Determine whether graphical representations of statistical analysis results are clearly communicated.
            • Read and Interpret Statistical Graphs
            Approximate time required for the readings for this lesson (at 144 words/minute): 3 hours and 17 minutes.

            Click here to start this lesson

            2 URLs, 1 Forum, 1 Quiz
            • Required Learning Resources and Activities
            • Comunicating Clearly with Graphs and Charts URL

              Read Up to and including Page 19. (20 minutes)

              State of Washington Government - 2017

            • How to Interpret Scientific and Statistical Graphs URL

              Read entire page. (13 minutes)

              Vanderbilt University, Dept of Biostatistics - 2021

            • Discussion Forum 2

              In this activity, you will discuss the interpretation of statistical graphs and the relationship between variables. 

              Step 1. Review

              Review the learning resources for this lesson before answering the question.

              Step 2. Analyze

              Analyze and discuss the question below.

              58

              Step 3. Respond

              Respond to the case problem by writing a 300-500-word discussion post with the following inclusions.

              Step 4. Share

              To share your work, click on the “Add a new discussion topic” button under this post and paste your work in the “Message” box. Make sure to reference others’ intellectual property when necessary. All references should follow 7th Edition APA formatting. For further instructions, see the resource on the Himmelfarb Health Sciences Library: APA citation resource (N.B. references are excluded from word counts).

              Step 5: Interact

              To complete the activity, you will need to reply to at least two posts by your peers respectfully and professionally. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If a peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “Post to the forum.”

            • Quiz: Module 2

              To access the quiz, click on the name of the quiz provided above. On the following screen, click the attempt quiz button to view the case studies and respond to the questions.

          • Module 3: Numerical Methods of Describing Data: Summary Numbers

            Competency covered in this module: 
            • MCAT: Use measures of Central Tendency and Measures of Dispersion to describe data.
            • MCAT: Demonstrate an understanding of managing data by: evaluating and analyzing methods for examining central tendency; Formulating various techniques to analyze data dispersion; Assessing use of fractile measures such as quartiles and percentiles.
            • MCAT: Use, analyze, and interpret data n figures, graphs, and tables.
            • Miami-Dade: Demonstrate an understanding of descriptive statistics by: Interpreting and assessing data displayed using visual graphic presentation methods.
            • MCAT: Reason about ethical issues in scientific research.
            • Module 3: Lesson 1: Measures of Central Tendency

              Student Learning Outcomes:
              Upon completion of this lesson, you will be able to:
              • Explain the concept of central tendency.
              • Compute the midrange, midquartile, mean, median, mode, weighted, or combined mean of a given data set.
              • Explain the weakness of the median and mean as measures of CT.
              • Determine whether it is appropriate to use the mean, the median, and the mode to express the center of a given dataset.
              Approximate time required for the readings for this lesson (at 144 words/minute): 1 hour and 28 minutes.

              Click here to start this lesson

              5 URLs
              • Required Learning Resources and Activities
              • What is Central Tendency? URL

                Read entire page. (12 minutes)

                Rice University - 2021

              • Summarizing Distributions - What is Central Tendency (Video) URL

                Watch the entire video. (11 minutes)

                Rice University - 2021

              • Measures of Central Tendency URL

                Read entire page and do the set of five (5) questions at the bottom of the page. (10 minutes)

                Rice University - 2021

              • Measures of Central Tendency (Video) URL

                Watch the entire video. (22 minutes)

                2022

              • Mean vs. Median: What do they mean and when do you use them? URL

                Read entire page. (3 minutes)

                Michigan State University - 2016

            • Module 3: Lesson 2: Measures of Dispersion

              Student Learning Outcomes:
              Upon completion of this lesson, you will be able to:
              • Explain dispersion in distributions.
              • Compute the range, interquartile range, variance, and standard deviation of a given data distribution.
              Approximate time required for the readings for this lesson (at 144 words/minute): 51 minutes.

              Click here to start this lesson

              3 URLs
              • Required Learning Resources and Activities
              • Measures of Variability URL

                Read entire page. (7 minutes)

                Rice University - 2021

              • Graphing Distributions - Measures of Variability (Video) URL

                Watch entire video. (7 minutes)

                Rice University - 2021

              • Variance Demonstration URL

                Watch all 4 slides. (3 minutes)

                Rice University - 2021

            • Module 3: Lesson 3: Measures of Position

              Student Learning Outcomes:
              Upon completion of this lesson, you will be able to:
              • Find percentile and quartiles of a distribution.
              • Explain the purpose of and compute the z-score of a measure within a distribution.
              • Normalize scores from different distributions to compare them.
              Approximate time required for the readings for this lesson (at 144 words/minute): 2 hours and 22 minutes.

              Click here to start this lesson
              3 URLs, 1 Quiz
              • Required Learning Resources and Activities
              • 1.5.2 - Measures of Position URL

                Read entire page. (7 minutes)

                Penn State University, Eberly College of Science - 2022

              • Z-scores: Location of scores and standardized distributions URL

                Watch all slides. (20 minutes)

                Cal State University, Northridge - 2021

              • Normalizing Data URL

                Read entire page. (6 minutes)

                University of Texas at Dallas - 2022

              • Quiz: Module 3: Lessons 1, 2 & 3

                To access the quiz, click on the name of the quiz provided above. On the following screen, click the "Preview quiz now" button to respond to the questions.

            • Module 3: Lesson 4: Using Boxplots to Summarize Datasets

              Student Learning Outcomes:
              Upon completion of this lesson, you will be able to:
              • Define basic terms including hinges (fences), H-spread, step, adjacent value, outside value (outlier), and far out value (far outlier).
              • Use the 5-number summary to create boxplots to describe a dataset.
              • Create and interpret side-by-side box (parallel) plots to compare two variables.
              • Create an adjusted boxplot to identify outliers.
              • Create an Adjusted Box Plot.
              • Find Grouped Mean and Variance.
              Approximate time required for the readings for this lesson (at 144 words/minute): 2 hours and 54 minutes.

