This textbook is a primer for students on statistics. It covers basic statistical operations, an introduction to probability, distributions and regression. The book is divided into a series of 10 chapters covering a basic introduction to common topics for beginners.
The goal of the book is to provide sufficient understanding of how to organize and summarize datasets through descriptive and inferential statistics for good decision-making. A chapter on ethics also informs readers about best practices for using statistics in research and analysis.
Topics covered:
1. Introduction to Statistics
2. Summarizing and Graphing
3. Basic Concepts of Probability
4. Discrete Random Variables
5. Continuous Random Variables
6. Sampling Distributions
7. Estimation
8. Hypothesis Testing
9. Correlation and Regression
10. Ethics
Author(s): Alandra Kahl
Publisher: Bentham Science Publishers
Year: 2023
Language: English
Pages: 178
City: Singapore
Cover
Title
Copyright
End User License Agreement
Contents
Preface
CONSENT FOR PUBLICATION
CONFLICT OF INTEREST
ACKNOWLEDGEMENT
Introduction to Statistics
INTRODUCTION
DATA TYPES
Sample Data
CONCLUSION
Summarizing and Graphing
INTRODUCTION
FREQUENCY DISTRIBUTIONS AND HISTOGRAMS
GRAPHS
CONCLUSION
Basic Concepts of Probability
INTRODUCTION
SAMPLES EVENTS AND THEIR PROBABILITIES
Sample Spaces
Event
Examples
Example 1
Example 2
Example 3
Example 4
EXPERIMENT
Definition:
Example 5
PROBABILITY
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
COMPLEMENTS, INTERSECTIONS, AND UNIONS
Complement
Examples
Example 1
Probability Rule for Complements
Example 2
Intersection of Events
Examples
Example 1
Example 2
Probability Rule for Mutually Exclusive Events
Example
Union of Events
Examples
Example 1
Example 2
Additive Rule of Probability
Example 3
Example 4
Example 5
CONDITIONAL PROBABILITY AND INDEPENDENT OCCURRENCES
Conditional Probability
Examples
Example 1
Example 2
Example 3
Independent Events
Examples
Example 1
Example 2
Example 3
Example 4
Probability in Tree Diagrams
Example
Principles
CONCLUSION
Discrete Random Variables
INTRODUCTION
Random Variables
Understanding Random Variables
Types of Random Variables
Example of Random Variable
Example:
Examples of Probability Distributions for Discrete Random Variables (DRV)
Example 1
Example 2
Examples
Example # 1
Example # 2
Example # 3
Variance of Discrete Random Variables
Characteristics and Notations
Binominal Distribution
Understanding Binominal Distribution
Analyzing Binominal Distribution
Criteria for Binominal Distribution
Examples of Binominal Distributions
Trial 1
Trial 2
Trial 3
Cumulative Binominal Probability
Negative Binominal Distribution
Notations
The Mean of Negative Binominal Distribution
CONCLUSION
Continuous Random Variables
INTRODUCTION
Probability Distribution of Continuous Random Variable
Properties
Probability Density Functions
Cumulative Distribution Functions
Examples of Probability Distribution of Continuous Random Variable
Example # 1
The Normal Distribution
Understanding Normal Distribution
Kurtosis and Skewness
Central Limit Theorem
Sample Mean
Convergence to Normal Distribution
The Standard Normal Distribution
The Standard Normal Distribution Vs. Normal Distribution
Standardizing Normal Distribution
How to Calculate Z-score
Example of Finding Z -score
To Find Probability using The Normal Standard Distribution
P values and Z-Tests
How to Use Z-Table
Example: Using Z distribution to Find Probability
Areas of Tails of Distribution
Tails of Standard Normal Distribution
CONCLUSION
Sampling Distributions
INTRODUCTION
THE MEAN AND STANDARD DEVIATION (SD) OF THE SAMPLE MEAN
Examples
Example 1
Example 2
The Sampling Distribution of the Sample Mean
The Central Limit Theorem
Examples
Example 1
Example 2
Solution [44]
Example 3
Example 4
Normally Distributed Populations
Standard Deviation of x¯ (Standard Error) [44]
Z-Score of the Sample Mean [44]
Examples
Example 1
Example 2
Example 3
The Sample Proportion
Sample Proportions in a Small Population:
The Sampling Distribution of the Sample Proportion
Examples
Example 1
Example 2
Example 3
CONCLUSION
Estimation
INTRODUCTION
Construction of Confidence Intervals
Interval Estimate vs. Point Estimate
Intervals of Confidence
Confidence Level
The Error Margin
Estimator
Interval vs. Point Estimator
Types of Estimators
WHAT IS STANDARD ERROR (SDE)?
Standard Deviation (SD) of Sample Estimates
Standard Error (SE) of Sample Estimates
Margin of Error
How to Calculate the Error Margin
What is the Critical Value and How Do I Find it?
What is a Confidence Interval, and How Does It Work?
Confidence Intervals and How to Interpret Them
Data Requirements for Confidence Interval
What is a Confidence Interval, and How Do I Make One?
Bias and Error
MSE stands for Mean Squared Error
Sample Size and Estimates
Determining the Sample Size is Necessary to Estimate the Population Mean
Examples
Example
Large Sample Estimation of a Population Mean
Large Sample 100 (1 - α) % Confidence Interval for a Population Mean
Example
Small Sample Estimation of a Population Mean
Small Sample 100 (1 -α) % Confidence Interval for a Population Mean [53]
Example 1
Example 2
Determining Sample Size Required to Estimate Population Proportion (p)
Example
Estimating the Target Parameter: Point Estimation
Maximum Likelihood
Linear Least Squares (LLS)
Estimating the Target Parameter: Interval Estimation
Example
The t Distribution
Estimating a Population Proportion
Using Confidence Intervals to Determine the Population Proportion
Examples
Example 1
The “Plus Four” Confidence Interval
Calculating the Sample Size n
Sample Size Considerations
The Cost of Collecting Samples
Pre-existing knowledge
Variability That is Inherent
Determination of the Sample Size
Proportions of Samples Taken
CONCLUSION
Hypothesis Testing
INTRODUCTION
Z-Test
T-Test
CONCLUSION
Correlation and Regression
INTRODUCTION
CORRELATION
REGRESSION
CONCLUSION
Ethics
INTRODUCTION
ETHICS
CONCLUSION
References
Subject Index
Back Cover
