MATH 2441 Probability and Statistics for Biological Sciences BCIT
(BCIT Mathematics Department)


This is a list of the topics covered in the course in the order in which they will be addressed.  Links are to pages which give additional information on each topic along with examples, sample problem sets, etc. 

Table of Contents*

Introduction
What Is/Are "statistics"?
Looking Ahead:  Terminology and Directions.
The Real Problem ... An Initial Experiment

Descriptive Statistics I:  Simple Graphical Methods.
Introduction to Descriptive Statistics
Types of Data
Frequency Tables
Histograms
Stemplots

Example Data Sets

Descriptive Statistics II:  Numerical Summaries
Review of Subscripts and Summation Notation
Measures of Central Tendency
Mean, Median, etc.
Sampling Issues (experiment)
Measures of Variation or Dispersion
Range, Variance/Standard Deviation, Interquartile Range, etc.
Sampling Issues (experiment)
Categorical Data
Qualitative or Categorical Data
Sampling Issues (computer simulation)
Characterising Relationships
Scatterplots
Correlation Coefficients
Linear Regression/Least Squares
Sampling Issues (computer simulation)
Recognizing Statistical Language in Reports

Descriptive Statistics III:  Miscellaneous Topics
Use of Model Distributions
Rough Cuts (Tchebychev et al!)
Measures of Relative Standing (percentiles)
The Five-number Summary, Boxplots, and the Treatment of Outliers

Introduction to Probability
Introduction to Probability
Calculating Probabilities I: equally-likely simple events and  branching diagrams
Calculating Probabilities II:  some basic relationships between probabilities
Calculating Probabilities III:  random variables and probability distributions

The Normal Distribution
Calculating Normal Probabilities
Percentiles of the Normal Distribution

Review of the Sampling Process
Sampling Distributions (sample mean, sample proportion, etc.)

Statistical Estimation
Notion of a Point Estimate
Confidence Interval Estimates -- Single Populations
Population Mean, Large Samples
Population Mean, Small Samples
The t-distribution
Normal Probability Plots
Population Proportion, Large Samples
Population Variance
The chi-square Distribution
Confidence Interval Estimates -- Two Populations
Difference of Two Population Means, Large Samples
Difference of Two Population Means, Small Samples
Difference of Two Population Proportions
Relative Risk and the Odds Ratio
Communicating Statistical Estimates

Hypothesis Testing
Terminology, Concepts, General Formalism
Hypothesis Testing and the Criminal Justice System
Single Population Tests
Population Means
Population Proportions
Population Variances
Two Population Tests
Difference of Two Population Means (independent samples)
Difference of Two Population Proportions (large samples)
Comparison of Two Population Variances
The F-distribution
Paired-Differences Tests
Hypotheses Involved in Linear Regression and Correlation Calculations
Recap of Hypothesis Testing Concepts/Strategies


Introduction to ANOVA and the F-test


Basic Probability and Discrete Probability Distributions
Counting Techniques (permutations, combinations, branching diagrams)
Conditional Probability and the Concept of Independence
Bayes' Formula and Applications
Binomial Distribution and Applications
Poisson distribution and applications


Analysis of Categorical Data
Chi-Squared Test for Goodness-of-fit
Chi-Squared Test for Independence
Chi-Squared Test for Homogeneity



Statistical Tables

 

Copies of the statistical tables used in this course are usually included in the documents in which their use is first described or explained.  Most of these tables have been generated using Microsoft Excel (one exception is the table of mean values of normal distribution order statistics for use in constructing normal probability plots -- the evaluation of the required integrals was done here using Maple V).  Here, we collect links to the tables in various formats and links to the documents in which their use is described.

 

 

 

*The material on this page and those to which it is linked is intended as a resource for students enrolled in MATH 2441 at BCIT, and does not constitute an official specification of the course.  These materials are being developed concurrently with the course, and so should probably be considered to be "under construction" and subject to revision for the forseeable future.  If it turns out that no notes or problem sheets become available via this web site for a certain topic, it is most likely that the author was unable to prepare the web-able material in time than it is that the topic was not covered in the classroom.
The official BCIT course outline for MATH 2441, Winter/2003 is available for download as an MS Word document here
The best possible attempt will be made to keep the information on this web site current with the progress of the course, but the schedule of material, quizzes, tests, and other classroom activities as announced in the classroom take precedence over this on-line information.  In other words:  if you are enrolled in this course for credit, you must come to class regularly to ensure that you don't miss material that you will be responsible for learning, or announcements of quizzes, tests, and assignments. 


Maintained by David W. Sabo.
Last Revisions: April 8, 2003