              Click here to start this lesson
              3 URLs, 1 Forum
              • Required Learning Resources and Activities
              • Box Plots URL

                Read entire Page and answer questions at the bottom of the page. (11 minutes)

                Rice University - 2021

              • Graphing Distributions - Box Plots (Video) URL

                Watch entire video. (8 minutes)

                Rice University - 2021

              • Adjusted Box Plots, Grouped Mean and Variance (Video) URL

                Watch entire video. (17 minutes)

              • Practical Activity 2 Forum

                Student Learning outcome: Use the Five-Number Summary to Create a Boxplot to Describe a Data Set
                In this activity, you will investigate the relationship between boxplot shapes and the corresponding five-number summary.

                Step 1. Review

                Review the learning resources for this lesson before studying the case problem.

                Step 2. Analyze

                Analyze the case problem below.

                The accompanying figure shows four boxplots labeled A to D. Also given are four five-number summaries, labeled I to IV. Match each five-number summary to the appropriate boxplot. Note that scales are not included on the boxplots, so you will have to consider what the five-number summary implies about the characteristics of the boxplot.


                986

                Step 3. Respond

                Respond to the case problem by showing the boxplot properties, logic steps, and reasoning you used to match each figure with its corresponding five-number summary.

                Step 4. Share

                To share your work, access to the first post below and click on the “Reply” button under this post and paste your work into the “Message” box. Make sure to reference others’ intellectual property when necessary. All references should follow 7th Edition APA formatting. For further instructions, see the resource on the Himmelfarb Health Sciences Library: APA citation resource (N.B. references are excluded from word counts).

                Step 5: Interact

                To complete the activity, you will need to reply to at least two posts by your peers respectfully and professionally. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If a peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “post to the forum.”


            • Module 3: Lesson 5: Extra Topics on Describing Data

              Student Learning Outcomes:
              Upon completion of this lesson, you will be able to:
              • Distinguish between parameters and statistics.
              • Explain and give examples of skew and kurtosis of a distribution.
              • Identify and compare the relative positions of the mean and median and the difference between them as they are affected by skew.
              • Illustrate some ways in which graphs and statistics can be used to mislead.
              • Graph mixed bivariate data sets-
              • interpret graphs for Time Series Data.
              • Use numerical summaries with control charts to determine when a system is out-of-control.
              Approximate time required for the readings for this lesson (at 144 words/minute): 4 hours and 46 minutes.

              Click here to start this lesson
              6 URLs, 1 Forum, 2 Quizzes
              • Required Learning Resources and Activities
              • Basic terminology URL

                Read the page to the end of 'Samples and Statistics' section. (5 minutes)

                Penn State University - 2022

              • Measures of Shape: Skewness and Kurtosis URL

                Read entire page, paying more attention to the concepts than to the formulas. (8 minutes)

                Mustansiriyah University - 2021

              • 2.7: Skewness and the Mean, Median, and Mode URL

                Read entire page. (7 minutes)

                UC Davis - 2022

              • Misleading Graphs and Statistics URL

                Read entire page. (10 minutes)

                Arkansas Tech University - 2021

              • Bivariate Data 2 (Video) URL

                Watch entire video. (12 minutes)

              • Control Chart URL

                Read entire page. (8 minutes)

                (ASQ) American Society for Quality - 2022

              • Discussion Forum 3

                In this activity, you will discuss factors of data collection that affect the shape, particularly the skewness, of the data distribution. 

                Step 1. Review

                Review the learning resources for this lesson before answering the question.

                Step 2. Analyze

                Analyze and discuss the question below.

                258
                Step 3. Respond

                Respond to the case problem by writing a 300-500-word discussion post with the following inclusions.

                Step 4. Share

                To share your work, click on the “Add a new discussion topic” button under this post and paste your work into the “Message” box. Make sure to reference others’ intellectual property when necessary. All references should follow 7th Edition APA formatting. For further instructions, see the resource on the Himmelfarb Health Sciences Library: APA citation resource (N.B. references are excluded from word counts).

                Step 5: Interact

                To complete the activity, you will need to reply to at least two posts made by your peers respectfully and professionally. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If a peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “Post to the forum.”

              • Quiz: Module 3: Lessons 4 & 5

                To access the quiz, click on the name of the quiz provided above. On the following screen, click the attempt quiz button to view the case studies and respond to the questions.

              • Quiz: Module 3

                To access the quiz, click on the name of the quiz provided above. On the following screen, click the "Preview quiz now" button to respond to the questions.

            • Module 4: Probability, Random Variables, and Distributions

              Competency covered in this module: 
              • Miami-Dade: Compute basic probabilities as used in statistical applications by comparing the concepts of probability; demonstrating the elementary rules of probability; creating used for Bayes' Theorem, and differing among the counting rules.
              • Yale: random Variables, discrete, continuous, density functions. Mean and Variance of random variables, definitions, and properties.
              • Module 4: Lesson 1: Counting Rules

                Student Learning Outcomes:
                Upon completion of this lesson, you will be able to:
                • Determine the permutations and combinations of n items arranged r at a time.
                Approximate time required for the readings for this lesson (at 144 words/minute): 1 hour and 15 minutes.

