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Home » Mathematics » Statistics
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Duration
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36:33

• Level Intermediate
• 49 Lessons (36hr : 33min)
• Audio: English
• English

Join Dr. Ji Son’s General Statistics online course which combines clear explanations of concepts, tons of diagrams, and step-by-step examples. Dr. Son also utilizes Excel to break down difficult concepts into understandable ideas and showcases the power of digital statistics analysis.

## Section 1: Introduction

Descriptive Statistics vs. Inferential Statistics 25:31
Intro 0:00
Statistics 0:35
Statistics 0:36
Let's Think About High School Science 1:12
Measurement and Find Patterns (Mathematical Formula) 1:13
Statistics = Math of Distributions 4:58
Distributions 4:59
Problematic… but also GREAT 5:58
Statistics 7:33
How is It Different from Other Specializations in Mathematics? 7:34
Statistics is Fundamental in Natural and Social Sciences 7:53
Two Skills of Statistics 8:20
Description (Exploration) 8:21
Inference 9:13
Descriptive Statistics vs. Inferential Statistics: Apply to Distributions 9:58
Descriptive Statistics 9:59
Inferential Statistics 11:05
Populations vs. Samples 12:19
Populations vs. Samples: Is it the Truth? 12:20
Populations vs. Samples: Pros & Cons 13:36
Populations vs. Samples: Descriptive Values 16:12
Putting Together Descriptive/Inferential Stats & Populations/Samples 17:10
Putting Together Descriptive/Inferential Stats & Populations/Samples 17:11
Example 1: Descriptive Statistics vs. Inferential Statistics 19:09
Example 2: Descriptive Statistics vs. Inferential Statistics 20:47
Example 3: Sample, Parameter, Population, and Statistic 21:40
Example 4: Sample, Parameter, Population, and Statistic 23:28

## Section 2: About Samples: Cases, Variables, Measurements

About Samples: Cases, Variables, Measurements 32:14
Intro 0:00
Data 0:09
Data, Cases, Variables, and Values 0:10
Rows, Columns, and Cells 2:03
Example: Aircrafts 3:52
How Do We Get Data? 5:38
Research: Question and Hypothesis 5:39
Research Design 7:11
Measurement 7:29
Research Analysis 8:33
Research Conclusion 9:30
Types of Variables 10:03
Discrete Variables 10:04
Continuous Variables 12:07
Types of Measurements 14:17
Types of Measurements 14:18
Types of Measurements (Scales) 17:22
Nominal 17:23
Ordinal 19:11
Interval 21:33
Ratio 24:24
Example 1: Cases, Variables, Measurements 25:20
Example 2: Which Scale of Measurement is Used? 26:55
Example 3: What Kind of a Scale of Measurement is This? 27:26
Example 4: Discrete vs. Continuous Variables. 30:31

