Elementary Statistics I

Course Number:

STAT 243Z

Transcript Title:

Elementary Statistics I

Created:

Aug 15, 2022

Updated:

Oct 24, 2023

Total Credits:

4

Lecture Hours:

30

Lecture / Lab Hours:

20

Lab Hours:

0

Satisfies Cultural Literacy requirement:

No

Satisfies General Education requirement:

Yes

Grading Options

A-F, P/NP, Audit

Default Grading Options

A-F

Repeats available for credit:

0

Alignment with Institutional Learning Outcomes

Major

1. Communicate effectively using appropriate reading, writing, listening, and speaking skills. (Communication)

Major

2. Creatively solve problems by using relevant methods of research, personal reflection, reasoning, and evaluation of information. (Critical thinking and Problem-Solving)

Major

3. Extract, interpret, evaluate, communicate, and apply quantitative information and methods to solve problems, evaluate claims, and support decisions in their academic, professional and private lives. (Quantitative Literacy)

Not Addressed

4. Use an understanding of cultural differences to constructively address issues that arise in the workplace and community. (Cultural Awareness)

Major

5. Recognize the consequences of human activity upon our social and natural world. (Community and Environmental Responsibility)

To establish an intentional learning environment, Institutional Learning Outcomes (ILOs) require a clear definition of instructional strategies, evidence of recurrent instruction, and employment of several assessment modes.

Major Designation

1. The outcome is addressed recurrently in the curriculum, regularly enough to establish a thorough understanding.
2. Students can demonstrate and are assessed on a thorough understanding of the outcome.
   • The course includes at least one assignment that can be assessed by applying the appropriate CLO rubric.

Minor Designation

1. The outcome is addressed adequately in the curriculum, establishing fundamental understanding.
2. Students can demonstrate and are assessed on a fundamental understanding of the outcome.
   • The course includes at least one assignment that can be assessed by applying the appropriate CLO rubric.

Suggested Outcome Assessment Strategies

The determination of assessment strategies is generally left to the discretion of the instructor. Here are some strategies that you might consider when designing your course: writings (journals, self-reflections, pre writing exercises, essays), quizzes, tests, midterm and final exams, group projects, presentations (in person, videos, etc), self-assessments, experimentations, lab reports, peer critiques, responses (to texts, podcasts, videos, films, etc), student generated questions, Escape Room, interviews, and/or portfolios.

Course Activities and Design

The determination of teaching strategies used in the delivery of outcomes is generally left to the discretion of the instructor. Here are some strategies that you might consider when designing your course: lecture, small group/forum discussion, flipped classroom, dyads, oral presentation, role play, simulation scenarios, group projects, service learning projects, hands-on lab, peer review/workshops, cooperative learning (jigsaw, fishbowl), inquiry based instruction, differentiated instruction (learning centers), graphic organizers, etc.

Course Content

Outcome #1: Critically read, interpret, report, and communicate the results of a statistical study along with evaluating assumptions, potential for bias, scope, and limitations of statistical inference.

1. Classify study designs and variable types and identify methods of summary and analysis.

• Common statistical terminology including: population, sample, variable, and statistical inference.
• Distinction between qualitative and quantitative data and discrete and continuous data.
• Data distributions and their shape, including whether they are symmetric or skewed, heavy or light tailed, unimodal, bimodal, or multimodal.
• Numerical summaries of central tendency, mean, median, and mode, and of dispersion or spread, range, interquartile range, variance, and standard deviation.
• Calculation and interpretation of measures of relative standing, including quantiles, quartiles, percentiles, and z-scores.
• Methods of data production, including differences between experiments and observational studies, and various forms of sampling designs, including voluntary response, simple random, stratified, multistage, systematic, and cluster sampling.
• Identify elements of experiments and observational studies, including experimental units, factors, placebo, bias, control, replication, and randomization.
• Sampling distributions and sampling statistics.
• Estimation and significance testing.

Outcome #2: Produce and interpret summaries of numerical and categorical data as well as appropriate graphical and/or tabular representations.

1. Identify patterns and striking deviations from patterns in data.
2. Identify associations between variables from bivariate data.
3. Apply technology to calculate statistical summaries and produce graphical representations.

• Distinction between qualitative and quantitative data and discrete and continuous data.
• Data distributions and their shape, including whether they are symmetric or skewed, heavy or light tailed, unimodal, bimodal, or multimodal.
• Calculate and interpret contingency tables.
• Use of technology to input and edit data, create statistical graphics, calculate summary statistics.
• Relationships between two variables, including response and explanatory variables, scatterplots, association between variables, calculation and interpretation of correlation coefficients and the coefficient of determination.
• Fitting lines to data via least-squares regression.

Outcome #3: Use the distribution of sample statistics to quantify uncertainty and apply the basic concepts of probability into statistical arguments.

1. Interpret point and interval estimates.

• Elementary probability theory, including sample space, simple event, disjoint events, independent events, and complementary events.
• Axioms of probability and the calculation and interpretation of probabilities, including marginal, joint, and conditional probabilities.
• The Law of Large Numbers and its application to probability theory.
• Random variables, including their distribution, density function, expected value, variance, and standard deviation.
• Discrete and continuous random variables, including binomially and normally distributed random variables.
• Sampling distributions of statistics, including the sampling distribution of the mean.
• The Central Limit Theorem and its application to statistical arguments.
• Production and interpretation of point and interval estimators, including calculation and interpretation of confidence intervals for a given confidence level.
• Calculate and interpret large-sample estimators of population means and proportions.

Outcome #4: Identify, conduct, and interpret appropriate parametric hypothesis tests.

1. Identify the appropriate test based on variable type.
2. Identify situations where a one or two tailed test would be appropriate.
3. Conduct tests of one mean.
4. Conduct tests of one proportion.
5. Explain the difference between statistical and practical significance and the potential for error in hypothesis test conclusions.
6. Apply technology to perform hypothesis tests calculations.

• Significance testing, including null hypotheses, alternative hypotheses, one- and two-sided tests of significance, significance level, p-value, and statistical significance.
• Verification of conditions for tests of significance.
• Use of technology to compute p-values.
• Assessment of significance tests for predetermined significance levels.
• Distinction between statistical and practical significance.
• Comparison of information from confidence intervals and significance tests.

Outcome #5: Assess relationships in quantitative bivariate data.

1. Address questions relating correlation as a linear association between variables.
2. Distinguish between correlation and causation within data.
3. Apply technology to explore bivariate data.

• Relationship between response and explanatory variables.
• Production and interpretation of scatterplots.
• Identify and interpret positive and negative association between response and explanatory variables.
• Calculate and interpret correlation coefficient and coefficient of determination.
• Use technology to compute least-squares regression lines and to predict values from the resulting regression models.
• Investigate residuals and confounders and their influence on regression models and regression model interpretation.
• Distinguish between causation and association.

Suggested Texts and Materials

• Moore, D. et al., Introduction to the Practice of Statistics,7th Ed., W. H. Freeman, 2012.
• Graphing calculator or graphing app such as Desmos, or R (free computer statistical software)

Department Notes

This is the first term of a two-term sequence (MTH 243 and 244). This course is intended to provide an introduction to statistics in a data-based setting.