                Click here to start this lesson

                1 URL
                • Required Learning Resources and Activities
                • The Fundamental Counting Principle URL

                  Read entire page. (25 minutes)

                  Dux College, Australia - 2022

              • Module 4: Lesson 2: Probability Basics

                Student Learning Outcomes:
                Upon completion of this lesson, you will be able to:
                • Explain the meaning of the probability of an event A in a sample space S.
                • Calculate the probability of a specified simple event in a chance experiment with equally likely outcomes determine simple probabilities using the complement rule, and frequencies or count.
                • Determine compound probabilities using the addition rules for disjoint and non-disjoint events.
                • Find the conditional probabilities of events.
                • determine if two given events are independent.
                • Find probabilities using the multiplication rule.
                • Find probabilities using Bayes' Rule.
                • Determine Sensitivity, Specificity, False Negative, and False Positive probabilities, the Prevalence of a disease, the Predictive Value Positive, and Predictive Value Negative of a Screening Test from a contingency table.
                Approximate time required for the readings for this lesson (at 144 words/minute): 8 hours and 10 minutes.

                Click here to start this lesson

                8 URLs, 1 Forum
                • Required Learning Resources and Activities
                • Probability URL

                  Read entire page. (4 minutes)

                  Institute for Work and Health - 2010

                • Basic Probability Rules URL

                  Read entire page and watch the video included. (25 minutes)

                  University of Florida - 2022

                • Conditional Probability and Independence URL

                  Read the entire page. (25 minutes)

                • Conditional Probability and Independence (Video) URL

                  Watch entire video. (5 minutes)

                  Khan Academy - 2022

                • General Multiplication Rule URL

                  Read entire page. (25 minutes)

                  University of Florida - 2022

                • Bayes’ Rule for Clinicians: An Introduction URL

                  Read entire page. (32 minutes)

                  NIH - National Library of Medicine - 2021

                • Evaluating Screening Tests URL

                  Read entire page. (10 minutes)

                  Boston University School of Public Health - 2021

                • Probabilities with Contingency Tables URL

                  Watch entire Video. (32 minutes)

                  2022

                • Practical Activity 3 Forum

                  Student Learning Outcome (Module 4 Lesson 2): Determine Sensitivity, Specificity, False Negative, and False Positive probabilities, the Prevalence of a disease, the Predictive Value Positive, and Predictive Value Negative of a Screening Test from a contingency table.

                  Step 1. Review

                  Review the learning resources for this lesson before studying the case problem.

                  Step 2. Analyze

                  Analyze the case problem below.

                  The paper “Good for Men, Good for Women, bad for People: Simpson’s Paradox and the Important of Sec-Specific Analysis in Observational Studies” (Journal of Women’s Health and Gender-Based Medicine [2001]: 867-872) described a medical study in which one treatment was shown to be better for men and better for women than a competing treatment when the data for men and women were analyzed separately. However, if the data for men and women are combined, it appears as though the competing treatment is better. 

                  To see how this can happen, consider the accompanying data tables constructed from the information in the paper. Subjects in the study were given either Treatment A or Treatment B, and survival was noted. Let S be the event that a patient selected at random survives, A be the event that a patient selected at random received Treatment A, and B be the event that a patient selected at random received Treatment B. 

                  The following table summarizes data for the men who participated in the study:

                  65455

                  1. Find PS.
                  2. Find PS|A.
                  3. Find PS|B.
                  4. Which treatment appears to be better?

                  Now consider the summary data for women who participated in the study:

                  64

                  5. Find PS.
                  6. Find PS|A.
                  7. Find PS|B.
                  8. Which treatment appears to be better?

                  Now consider the data summary for men and women combined:

                  5

                  9. Find PS.
                  10.  Find PS|A.
                  11. Find PS|B.
                  12.  Which treatment appears to be better?

                  This is an example of what is called Simpson’s paradox.

                  Step 3. Respond

                  Respond to the case problem by writing a brief explanation of why this apparent inconsistency occurs for this data set.

                  Step 4. Share

                  To share your work, access to the first post below and click on the “Reply” button under this post and paste your work into the “Message” box. Make sure to reference others’ intellectual property when necessary. All references should follow 7th Edition APA formatting. For further instructions, see the resource on the Himmelfarb Health Sciences Library: APA citation resource (N.B. references are excluded from word counts).

                  Step 5: Interact

                  To complete the activity, you will need to reply to at least two posts by your peers respectfully and professionally. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If a peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “post to the forum.”

              • Module 4: Lesson 3: Random Variables

                Student Learning Outcomes:
                Upon completion of this lesson, you will be able to:
                • Explain the concept of a random variable.
                • Distinguish between discrete and continuous random variables.
                • Given the experiment, and the random variable defined, create the frequency, probability, and cumulative distributions, and their attendant graphs.
                • Answer probability questions based on the distributions created from the random variable
                Approximate time required for the readings for this lesson (at 144 words/minute): 1 hour and 53 minutes.

                Click here to start this lesson

                2 URLs, 1 Quiz
                • Required Learning Resources and Activities
                • Random Variables URL

                  Read the entire page and watch the included video. (17 minutes)

                  University of Florida - 2022

                • Anatomy of a Random Variable URL

                  Watch the entire video. (24 minutes)

                • Quiz: Module 4: Lessons 1, 2 & 3

                  To access the quiz, click on the name of the quiz provided above. On the following screen, click the attempt quiz button to view the case studies and respond to the questions.

              • Module 4: Lesson 4: Discrete Random Variables and Discrete Distributions of Random Variables

                Student Learning Outcomes:
                Upon completion of this lesson, you will be able to:
                • Find the expected value (mean), variance, and standard deviation of a discrete random variable.
                • Identify a situation in which a binomial random variable can be used to model and predict.
                • Compute and interpret the mean and standard deviation of a binomial random variable.
                • Calculate probabilities using the binomial distribution.
                • Identify a situation in which a Poisson random variable can be used to model and predict.
                • Calculate probabilities using the Poisson distribution.
                Approximate time required for the readings for this lesson (at 144 words/minute): 3 hours and 48 minutes.

