Introduction to Statistics (for Life Sciences)

An introductory statistics course (MAT150)

Course Description

In this course, students apply research design and statistics principles to analyze and interpret data and draw conclusions about experimental situations relevant to the sciences. Topics include random sampling, graphic and numeric descriptive data analysis, normal distribution, hypothesis testing, t-tests, analysis of variance, correlation, and regression. Students will use the statistical software R to examine data graphically and perform statistical analyses.

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Objectives

In this course, students will learn the fundamentals of graphic and numeric data analysis, inferences about population means, and hypothesis testing that they can use to answer research questions in various experimental situations. You will also learn how to use a comprehensive statistical software called R (RStudio Cloud) to conduct your analyses and interpret, organize, and explain your results and conclusions in written and verbal formats. This course fulfills a requirement in the applied mathematics major, data science major, and many other major programs. It can also be used for a mathematics minor.

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Textbook

Peck, R., & Devore, J. (2012). Statistics: The Exploration and Analysis of Data(7thEd). Boston, MA: Brooks/Cole Cengage Learning. E-books, used books, and rented books are acceptable.

@book{peck2011statistics,
  title={Statistics: The exploration \& analysis of data},
  author={Peck, Roxy and Devore, Jay L},
  year={2011},
  publisher={Cengage Learning}
}

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Learning Outcomes

Upon successful completion of this course, you will be able to:

1. Distinguish among different types of data.
2. Describe and apply a variety of random sampling methods.
3. Summarize data sets numerically and graphically with the aid of technology.
4. Identify appropriate statistical analyses for different experimental situations with numerical data.
5. Identify the underlying assumptions and perform inferential hypothesis testing using manual and computer statistical analysis methods, including t-tests, analysis of variance, multiple comparisons, correlation, and regression.
6. Interpret the results of experimental situations based on statistical data analysis.
7. Recognize some sources of bias and limitations of statistical analysis and inferences.
8. Apply the understanding of statistics to interpret and evaluate research reported by others.
9. Discuss and present statistical analysis, including methods, results, conclusions, and justifications based on supporting evidence in verbal and written formats.

Furthermore, MAT150 will help students build mathematical habits of mind by:

• developing their critical thinking and communication skills through activities that teach students how to:

  • state problems clearly,
  • articulate assumptions,
  • understand the importance of precise definitions and reason logically to conclusions,
  • identify and model essential features of a complex situation, modify models as needed for traceability, draw valuable conclusions, and
  • use and compare analytical, visual, and numeracy methods;

• linking theory to practice by being exposed to a variety of contemporary applications in mathematics that motivate and illustrate the concepts they are learning, as well as becoming aware of connections to other fields (both within and outside of mathematics) and learning to apply mathematical concepts to problems in those fields;

• developing mathematical independence and participating in open-ended inquiry;

• operating current technologies; and

• learning to read, interpret, analyze, and write proofs.

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Topics

1. The role of statistics and the data analysis process
2. Data collection
3. Visual descriptions of data
4. Numerical descriptions of data
5. Summarizing bivariate data
6. Probability
7. Population distributions
8. Sample variation and sample distributions
9. Estimation
10. Hypothesis testing
11. Comparing two populations
12. Analysis of variance (ANOVA)

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Core Curriculum

This course is part of the Core Curriculum taken by undergraduates and provides a foundation in key themes in the liberal arts. It addresses the Quantitative Reasoning (QR) component of the Core and the following QR learning outcomes. Upon successful completion of this course, students will be able to:

1. Read and analyze data and draw inferences.
2. Formulate and solve real-world problems using mathematical and statistical models.
3. Communicate quantitative information using symbolic, numeric, graphic, and verbal representations.
4. Judge the soundness and accuracy of quantitative results.
5. Make informed decisions using appropriate digital tools and resources.