TABLE OF CONTENT
PREFACE
i
ORGANIZATION OF THE BOOK
i
TABLE OF CONTENT
iii i
CHAPTER 1. The Role of Statistics in Educational Research 1
A. Learning Objectives 1
B. The Nature of Data 2
C. Analysis of Individual Observations 8
CHAPTER 2 Descriptive Statistics
11 A. Introductiom
11 B. Univariate Analysis
16 C. Descriptive statistics for measurements of a single variable
19 D. Summary: descriptive statistics function
29
CHAPTER 3 Probability
31 A. Introduction
31 B. Sample Spaces and Events
31 C. Basic Probability Theory
35 D. Conditional Probability and Independence
38 E. Random Variable
39 F. Distribution Functions
40 G. Density and Mass Function
41
CHAPTER 4 Probability Distributions 1 Discrete Random Variables 43
A. Discrete Random Variables 43
B. Distribution Function 53
C. Discrete Random Variable 56
D. Expectation Mean 58
E. Expectation of a Function of a Random Variable 60
F. Variance 64
G. The Bernoulli and Binomial Random Variables 66
H. The Poisson Random Variable 69
CHAPTER 5 Probability Distributions 2 Continuous Random Variables
71 A. Introduction
71 B. Normal Distributions
72 C. The Standard Normal Distribution
74 D. Calculating Probabilities for a Normal Random Variable
76 E. Calculating Values Using the Standard Normal Table
76 F. The Central Limit Theorem
76
CHAPTER 6 Point Estimation Of Parameters
79 A. Introduction
79 B. Properties of Point Estimators and Methods of Estimation
86 C. The Rao-Blackwell Theorem
90 D. The Method of Moments
91 E. Method of Maximum Likelihood
92 F. The Factorization Theorem
93
CHAPTER 7 Tests of Hypotheses for a Single Sample
95 A. Hypothesis Testing
95 B. General Statistical Tests
104 C. Tests on a Population Proportion
118 D. Testing for Goodness of Fit
122
CHAPTER 8 Statistical Inference for Two Samples 130
A. Introduction 130
B. One- and Two-Sample Estimation Problems 130
C. Single Sample: Estimating the Mean 134
D. Two Samples: Estimating the Difference Between Two Means 145
E. Single Sample: Estimating a Proportion probability of a success 151
F. Two Samples: Estimating the Difference Between Two Proportions 153
CHAPTER 9 Simple Linear Regression and Correlation 155