                Click here to start this lesson

                4 URLs
                • Required Learning Resources and Activities
                • Discrete Random Variables URL

                  Read the entire page and watch the included video. (26 minutes)

                  University of Florida - 2022

                • Binomial Random Variables URL

                  Read the entire page and watch the included video. (22 minutes)

                • The Poisson Distribution URL

                  Read the entire page and watch the two short videos included. (15 minutes)

                  Penn State University - 2021

                • Finding Poisson Probabilities URL

                  Read the entire page and watch the two short videos included. (13 minutes)

              • Module 4: Lesson 5: Continuous Random Variables and the Normal Distribution

                Student Learning Outcomes:
                Upon completion of this lesson, you will be able to:
                • Interpret the mean, standard deviation, and shape of probability distributions of continuous random variables.
                • Explain the key features of the normal distribution.
                • Calculate probabilities of a non-standard normal distribution using the standard normal distribution tables.
                • Use the Empirical Rule to compute percentages under the curve of the normal distribution.
                • Standard Normal Distribution Tables.
                Approximate time required for the readings for this lesson (at 144 words/minute): 5 hours and 56 minutes.

                Click here to start this lesson

                3 URLs, 1 Forum, 2 Quizzes
                • Required Learning Resources and Activities
                • Continuous Random Variables URL

                  Read the entire page and watch the included video. (17 minutes)

                  Florida State University - 2022

                • Normal Random Variables URL

                  Read the entire page and watch the included video. (20 minutes)

                  Florida State University - 2022

                • The Sandard Normal Distribution URL

                  Read the entire page and watch the included video. (24 minutes)

                  Florida State University - 2022

                • Discussion Forum 4

                  In this activity, you will discuss some of the key features and properties of the normal distribution. 

                  Step 1. Review

                  Review the learning resources for this lesson before answering the question.

                  Step 2. Analyze

                  Analyze and discuss the question below.

                  65

                  Step 3. Respond

                  Respond to the case problem by writing a 300-500-word discussion post with the following inclusions.

                  Step 4. Share

                  To share your work, click on the “Add a new discussion topic” button under this post and paste your work in the “Message” box. Make sure to reference others’ intellectual property when necessary. All references should follow 7th Edition APA formatting. For further instructions, see the resource on the Himmelfarb Health Sciences Library: APA citation resource (N.B. references are excluded from word counts).

                  Step 5: Interact

                  To complete the activity, you will need to reply to at least two posts made by your peers respectfully and professionally. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If a peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “Post to the forum.”

                • Quiz: Module 4: Lessons 4 & 5

                  To access the quiz, click on the name of the quiz provided above. On the following screen, click the attempt quiz button to view the case studies and respond to the questions.

                • Quiz: Module 4

                  To access the quiz, click on the name of the quiz provided above. On the following screen, click the "Preview quiz now" button to respond to the questions.

              • Module 5: Sampling Distributions

                Competency covered in this module: 
                • MCAT: Reason about statistical significance and uncertainty (e.g., interpreting statistical significance leve and confidence intervals.
                • Module 5: Lesson 1: Sampling Variablilty

                  Student Learning Outcomes:
                  Upon completion of this lesson, you will be able to:
                  • Discuss the concept of variability of the sample statistics, and the connection between variability, the population parameter, and sample size.
                  Approximate time required for the readings for this lesson (at 144 words/minute): 48 minutes.

                  Click here to start this lesson

                  1 URL
                  • Required Learning Resources and Activities
                  • Sample Variablility and Sampling Distributions URL

                    Read entire Page and watch included video. (16 minutes)

                    University of Bristol - 2021

                • Module 5: Lesson 2: Sampling Distributions

                  Student Learning Outcomes:
                  Upon completion of this lesson, you will be able to:
                  • Explain the concept of a sampling distribution.
                  • Distinguish between the Sampling Distribution of the Mean, a distribution of the sample, and the population distribution.
                  Approximate time required for the readings for this lesson (at 144 words/minute): 27 minutes.

                  Click here to start this lesson
                  1 URL
                  • Required Learning Resources and Activities
                  • Introduction to sampling distributions URL

                    Watch entire Video. (10 minutes)

                    Khan Academy - 2022

                • Module 5: Lesson 3: The Central Limit Theorem

                  Student Learning Outcomes:
                  Upon completion of this lesson, you will be able to:
                  • Explain the Central Limit Theorem (CLT) and its importance in Inferential Statistics.
                  • Find and apply the mean and standard error of the sampling distribution of the mean, as summarized by the CLT.
                  Approximate time required for the readings for this lesson (at 144 words/minute): 3 hours and 35 minutes.

                  Click here to start this lesson

                  2 URLs, 1 Forum, 1 Quiz
                  • Required Learning Resources and Activities
                  • The Central Limit Theorem URL

                    Watch entire Video. (10 minutes)

                    Khan Academy - 2022

                  • Sampling Distribution of the Sample Mean, x-bar URL

                    Read entire page. (20 minutes)

                    Florida state University - 2022

                  • Practical Activity 4 Forum

                    Student Learning Outcome (Module 5 Lesson 3): Find and apply the mean and standard error of the sampling distribution of the mean, as summarized by the Central Limit Theorem.

                    Step 1. Review

                    Review the learning resources for this lesson before studying the case problem.

                    Step 2. Analyze

                    Analyze the case problem below.

