Introduction to Statistics Training

• Introduction to Statistical Thinking including use and misuse of Statistics
• Data collection and sampling techniques
• Methods of frequency distribution and graphs
• Measures of Central tendency, Variation range, and position
• Sample spaces and Probability, Basic Counting Methods
• Types of probability distribution including Binomial Distribution and Poisson Distribution
• Ways of finding Normal Distribution and its applications
• Confidence Interval Estimation
• Hypothesis Testing, including z-, t-, and χ2 Tests
• Correlation and Regression
• Test for Goodness of Fit, and Independence
• One-Way and two-way Analysis of Variance (ANOVA)
• Use nonparametric statistics methods
• Sampling and Simulation techniques

• Academicians
• PhD scholars
• Data analyst
• Decision makers

1: The Nature of Probability and Statistics

• Introduction
• Descriptive and Inferential Statistics
• Variables and Types of Data
• Data Collection and Sampling Techniques
• Random Sampling
• Systematic Sampling
• Stratified Sampling
• Cluster Sampling
• Other Sampling Methods
• Observational and Experimental Studies
• Uses and Misuses of Statistics
• Suspect Samples
• Ambiguous Averages
• Changing the Subject
• Detached Statistics
• Implied Connections
• Misleading Graphs
• Faulty Survey Questions
• Computers and Calculators

2: Frequency Distributions and Graphs

• Introduction
• Organizing Data
• Categorical Frequency Distributions
• Grouped Frequency Distributions
• The Histogram
• The Frequency Polygon
• The Ogive
• Relative Frequency Graphs
• Distribution Shapes
• Other Types of Graphs
• Bar Graphs
• Pareto Charts
• The Time Series Graph
• The Pie Graph
• Misleading Graphs
• Stem and Leaf Plots
• Summary

3: Data Description

• Introduction
• Measures of Central Tendency
• The Mean
• The Median
• The Mode
• The Midrange
• The Weighted Mean
• Distribution Shapes
• Measures of Variation Range
• Population Variance and Standard Deviation
• Sample Variance and Standard Deviation
• Variance and Standard Deviation  for Grouped Data
• Coefficient of Variation
• Range Rule of Thumb
• Chebyshev’s Theorem
• The Empirical (Normal) Rule
• Measures of Position
• Standard Scores
• Percentiles
• Quartiles and Deciles
• Outliers
• Exploratory Data Analysis
• The Five-Number Summary and Boxplots

4: Probability and Counting Rules

• Introduction
• Sample Spaces and Probability
• Basic Concepts
• Classical Probability
• Complementary Events
• Empirical Probability
• Law of Large Numbers
• Subjective Probability
• Probability and Risk Taking
• The Addition Rules for  Probability
• The Multiplication Rules and Conditional Probability
• The Multiplication Rules
• Conditional Probability
• Probabilities for “At Least”
• Counting Rules
• The Fundamental Counting Rule
• Factorial Notation
• Permutations
• Combinations
• Probability and Counting Rules

5: Discrete Probability Distributions

Introduction

• Probability Distributions
• Mean
• Variance and Standard Deviation
• Expectation
• The Binomial Distribution
• Other Types of Distributions (Optional)
• The Multinomial Distribution
• The Poisson Distribution
• The Hypergeometric Distribution

6: The Normal Distribution

• Introduction
• Normal Distributions
• The Standard Normal Distribution
• Finding Areas Under the Standard Normal Distribution Curve
• A Normal Distribution Curve as a Probability Distribution Curve
• Applications of the Normal
• Distribution
• Finding Data Values Given Specific Probabilities
• Determining Normality
• The Central Limit Theorem
• Distribution of Sample Means
• Finite Population Correction Factor (Optional)
•  The Normal Approximation to the Binomial
• Distribution

7: Confidence Intervals and Sample Size

• Introduction
• Confidence Intervals for the Mean When σ is Known
• Confidence Intervals
• Sample Size
• Confidence Intervals for the Mean  When σ is Unknown
• Confidence Intervals and Sample Size for Proportions
• Confidence Intervals
• Sample Size for Proportions
• Confidence Intervals for Variances and Standard Deviations

8: Hypothesis Testing

• Introduction
• Steps in Hypothesis
• Testing—Traditional  Method
• z Test for a Mean
• P-Value Method for Hypothesis Testing
• t Test for a Mean
• z Test for a Proportion
• χ2  Test for a Variance or Standard Deviation
• Additional Topics Regarding Hypothesis Testing
• Confidence Intervals and Hypothesis Testing
• Type II Error and the Power of a Test

9: Testing the Difference between Two Means, Two Proportions, and Two Variances

• Introduction
• Testing the Difference Between
• Two Means: Using the z Test
• Testing the Difference Between Two
• Means of Independent Samples:  Using the t Test
• Testing the Difference Between Two Means: Dependent Samples
• Testing the Difference Between Proportions
• Testing the Difference Between Two Variances

10: Correlation and Regression

• Introduction
• Scatter Plots and Correlation
• Regression
• Line of Best Fit
• Determination of the Regression Line Equation
• Coefficient of Determination  and Standard Error of the Estimate
• Types of Variation for the Regression Model
• Residual Plots
• Coefficient of Determination
• Standard Error of the Estimate
• Prediction Interval
• Multiple Regression
• The Multiple Regression Equation
• Testing the Significance of R
• Adjusted R2

11:  Other Chi-Square Tests

• Introduction
• Test for Goodness of Fit
• Test of Normality
• Tests Using Contingency Tables
• Test for Independence
• Test for Homogeneity of Proportions

12: Analysis of Variance (ANOVA)

• Introduction
• One-Way Analysis of Variance
• Scheffé Test
• Tukey Test
• Two-Way Analysis of  Variance
• Hypothesis-Testing

13: Nonparametric Statistics

• Introduction
• Nonparametric Methods
• Advantages
• Disadvantages
• Ranking
• The Sign Test
• Single-Sample Sign Test
• Paired-Sample Sign Test
• The Wilcoxon Rank Sum Test
• The Wilcoxon Signed-Rank Test
• The Kruskal-Wallis Test
• The Spearman Rank Correlation Coefficient and the Runs Test
• Rank Correlation Coefficient
• The Runs Test
• Hypothesis-Testing Summary

14: Sampling and Simulation

• Introduction
• Common Sampling
• Techniques
• Random Sampling
• Systematic Sampling
• Stratified Sampling
• Cluster Sampling
• Other Types of Sampling Techniques
• Surveys and Questionnaire Design
• Simulation Techniques and the Monte Carlo Method