Introductory statistics

Statistics is the study of the collection, organization, and interpretation of numerical values, which we call data. As human beings in a modern world, we are bombarded by data on a daily basis: the latest poll results in a political campaign, the daily weather forecast, an advertisement claiming doctors prefer one product (as compared to others), or a debate about how to improve high school graduation rates. The goal of statistics is the use of data to enhance understanding. Statistics relies on math and calculations as one step in the process of making sense of data, but just as important is how the data were collected and what interpretations and decisions can we make based on the data.

Introductory Statistics introduces students to the major concepts, logic, and issues in statistical reasoning and to the tools involved in collecting, analyzing and drawing conclusions from data. Four broad conceptual themes are explored:

• Exploratory analysis: Observing patterns and departures from patterns
• Producing data: Deciding what and how to measure
• Probability: Investigating patterns via models which use probability and simulation
• Statistical inference: Confirming models

Objectives

During an introductory course of study, students are encouraged to: Think statistically. Using statistical tools, accurately apply the statistical methods to realistic data samples. Effectively interpret the results of analyses. Communicate accurately and comprehensively about data results, conclusions and interpretations. Use a critical framework to evaluate study designs and results.

Topic pages

Introductory learning materials are listed for each of the four broad themes in statistics.

Exploratory analysis

Variance and standard deviation

Inference

Type I and type II errors

Statistical power

Supporting activities

When learning a new concept in statistics, working through a somewhat realistic analysis is often helpful:

Probability

• Probability_simulation_-_true-false_test - a collaborative activity to simulate the results of pure guessing

Inference

• Point estimation - German tank problem - a collaborative activity on estimating the total number of German tanks given a small sample
• Hypothesis testing - unfair deck of cards - a demonstration wherein students intuit and calculate Ho, Ha, p-value, and alpha
• Hypothesis testing of a single mean and/or single proportion - a collaborative activity to practice the steps to be performed in hypothesis testing
• Hypothesis testing of a single mean--hrs/wk watching tv - a collaborative practice activity
• Hypothesis testing of a single mean--verbal and math ability of CS students - independent practice
• Comparing means for two independent samples--math ability of male and female CS students - a collaborative practice activity
• Comparing means for two independent samples--teacher ratings - independent practice
• Matched pairs--ADHD treatment - a collaborative practice activity
• Hypothesis testing - case studies using research reports
• Hypothesis testing - exploring research studies
• Two-way tables--drinking and class attendance - a collaborative practice activity
• One-way ANOVA--music training and spatial temporal reasoning in preschool children - independent practice
• One-way ANOVA--smiles and leniency - independent practice
• Multiple regression--predicting achievement index score for elementary schools - an independent practice activity
• Two-way ANOVA--do level of education and gender explain US income?

Resources

Rich datasets

Instructions for use of statistical software

The following pages offer instruction in how to perform a particular analysis using the specified statistical software.

SPSS

• Histogram
• Independent samples t test