                    Part 1:

                    Use the set of numbers {10, 20, 30, 40, 50} to perform he following tasks:

                    1. Make a list of all possible samples of size 2 that could be drawn with replacement from this set of numbers, for example, (20, 30), (10, 50), (40, 40).
                    2. Find all the sample means and construct the sampling distribution of sample means in tabular form, an example of which is shown below.

                    82

                    3. Find all the sample ranges and construct the sampling distribution of sample ranges in tabular form, an example of which is shown below.

                    22

                    Part 2:

                    4. Using the Central Limit Theorem, calculate the mean and standard error of the sampling distribution of sample means.

                    Step 3. Respond

                    Respond to the case problem by writing answers to Questions 1, 2, 3, and 4.

                    Step 4. Share

                    To share your work, access to the first post below and click on the “Reply” button under this post and paste your work into the “Message” box. Make sure to reference others’ intellectual property when necessary. All references should follow 7th Edition APA formatting. For further instructions, see the resource on the Himmelfarb Health Sciences Library: APA citation resource (N.B. references are excluded from word counts).

                    Step 5: Interact

                    To complete the activity, you will need to reply to at least two posts by your peers respectfully and professionally. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If a peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “post to the forum.”

                  • Quiz: Module 5

                    To access the quiz, click on the name of the quiz provided above. On the following screen, click the attempt quiz button to respond to the questions.

                • Module 6: Estimation

                  Competency covered in this module: 
                  • MCAT: Relating statistical significance and uncertainty to conclusions that can or cannot be made about the study.
                  • MCAT: Using data to explain relationships between variables.
                  • Module 6: Lesson 1: Estimation

                    Student Learning Outcomes:
                    Upon completion of this lesson, you will be able to:
                    • Explain why we need to estimate.
                    • Distinguish between point and interval estimates.
                    • Explain what a margin of error is.
                    • Find the margin of error given the confidence interval limits.
                    • Explain what a confidence interval is.
                    Approximate time required for the readings for this lesson (at 144 words/minute): 1 hour and 12 minutes.

                    Click here to start this lesson

                    1 URL
                    • Required Learning Resources and Activities
                    • Confidence Intervals Introduction URL

                      Read entire page: Confidence Intervals Introduction and watch accompanying video. (24 minutes)

                      Rice University - 2021

                  • Module 6: Lesson 2: Confidence Intervals on Single Means and Proportions

                    Student Learning Outcomes:
                    Upon completion of this lesson, you will be able to:
                    • Compute and interpret a confidence interval on the mean when σ is known.
                    • t-Distribution Tables.
                    • Determine whether to use a t-distribution or a normal distribution to compute confidence intervals.
                    • Compute a confidence interval on the mean when σ is estimated.
                    • Compute and interpret confidence intervals for proportions.
                    Approximate time required for the readings for this lesson (at 144 words/minute): 2 hours and 57 minutes.

                    Click here to start this lesson

                    2 URLs, 1 Forum
                    • Required Learning Resources and Activities
                    • Confidence Interval on the Mean URL

                      Read entire page and watch accompanying video: Confidence Interval on the Mean. (18 minutes)

                      2021

                    • Proportion URL

                      Read entire page: Confidence Intervals for Proportions and watch accompanying video. (11 minutes)

                    • Practical Activity 5 Forum

                      Student Learning Outcome (Module 6 Lesson 2): Compute and interpret confidence intervals for proportions.

                      Step 1. Review

                      Review the learning resources for this lesson before studying the case problem.

                      Step 2. Analyze

                      Analyze the case problem below.

                      The article “Doctors Cite Burnout in Mistakes” (San Luis Obispo Tribune, March 5, 2002) reported that many doctors completing their residency have financial struggles that could interfere with training. In a sample of 115 residents, 38 reported working moonlighting jobs, and 22 reported high credit card debt. Suppose that it is reasonable to consider this sample of 115 a random sample of all medical residents in the United States. 

                      1. Construct and interpret a 95% confidence interval for the proportion of U.S. medical residents who work moonlighting jobs.

                      2. Construct and interpret a 90% confidence interval for the proportion of U.S. medical residents who report high credit card debt.

                      3. Give two reasons why the confidence interval in Part 1 is wider than in Part 2.

                      4. Consider the following statement: If the process of selecting a sample of size 115 and then computing the corresponding confidence interval is repeated 100 times, 95% of the resulting intervals will include the true population proportion. Is this statement correct? Why or why not?

                      Step 3. Respond

                      Respond to the case problem by writing answers to Parts 3 and 4.

                      Step 4. Share

                      To share your work, access to the first post below and click on the “Reply” button under this post and paste your work into the “Message” box. Make sure to reference others’ intellectual property when necessary. All references should follow 7th Edition APA formatting. For further instructions, see the resource on the Himmelfarb Health Sciences Library: APA citation resource (N.B. references are excluded from word counts).

                      Step 5: Interact

                      To complete the activity, you will need to reply to at least two posts by your peers respectfully and professionally. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If a peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “post to the forum.”

                  • Module 6: Lesson 3: Confidence Intervals on Differences of Two Means and Proportions

                    Student Learning Outcomes:
                    Upon completion of this lesson, you will be able to:
                    • Find and Interpret the Confidence Interval for the Difference in Means of Two Independent Samples.
                    • Find and Interpret the Confidence Interval for the Difference in Two Proportions.
                    Approximate time required for the readings for this lesson (at 144 words/minute): 2 hours and 29 minutes.

                    Click here to start this lesson

                    2 URLs, 1 Quiz
                    • Required Learning Resources and Activities
                    • Confidence Interval for Two Independent Samples, Continuous Outcome URL

                      Read entire Page. (20 minutes)

                      Bistibn University School of Public Health - 2021

                    • Confidence Interval for Two Independent Samples, Dichotomous Outcome URL

                      (13 minutes)

                      Bistibn University School of Public Health - 2021

                    • Quiz: Module 6

                      To access the quiz, click on the name of the quiz provided above. On the following screen, click the attempt quiz button to respond to the questions.

