# Introduction to Statistics Training

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Introduction to Statistics training lays the foundation to understand applied statistics. The participants will learn about the principles, concepts, and techniques of business statistics. The flow of training will gradually build your business statistical thinking skills`, interpret business data, and guide about its implication in different real life scenarios. The participants are exposed to both quantitative and logical reasoning that helps in encountering business needs of all domains.

This statistical data analysis training will impart you knowledge on the following topics:

• 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
Target audience
• PhD scholars
• Data analyst
• Decision makers
Prerequisites

The candidates with mathematics background can undergo this training.

## 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
• 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
• 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
• 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

## 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
• 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

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