Statistical Methods in the Biological & Health Sciences

Milton's Statistical Methods in the Biological and Health Sciences offers comprehensive coverage for the applied statistics course for health and bio-related majors. This course focuses primarily on developing basic statistical techniques and relevant applications within a framework that addresses the needs of these specific audiences.

1 Descriptive Methods

1.1 Distribution Tables: Discrete Data

Bar Graphs

Bivariate Data: Two-Way Tables

1.2 A Quick Look at Distribution: Stem and Leaf

Constructing a Simple Stem-and-Leaf Diagram

1.3 Frequency Distributions: Histograms

Rules for Breaking Data into Classes

Cumulative Distribution

1.4 Measures of Location or Central Tendency

Sample Mean

Sample Median

1.5 Measures of Variability or Dispersion

Sample Variance

Sample Standard Deviation

Sample Range

Interquartile Range

Finding the Sample Interquartile Range

Multiple Data Sets

1.6 Box Plots

Constructing a Box Plot

1.7 Handling Grouped Data

2 Introduction to Probability and Counting

2.1 Interpreting Probablilities

2.2 Tree Diagrams and Elementary Genetics

Elementary Genetics

2.3 Permutations and Combinations

2.4 Multiplication Principle

Guidelines for Using the Multiplication Principle

2.5 Permutations of Indistinguishable Objects

2.6 Combinations

3 Probability and Problem Solving

3.1 Venn Diagrams and the Axioms of Probability

Venn Diagrams

Axioms of Probability

3.2 General Addition Rule

3.3 Conditional Probability

3.4 Diagnostic Tests and Relative Risk

Relative Risk

3.5 Independence

3.6 The Multiplication Rule

3.7 Bayes' Theorem

4 Discrete Random Variables

4.1 Discrete and Continuous Variables

4.2 Discrete Density Functions and Expectation

Expectation

4.3 Cumulative Distribution Function

4.4 Binomial Distribution

Expected Value and Variance: Binomial

Calculating Binomial Probabilities: Cumulative Distribution

4.5 Poisson Distribution

5 Continuous Random Variables

5.1 Continuous Random Variables

Expectation

5.2 Cumulative Distribution Function

5.3 Normal Distribution

Properties of Normal Curves

Standard Normal Distribution

Standardization

5.4 Normal Probability Rule and Medical Tables

6 Inferences on the Mean

6.1 Random Sampling and Randomization

Simple Random Sampling

Randomization

6.2 Point Estimation of the Mean and Introduction to Interval Estimation:

Central Limit Theorem

Interval Estimation

Central Limit Theorem

6.3 Confidence Interval on the Population Mean and the T Distribution

Properties of T Random Variables

6.4 Introduction to Hypothesis Testing

6.5 Testing Hypotheses on the Population

Mean: T Test

Preset Alpha Values

6.6 Sample Size: Confidence Intervals and Power

Sample Size: Hypothesis Testing

7 Chi-Squared Distribution and Inferences on the Variance

7.1 Chi-Squared Distribution and Interval

Estimation of the Population Variance

Confidence Interval on s2

7.2 Testing Hypotheses on the Population Variance

8 Inferences on Proportions

8.1 Point Estimation

8.2 Interval Estimation of p

8.3 Sample Size for Estimating p

8.4 Hypothesis Testing on p

8.5 Comparing Two Proportions: Estimation

Confidence Interval on the Difference in Two Proportions

8.6 Comparing Two Proportions: Hypothesis Testing

Testing That the Null Value Is Zero:

Pooled Test

9 Comparing Two Means and Two Variances

9.1 Comparing Two Means and Two Variances

9.2 Comparing Variances: F Distribution

Rule of Thumb Variance Comparison

F Test for Comparing Variances: F Distribution

9.3 Inferences on m1 - m2: Pooled T

Interval Estimation of m1 - m2

Pooled T Tests

9.4 Inferences on m1 - m2: Unequal Variances

9.5 Inferences on m1 - m2: Paired T

Paired T Test

10 k-Sample Procedures: Introduction to Design

10.1 One-Way Classification, Completely Random Design with Fixed Effects

Data Format and Notation

10.2 Paired and Multiple Comparisons

Bonferroni T Tests: Paired Comparisons

Duncan's Multiple Range Test

A Note on Computing

10.3 Random Effects

10.4 Randomized Complete Blocks

Data Format and Notation

Testing HO: m1. = m2. = @ @ @ = mk.

Effectiveness of Blocking

Paired and Multiple Comparisons

A Note on Computing

10.5 Factorial Experiments

Data Format and Notation

Testing Main Effects and Interaction

Multiple and Paired Comparisons

A Note on Computing

11 Regression and Correlation

11.1 Introduction To Simple Linear Regression

11.2 Method of Least Squares

Estimating an Individual Response

A Note on Computing

11.3 Introduction to Correlation

Estimating r

11.4 Evaluating the Strength of the Linear Relationship

Coefficient of Determination

Analysis of Variance

A Note on Computing

11.5 Confidence Interval Estimation

11.6 Multiple Regression

12 Categorical Data

12.1 2 ´ 2 Contingency Tables

Test of Independence

Test of Homogeneity

12.2 r ´ c Contingency Tables

13 Some Additional Procedures and Distribution-Free Alternatives

13.1 Testing for Normality: The Lilliefors Test

13.2 Tests of Location: One Sample

Sign Test for Median

Wilcoxon Signed-Rank Test

13.3 Tests of Location: Paired Data

Sign Test for Median Difference

Wilcoxon Signed-Rank Test: Paired Data

13.4 Tests of Location: Unmatched Data

Wilcoxon Rank-Sum Test

13.5 Kruskal-Wallis k-Sample Test for

Location: Unmatched Data

Kruskal-Wallis k-Sample Test

13.6 Friedman k-Sample Test for Location: Matched Data

Friedman Test

13.7 Correlation

Spearman's Rank Correlation Coefficient

13.8 Bartlett's Test for Equality of Variances

13.9 Normal Approximations

13.10 A Small Sample Test on Proportions

Appendix A

Summation Notation and Rules for Expectation and Variance

Summation Notation

Rules for Expectation and Variance

Appendix B

Statistical Tables

References

Answers to Odd-Numbered Problems

Index