                  • Module 7: Testing of Hypotheses

                    Competency covered in this module: 
                    • MCAT: Use data to answer research questions and draw conclusions.
                    • MCAT: Identify testable research questions and hypotheses.
                    • MCAT: Identify conclusions that are supported by research results and determine the implications of results for real-world situations.
                    • MCAT: Distinguish between results that do and do not support generalizations about populations.
                    • Module 7: Lesson 1: The Basics of Hypothesis Testing

                      Student Learning Outcomes:
                      Upon completion of this lesson, you will be able to:
                      • Explain the meaning of the term "statistically significant."
                      • Determine the null and alternative hypotheses from a description of an experiment.
                      • Describe how a p-value is used to cast doubt on the null hypothesis.
                      • Differentiate between Type I and Type II errors.
                      • State the null hypothesis for both one-tailed and two-tailed tests for a given Hypothesis test.
                      Approximate time required for the readings for this lesson (at 144 words/minute): 3 hours and 30 minutes.

                      Click here to start this lesson

                      9 URLs
                      • Required Learning Resources and Activities
                      • Introduction: The Logic of Hypothesis Testing URL

                        Read entire page: Introduction to Hypothesis Testing. (8 minutes)

                        Rice University - 2021

                      • The Logic of Hypothesis Testing - Introduction (Video) URL

                        Watch the video: Introduction to Hypothesis Testing. (11 minutes)

                        Rice University - 2021

                      • The Elements of Hypothesis Testing URL

                        Read entire page - Section 8.1: Elements of Hypothesis Testing. (15 minutes)

                        LibreTexts - UC Davis - 2022

                      • Significance Testing URL

                        Read entire page: Significance Testing. (6 minutes)

                        Rice University - 2021

                      • The Logic of Hypothesis Testing: Significance Testing (Video) URL

                        Watch video: Significance Testing. (6 minutes)

                        Rice University - 2021

                      • Type I and Type II Errors URL

                        Read entire page: Type I and Type II Errors. (5 minutes)

                        Rice University - 2021

                      • The Logic of Hypothesis Testing: Type I and Type II Errors (Video) URL

                        Watch video: Type I and Type II Errors. (8 minutes)

                        Rice University - 2021

                      • One- and Two-Tailed Tests URL

                        Read entire page: One- and Two-Tailed Tests. (5 minutes)

                        Rice University - 2021

                      • The Logic of Hypothesis Testing: One- and Two-Tailed Tests (Video) URL

                        Watch the video: One- and Two-Tailed Tests. (6 minutes)

                        Rice University - 2021

                    • Module 7: Lesson 2: Hypothesis Testing of the Population Mean and Proportion

                      Student Learning Outcomes:
                      Upon completion of this lesson, you will be able to:
                      • Perform one- and two-tailed hypothesis tests for the mean in the case when is known (or for a large sample), using the steps involved in significance testing.
                      • Perform one- and two-tailed hypothesis tests for the mean in the case when has to be estimated (of for a small sample), using the steps involved in significance testing.
                      • Use the steps involved in significance testing to perform one- and two-tailed hypotheses tests for the single proportion.
                      Approximate time required for the readings for this lesson (at 144 words/minute): 3 hours and 25 minutes.

                      Click here to start this lesson

                      3 URLs, 1 Quiz
                      • Required Learning Resources and Activities
                      • 8.2: Large Sample Tests for a Population Mean URL

                        Read entire Page - Section 8.2: Largel Sample Test for the Mean. (20 minutes)

                        LibreBooks -UC Davis - 2022

                      • 8.4: Small Sample Tests for a Population Mean URL

                        Read Entire Page - Section 8.4: Small Sample Test for the Mean. (20 minutes)

                        LibreBooks -UC Davis - 2022

                      • 8.5: Large Sample Tests for a Population Proportion URL

                        Read entire page - Section 8.5: Large Sample Test for the Population Proportion. (25 minutes)

                        LibreBooks -UC Davis - 2022

                      • Quiz: Module 7: Lessons 1 & 2

                        To access the quiz, click on the name of the quiz provided above. On the following screen, click the attempt quiz button to respond to the questions.

                    • Module 7: Lesson 3: Testing Two Samples

                      Student Learning Outcomes:
                      Upon completion of this lesson, you will be able to:
                      • Explain the steps involved in significance testing for the difference in the means of two independent samples.
                      • Explain the steps involved in significance testing for the difference in the means of paired samples.
                      • Explain the steps involved in significance testing for the difference in two proportions.
                      Approximate time required for the readings for this lesson (at 144 words/minute): 3 hours and 15 minutes.

                      Click here to start this lesson

                      3 URLs
                      • Required Learning Resources and Activities
                      • 9.1: Comparison of Two Population Means- Large, Independent Samples URL

                        Read entire page - Section 9.1: Comparison of Two Population Means - Large, Independent samples. (20 minutes)

                        LibreBooks -UC Davis - 2022

                      • 9.3: Comparison of Two Population Means - Paired Samples URL

                        Read entire page - Section 9.3: Comparison of two population means, Paired Samples. (25 minutes)

                        LibreBooks -UC Davis - 2022

                      • 9.4: Comparison of Two Population Proportions URL

                        Read entire page - Section 9.4: Comparison of Two Population Proportions. (20 minutes)

                        LibreBooks -UC Davis - 2022

                    • Module 7: Lesson 4: Testing with Categorical Variables

                      Student Learning Outcomes:
                      Upon completion of this lesson, you will be able to:
                      • Describe the Chi-Square distribution.
                      • Perform and interpret a Chi-Square test for Independence.
                      • Perform and interpret a Chi-Square Goodness-of-Fit test.
                      Approximate time required for the readings for this lesson (at 144 words/minute): 7 hours and 19 minutes.

