APMA 0650 Essential Statistics
Basic Concepts and Methods of Statistical Reasoning
Syllabus

 

Essential Statistics is an introductory first course intended for students from a variety of disciplines.  The primary objective is to introduce basic statistical concepts that provide the framework for statistical reasoning and statistical judgment.  At the same time, the course will cover the most commonly used statistical methods, ranging from graphical and computational methods of exploratory data analysis to basic regression analysis.  In contrast to more traditional introductory courses, the primary focus is neither on the mathematical foundation of statistical inference nor on a limited body of methods that are of special interest within a single discipline.

 

There are no mathematical prerequisites beyond high school algebra.

 

Use of the methods on real data will be an integral part of the course.  Computation will typically be done using the Analysis Toolpak in Microsoft Excel.

 

The statistical concepts and basic methods will be illustrated by case studies.  Frequent use will be made of examples from the daily news.  Examples of such news items include:

 

“Driving While Black,” The Washington Post, August 16, 1998---describing a well-designed statistical study of racial profiling.

 

“A Closer Look at Therapeutic Touch,” J. American Medical Association, 1998; 279:1005-1010---an article that originated from a middle school science project and that debunks an alternative medicine procedure.

 

“Following Benford’s Law, or Looking Out for No. 1,” The New York Times, August 4, 1998---describing the use of statistics as an auditing tool to detect fraud.

 

“Two Sides in Census Battle Have Their Day in Court,” The New York Times, August 8, 1998---concerning the use of statistics to adjust US Census figures for undercount.

 

“How to Find a Trend When None Exists,” The New York Times, August 25, 2001---concerned with the media frenzy over shark attacks in summer 2001.

 

The textbook also supplies extensive case-study resources and real datasets.

 

Catalog Description: A first course in statistics emphasizing statistical reasoning and basic concepts.  Comprehensive treatment of most commonly used statistical methods through linear regression.  Elementary probability and the role of randomness.  Data analysis and statistical computing using Excel.  Examples, cautionary tales and applications from the popular press and the life, social and physical sciences.  No mathematical prerequisites beyond high school algebra.

 

Text: Introduction to the Practice of Statistics (5th Edition) by David S. Moore and George P. McCabe, W.H. Freeman & Company, 2005.

 

A Course Outline follows.

 

 

APMA 0650 Course Outline

 

Based on the textbook Introduction to the Practice of Statistics (5th Edition) by David S. Moore and George P. McCabe, W.H. Freeman & Company, 2005 (1st Edition 1989)

 

I.                    (2 weeks; 2 tutorials) Looking at Data¾Distributions

1.       The visual display of data using histograms

2.       Describing data via measures of central tendency and variability---average, medians and standard deviation, Box plots.

3.       Normal distribution

Selections from Chap 1

II.         (1.5 weeks; 2 tutorials) Looking at Data¾Relationships

1.       Scatterplots

2.       Correlation

3.       Least Squares regression line

4.       Estimation of regression coefficients

Selections from Chap 2

III.        (2.5 weeks; 2 tutorials) Probability¾Randomness and The Foundation for Statistics

1.       Basic notions of probability and associated rules for computation.

2.       Random variables discrete and continuous

3.       Means and variances of random variables

4.       Conditional probability, Bayes formula, probability trees

Chap 4

IV.        (1.5 weeks; 2 tutorials) Sampling Distributions

1.       Distributions of measurement data

2.       Binomial measurements

3.       Normal approximation to binomial

4.       Central limit theorem and distribution of the sample mean.

Selections from Chap 5

V.         (2 weeks; 2 tutorials) Introduction to Inference (characteristics of one random variable)

1.       Statistical confidence intervals and effect of sample size

2.       P-values and tests of significance for one Normal mean , known standard deviation

3.       Type I and Type II errors

4.       P-values and tests of significance for one Normal mean , unknown standard deviation¾the
t-distribution

5.       Tests using Matched pairs reduced to one variable

Selections from Chap 6 and Chap 7

VI.        (1 week; 1 tutorial) Comparing Two Quantities (comparing two random variables)

1.       P-values and tests of significance for two Normal means

2.       Two sample confidence intervals

Chap 7, Section 7.2

VII.       (1 week; 1 tutorial) Inference for Proportions

1.       P-values and tests of significance for one proportion

2.       Confidence intervals for one proportion

3.       P-values and tests of significance for two proportions

4.       Confidence intervals for two proportions

Chap 8

VIII.      (2 weeks; 1 tutorial) Inference for Regression

1.       Scatterplots reviewed

2.       Statistical model for linear regression

3.       Estimation of regression coefficients

4.       Confidence intervals and significant tests for regression coefficients

5.       Prediction intervals

Chap 10