MATH 2441 | Probability and Statistics for Biological Sciences | |

(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.

- 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.

Maintained by David W. Sabo.

Last Revisions: April 8, 2003