                      Click here to start this lesson

                      9 URLs, 1 Forum, 2 Quizzes
                      • Required Learning Resources and Activities
                      • The Chi-Square Distribution URL

                        Read entire page: The Chi-Square Distribution. (5 minutes)

                        Rice University - 2021

                      • The Chi-Square Distribution (Video) URL

                        Watch the video: Chi-Square Distribution. (3 minutes)

                        Rice University - 2021

                      • The Chi-Square Test for Independence URL

                        Read entire page: Section - 11.3: Chi Square Test for Independence. (6 minutes)

                        Eberly College of Science, Penn State University - 2022

                      • 11.3.1 - Example: Gender and Online Learning URL

                        Read entire page: Worked example. (8 minutes)

                        Eberly College of Science, Penn State University - 2022

                      • The Chi-Square Test for Independence (Video) URL

                        Watch the entire lecture video. (27 minutes)

                      • 11.2 - Goodness of Fit Test URL

                        Read entire page: Section - 11.2: Chi Square Goodness-of-Fit Test. (7 minutes)

                        Eberly College of Science, Penn State University - 2022

                      • 11.2.1 - Five Step Hypothesis Testing Procedure URL

                        Read entire page - Section 11.2.1 -Five-Step Procedure. (7 minutes)

                        Eberly College of Science, Penn State University - 2022

                      • 11.2.1.1 - Video: Cupcakes (Equal Proportions) URL

                        Watch video. (7 minutes)

                        Eberly College of Science, Penn State University - 2022

                      • 11.2.1.2- Cards (Equal Proportions) URL

                        Read entire page. (9 minutes)

                        Eberly College of Science, Penn State University - 2022

                      • Practical Activity 6 Forum

                        Student Learning Outcome (Module 7 Lesson 4): Perform and interpret a Chi-Square Test for Independence.

                        Step 1. Review

                        Review the learning resources for this lesson before studying the case problem.

                        Step 2. Analyze

                        Analyze the case problem below.

                        The following table is based on data from 21,870 physicians aged 40 – 84 who are participating in the Physicians Health Study (“Light-to-Moderate Alcohol Consumption and Risk of Stroke Among US Physicians,” New England Journal of Medicine [2019]: 1557 - 1564): 

                        1
4

                        1. Calculate row proportions by dividing each observed count by the corresponding row total. Are the proportions falling in each of the alcohol consumption categories similar for the three smoking categories?

                        2. Test the hypothesis using 𝛼 = 0.05 that Smoking Status and Alcohol Consumption are independent.

                        3. Is your test result in Part 2 consistent with what you expected based on your answer to Part 1? If not, explain why your initial impression based on the proportions may not have been accurate.

                        Step 3. Respond

                        Respond to the case problem by writing answers to Parts 1, 2, and 3.

                        Step 4. Share

                        To share your work, access to the first post below and click on the “Reply” button under this post and paste your work into the “Message” box. Make sure to reference others’ intellectual property when necessary. All references should follow 7th Edition APA formatting. For further instructions, see the resource on the Himmelfarb Health Sciences Library: APA citation resource (N.B. references are excluded from word counts).

                        Step 5: Interact

                        To complete the activity, you will need to reply to at least two posts by your peers respectfully and professionally. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If a peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “post to the forum.”

                      • Quiz: Module 7: Lessons 3 & 4

                        To access the quiz, click on the name of the quiz provided above. On the following screen, click the attempt quiz button to respond to the questions.

                      • Quiz: Module 7

                        To access the quiz, click on the name of the quiz provided above. On the following screen, click the attempt quiz button to respond to the questions.

                    • Module 8: Introduction to Linear Regression Analysis

                      Competency covered in this module: 
                      • MCAT: Use data to explain relationships between variables or make predictions.
                      • Module 8: Lesson 1: Linear Correlation

                        Student Learning Outcomes:
                        Upon completion of this lesson, you will be able to:
                        • Explain the concept of correlation and how it differs from causation.
                        • Identify positive and negative associations from a scatter plot.
                        • Calculate r, the correlation coefficient of the two variables.
                        • Utilize the rule of thumb for the interpretation of the calculated correlation coefficient.
                        • Differentiate between the coefficient of correlation and the coefficient of determination.
                        • Test the Correlation Coefficient for Significance.
                        Approximate time required for the readings for this lesson (at 144 words/minute): 3 hours and 48 minutes.

                        Click here to start this lesson

                        5 URLs, 1 Forum
                        • Required Learning Resources and Activities
                        • Correlation and causation URL

                          Read entire page. (3 minutes)

                          Social and Public Health Unit, University of Glasgow - 2022

                        • Scatterplots and Correlation URL

                          Read Entire section - Scatterplots and Correlation. (18 minutes)

                          University of West Georgia - 2021

                        • Correlation and Simple linear Regession URL

                          Read up to the end of Linear Correlation Coefficient (before Simple Linear Regression). (25 minutes)

                          Milne Library, SUNY at Genesco - 2022

                        • What is the difference between coefficient of determination, and coefficient of correlation? URL

                          Read entire page. (3 minutes)

                          University of Wisconsin, Green Bay - 2022

                        • 12.5: Testing the Significance of the Correlation Coefficient URL

                          Read entire page. (27 minutes)

                          LibeTexts, UC Davis - 2022

                        • Discussion Forum 5

                          In this activity, you will discuss the concepts of correlation and causation. 