## Section 3: Visualizing Distributions

Introduction to Excel 8:09
Intro 0:00
Before Visualizing Distribution 0:10
Excel 0:11
Excel: Organization 0:45
Workbook 0:46
Column x Rows 1:50
Tools: Menu Bar, Standard Toolbar, and Formula Bar 3:00
Excel + Data 6:07
Exce and Data 6:08
Frequency Distributions in Excel 39:10
Intro 0:00
Data in Excel and Frequency Distributions 0:09
Raw Data to Frequency Tables 0:42
Raw Data to Frequency Tables 0:43
Frequency Tables: Using Formulas and Pivot Tables 1:28
Example 1: Number of Births 7:17
Example 2: Age Distribution 20:41
Example 3: Height Distribution 27:45
Example 4: Height Distribution of Males 32:19
Frequency Distributions and Features 25:29
Intro 0:00
Data in Excel, Frequency Distributions, and Features of Frequency Distributions 0:11
Example #1 1:35
Uniform 1:36
Example #2 2:58
Unimodal, Skewed Right, and Asymmetric 2:59
Example #3 6:29
Bimodal 6:30
Example #4a 8:29
Symmetric, Unimodal, and Normal 8:30
Point of Inflection and Standard Deviation 11:13
Example #4b 12:43
Normal Distribution 12:44
Summary 13:56
Uniform, Skewed, Bimodal, and Normal 13:57
Sketch Problem 1: Driver's License 17:34
Sketch Problem 2: Life Expectancy 20:01
Sketch Problem 3: Telephone Numbers 22:01
Sketch Problem 4: Length of Time Used to Complete a Final Exam 23:43
Dotplots and Histograms in Excel 42:42
Intro 0:00
Previously 1:02
Data, Frequency Table, and visualization 1:03
Dotplots 1:22
Dotplots Excel Example 1:23
Dotplots: Pros and Cons 7:22
Pros and Cons of Dotplots 7:23
Dotplots Excel Example Cont. 9:07
Histograms 12:47
Histograms Overview 12:48
Example of Histograms 15:29
Histograms: Pros and Cons 31:39
Pros 31:40
Cons 32:31
Frequency vs. Relative Frequency 32:53
Frequency 32:54
Relative Frequency 33:36
Example 1: Dotplots vs. Histograms 34:36
Example 2: Age of Pennies Dotplot 36:21
Example 3: Histogram of Mammal Speeds 38:27
Example 4: Histogram of Life Expectancy 40:30
Stemplots 12:23
Intro 0:00
What Sets Stemplots Apart? 0:46
Data Sets, Dotplots, Histograms, and Stemplots 0:47
Example 1: What Do Stemplots Look Like? 1:58
Example 2: Back-to-Back Stemplots 5:00
Example 3: Quiz Grade Stemplot 7:46
Example 4: Quiz Grade & Afterschool Tutoring Stemplot 9:56
Bar Graphs 22:49
Intro 0:00
Review of Frequency Distributions 0:44
Y-axis and X-axis 0:45
Types of Frequency Visualizations Covered so Far 2:16
Introduction to Bar Graphs 4:07
Example 1: Bar Graph 5:32
Example 1: Bar Graph 5:33
Do Shapes, Center, and Spread of Distributions Apply to Bar Graphs? 11:07
Do Shapes, Center, and Spread of Distributions Apply to Bar Graphs? 11:08
Example 2: Create a Frequency Visualization for Gender 14:02
Example 3: Cases, Variables, and Frequency Visualization 16:34
Example 4: What Kind of Graphs are Shown Below? 19:29

