
General

MATH 2 Homepage
Welcome to Math 2, the second course in the Mathematics series for the PreHealth Sciences Training Certificate. This course and the Certificate are designed primarily for learners interested in preparing for and gaining entry for healthrelated programs, and to help address the prerequisites for the Medical College Admission Test (MCAT). This Math 2 course provides indepth learning related to general mathematical concepts and techniques used in the bachelor’slevel 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 competencybased, using competencies based on the Association of American Medical Colleges’ Medical College Admission Test. It uses learning resources from accredited, academic, professional, and worldclass 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 AsadiLari, a former MDPHD 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.
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 multiplechoice 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 multiplechoice 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 cosponsoring 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:
 Pretest
 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 partneruniversitysponsored 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 cosponsoring 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 selfassessments;
 A copy of your certificate of completion, with the cosponsoring organizations listed.
To obtain a degree, NextGenU.org cosponsors degree programs with institutional partners. To obtain a full degree cosponsored 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 pretest.
 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.
 MiamiDade: Demonstrate an understanding of descriptive statistics by contrasting between the levels of data.
 MCAT: Distinguish between samples and populations.
 MiamiDade: 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.
 MiamiDade: Demonstrate an understanding of descriptive statistics by: designing and formulating sources of decisionmaking 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)
 MiamiDade: Demonstrate an understanding of descriptive statistics by: designing and formulating sources of decisionmaking 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.
2 URLs, 1 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.
7 URLs, 1 Quiz 
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.
4 URLs 
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.
3 URLs, 1 Forum, 2 Quizzes 
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, Stemandleaf Plots, and Frequency tables.
8 URLs 
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.
5 URLs 
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
2 URLs, 1 Forum, 1 Quiz 
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.
 MiamiDade: 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.
5 URLs 
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.
3 URLs 
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 zscore of a measure within a distribution.
 Normalize scores from different distributions to compare them.
3 URLs, 1 Quiz 
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), Hspread, step, adjacent value, outside value (outlier), and far out value (far outlier).
 Use the 5number summary to create boxplots to describe a dataset.
 Create and interpret sidebyside box (parallel) plots to compare two variables.
 Create an adjusted boxplot to identify outliers.
 Create an Adjusted Box Plot.
 Find Grouped Mean and Variance.
Click here to start this lesson3 URLs, 1 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 outofcontrol.
6 URLs, 1 Forum, 2 Quizzes 
Module 4: Probability, Random Variables, and Distributions
Competency covered in this module:
MiamiDade: 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.
1 URL 
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 nondisjoint 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.
8 URLs, 1 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
2 URLs, 1 Quiz 
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.
4 URLs 
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 nonstandard 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.
3 URLs, 1 Forum, 2 Quizzes 
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.
1 URL 
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.
1 URL 
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.
2 URLs, 1 Forum, 1 Quiz 
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.
1 URL  Explain why we need to estimate.

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.

tDistribution Tables.
 Determine whether to use a tdistribution 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.
2 URLs, 1 Forum  Compute and interpret a confidence interval on the mean when σ is known.

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.
2 URLs, 1 Quiz  Find and Interpret the Confidence Interval for the Difference in Means of Two Independent Samples.

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 realworld 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 pvalue is used to cast doubt on the null hypothesis.
 Differentiate between Type I and Type II errors.
 State the null hypothesis for both onetailed and twotailed tests for a given Hypothesis test.
9 URLs  Explain the meaning of the term "statistically significant."

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 twotailed 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 twotailed 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 twotailed hypotheses tests for the single proportion.
3 URLs, 1 Quiz  Perform one and twotailed hypothesis tests for the mean in the case when is known (or for a large sample), using the steps involved in significance testing.

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.
3 URLs  Explain the steps involved in significance testing for the difference in the means of two independent samples.

Module 7: Lesson 4: Testing with Categorical Variables
Student Learning Outcomes:
Upon completion of this lesson, you will be able to: Describe the ChiSquare distribution.

Perform and interpret a ChiSquare test for Independence.
 Perform and interpret a ChiSquare GoodnessofFit test.
9 URLs, 1 Forum, 2 Quizzes  Describe the ChiSquare distribution.

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.
5 URLs, 1 Forum  Explain the concept of correlation and how it differs from causation.

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.
4 URLs, 1 Quiz  Explain the concept of Linear Regression.

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.