                          Step 1. Review

                          Review the learning resources for this lesson before answering the question.

                          Step 2. Analyze

                          Analyze and discuss the question below.

                          68

                          Step 3. Respond

                          Respond to the case problem by writing a 300-500-word discussion post with the following inclusions.

                          Step 4. Share

                          To share your work, click on the “Add a new discussion topic” button under this post and paste your work in the “Message” box. Make sure to reference others’ intellectual property when necessary. All references should follow 7th Edition APA formatting. For further instructions, see the resource on the Himmelfarb Health Sciences Library: APA citation resource (N.B. references are excluded from word counts).

                          Step 5: Interact

                          To complete the activity, you will need to reply to at least two posts made by your peers in a respectful and professional manner. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If a peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “Post to the forum.”

                      • Module 8: Lesson 2: The Basics of Linear Regression

                        Student Learning Outcomes:
                        Upon completion of this lesson, you will be able to:
                        • Explain the concept of Linear Regression.
                        • Find the Linear Regression equation and use it to Predict.
                        • Test the Outliers, Influential Observations, and Leverage Points.
                        Approximate time required for the readings for this lesson (at 144 words/minute): 4 hours and 52 minutes.

                        Click here to start this lesson

                        4 URLs, 1 Quiz
                        • Required Learning Resources and Activities
                        • Introduction to Linear Regression URL

                          Read entire page. (8 minutes)

                          Rice University - 2021

                        • Intro to Regression (Video) URL

                          Watch the entire video. (5 minutes)

                          Rice University - 2021

                        • What is Simple Linear Regression? URL

                          Read entire page. (5 minutes)

                          Penn State, Elberly College - 2020

                        • Applied Regression Analysis - Lesson 9.1: The Distinction Between Outliers and High Leverge Observations URL

                          Read entire page. (35 minutes)

                          Penn State University, Eberly College of Science

                        • Quiz: Module 8

                          To access the quiz, click on the name of the quiz provided above. On the following screen, click the attempt quiz button to respond to the questions.

                      • Final Exam

                        Click here to start Final Examination

                        • Final Exam Quiz
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                          To take the final exam, you must complete all quizzes and complete all the required activities. The final exam consists of 37 questions, and you will have 95 minutes to complete it. When the time is over, you will have two minutes to submit your attempt before it expires, and your progress is discarded. You will not be able to answer additional questions in the grace period.

                          To access the exam, click on the name of the exam provided above. On the following screen, click the attempt quiz button to respond to the questions.


                      • Course and Self Evaluation & Certificate

                        In this section, you can provide feedback about this course to help us make NextGenU.org better. Once evaluations are completed, you will be able to download your certificate of completion.

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                        • Course Evaluation Questionnaire
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                      • Course Activities

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                        • Practical Activities. Page
                        • Discussion Forums Page
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                      Course Activities and Resources
                      • Syllabus
                      • Resources
                      • Practical Activities
                      • Discussion Forums
                      • Quizzes
                      • MATH 2
                      • General
                      • How to create an account and enroll in the course?
                      • MATH 2 Homepage
                      • Module 1: Introduction to Statistics and Research in Health Care
                      • Module 1: Lesson 1: Research, The Scientific Method, and the Role of Statistics in the Health Care Field
                      • Module 1: Lesson 2: Data, Variables, Populations, Samples, and Measurement 
                      • Module 1: Lesson 3: Research Design and Data Collection
                      • Module 1: Lesson 4: Randomization and Sampling
                      • Module 2: Graphical Methods of Describing Data
                      • Module 2: Lesson 1: Displaying Univariate Data
                      • Module 2: Lesson 2: Displaying Bivariate Data
                      • Module 2: Lesson 3: Communicating and Interpreting the Results of Graphical Statistical Analysis
                      • Module 3: Numerical Methods of Describing Data: Summary Numbers
                      • Module 3: Lesson 1: Measures of Central Tendency
                      • Module 3: Lesson 2: Measures of Dispersion
                      • Module 3: Lesson 3: Measures of Position
                      • Module 3: Lesson 4: Using Boxplots to Summarize Datasets
                      • Module 3: Lesson 5: Extra Topics on Describing Data
                      • Module 4: Probability, Random Variables, and Distributions
                      • Module 4: Lesson 1: Counting Rules
                      • Module 4: Lesson 2: Probability Basics
                      • Module 4: Lesson 3: Random Variables
                      • Module 4: Lesson 4: Discrete Random Variables and Discrete Distributions of Random Variables
                      • Module 4: Lesson 5: Continuous Random Variables and the Normal Distribution
                      • Module 5: Sampling Distributions
                      • Module 5: Lesson 1: Sampling Variablilty
                      • Module 5: Lesson 2: Sampling Distributions
                      • Module 5: Lesson 3: The Central Limit Theorem
                      • Module 6: Estimation
                      • Module 6: Lesson 1: Estimation
                      • Module 6: Lesson 2: Confidence Intervals on Single Means and Proportions
                      • Module 6: Lesson 3: Confidence Intervals on Differences of Two Means and Proportions
                      • Module 7: Testing of Hypotheses
                      • Module 7: Lesson 1: The Basics of Hypothesis Testing
                      • Module 7: Lesson 2: Hypothesis Testing of the Population Mean and Proportion
                      • Module 7: Lesson 3: Testing Two Samples
                      • Module 7: Lesson 4: Testing with Categorical Variables
                      • Module 8: Introduction to Linear Regression Analysis
                      • Module 8: Lesson 1: Linear Correlation
                      • Module 8: Lesson 2: The Basics of Linear Regression
                      • Final Exam
                      • Course and Self Evaluation & Certificate
                      • Course Activities
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