## Section 4: Summarizing Distributions

Central Tendency: Mean, Median, Mode 38:50
Intro 0:00
Central Tendency 1 0:56
Way to Summarize a Distribution of Scores 0:57
Mode 1:32
Median 2:02
Mean 2:36
Central Tendency 2 3:47
Mode 3:48
Median 4:20
Mean 5:25
Summation Symbol 6:11
Summation Symbol 6:12
Population vs. Sample 10:46
Population vs. Sample 10:47
Excel Examples 15:08
Finding Mode, Median, and Mean in Excel 15:09
Median vs. Mean 21:45
Effect of Outliers 21:46
Relationship Between Parameter and Statistic 22:44
Type of Measurements 24:00
Which Distributions to Use With 24:55
Example 1: Mean 25:30
Example 2: Using Summation Symbol 29:50
Example 3: Average Calorie Count 32:50
Example 4: Creating an Example Set 35:46
Variability 42:40
Intro 0:00
Range, Quartiles and Interquartile Range 6:37
Range 6:38
Interquartile Range 8:42
Interquartile Range Example 10:58
Interquartile Range Example 10:59
Variance and Standard Deviation 12:27
Deviations 12:28
Sum of Squares 14:35
Variance 16:55
Standard Deviation 17:44
Sum of Squares (SS) 18:34
Sum of Squares (SS) 18:35
Population vs. Sample SD 22:00
Population vs. Sample SD 22:01
Population vs. Sample 23:20
Mean 23:21
SD 23:51
Example 1: Find the Mean and Standard Deviation of the Variable Friends in the Excel File 27:21
Example 2: Find the Mean and Standard Deviation of the Tagged Photos in the Excel File 35:25
Example 3: Sum of Squares 38:58
Example 4: Standard Deviation 41:48
Five Number Summary & Boxplots 57:15
Intro 0:00
Summarizing Distributions 0:37
5 Number Summary 1:14
Boxplot: Visualizing 5 Number Summary 3:37
Boxplot: Visualizing 5 Number Summary 3:38
Boxplots on Excel 9:01
Using 'Stocks' and Using Stacked Columns 9:02
Boxplots on Excel Example 10:14
When are Boxplots Useful? 32:14
Pros 32:15
Cons 32:59
How to Determine Outlier Status 33:24
Rule of Thumb: Upper Limit 33:25
Rule of Thumb: Lower Limit 34:16
Signal Outliers in an Excel Data File Using Conditional Formatting 34:52
Modified Boxplot 48:38
Modified Boxplot 48:39
Example 1: Percentage Values & Lower and Upper Whisker 49:10
Example 2: Boxplot 50:10
Example 3: Estimating IQR From Boxplot 53:46
Example 4: Boxplot and Missing Whisker 54:35
Shape: Calculating Skewness & Kurtosis 41:51
Intro 0:00
Skewness Concept 1:09
Skewness Concept 1:10
Calculating Skewness 3:26
Calculating Skewness 3:27
Interpreting Skewness 7:36
Interpreting Skewness 7:37
Excel Example 8:49
Kurtosis Concept 20:29
Kurtosis Concept 20:30
Calculating Kurtosis 24:17
Calculating Kurtosis 24:18
Interpreting Kurtosis 29:01
Leptokurtic 29:35
Mesokurtic 30:10
Platykurtic 31:06
Excel Example 32:04
Example 1: Shape of Distribution 38:28
Example 2: Shape of Distribution 39:29
Example 3: Shape of Distribution 40:14
Example 4: Kurtosis 41:10
Normal Distribution 34:33
Intro 0:00
What is a Normal Distribution 0:44
The Normal Distribution As a Theoretical Model 0:45
Possible Range of Probabilities 3:05
Possible Range of Probabilities 3:06
What is a Normal Distribution 5:07
Can Be Described By 5:08
Properties 5:49
'Same' Shape: Illusion of Different Shape! 7:35
'Same' Shape: Illusion of Different Shape! 7:36
Types of Problems 13:45
Example: Distribution of SAT Scores 13:46
Shape Analogy 19:48
Shape Analogy 19:49
Example 1: The Standard Normal Distribution and Z-Scores 22:34
Example 2: The Standard Normal Distribution and Z-Scores 25:54
Example 3: Sketching and Normal Distribution 28:55
Example 4: Sketching and Normal Distribution 32:32
Standard Normal Distributions & Z-Scores 41:44
Intro 0:00
A Family of Distributions 0:28
Infinite Set of Distributions 0:29
Transforming Normal Distributions to 'Standard' Normal Distribution 1:04
Normal Distribution vs. Standard Normal Distribution 2:58
Normal Distribution vs. Standard Normal Distribution 2:59
Z-Score, Raw Score, Mean, & SD 4:08
Z-Score, Raw Score, Mean, & SD 4:09
Weird Z-Scores 9:40
Weird Z-Scores 9:41
Excel 16:45
For Normal Distributions 16:46
For Standard Normal Distributions 19:11
Excel Example 20:24
Types of Problems 25:18
Percentage Problem: P(x) 25:19
Raw Score and Z-Score Problems 26:28
Standard Deviation Problems 27:01
Shape Analogy 27:44
Shape Analogy 27:45
Example 1: Deaths Due to Heart Disease vs. Deaths Due to Cancer 28:24
Example 2: Heights of Male College Students 33:15
Example 3: Mean and Standard Deviation 37:14
Example 4: Finding Percentage of Values in a Standard Normal Distribution 37:49
Normal Distribution: PDF vs. CDF 55:44
Intro 0:00
Frequency vs. Cumulative Frequency 0:56
Frequency vs. Cumulative Frequency 0:57
Frequency vs. Cumulative Frequency 4:32
Frequency vs. Cumulative Frequency Cont. 4:33
Calculus in Brief 6:21
Derivative-Integral Continuum 6:22
PDF 10:08
PDF for Standard Normal Distribution 10:09
PDF for Normal Distribution 14:32
Integral of PDF = CDF 21:27
Integral of PDF = CDF 21:28
Example 1: Cumulative Frequency Graph 23:31
Example 2: Mean, Standard Deviation, and Probability 24:43
Example 3: Mean and Standard Deviation 35:50
Example 4: Age of Cars 49:32

## Section 5: Linear Regression

Scatterplots 47:19
Intro 0:00
Previous Visualizations 0:30
Frequency Distributions 0:31
Compare & Contrast 2:26
Frequency Distributions Vs. Scatterplots 2:27
Summary Values 4:53
Shape 4:54
Center & Trend 6:41
Univariate & Bivariate 10:25
Example Scatterplot 10:48
Shape, Trend, and Strength 10:49
Positive and Negative Association 14:05
Positive and Negative Association 14:06
Linearity, Strength, and Consistency 18:30
Linearity 18:31
Strength 19:14
Consistency 20:40
Summarizing a Scatterplot 22:58
Summarizing a Scatterplot 22:59
Example 1: Gapminder.org, Income x Life Expectancy 26:32
Example 2: Gapminder.org, Income x Infant Mortality 36:12
Example 3: Trend and Strength of Variables 40:14
Example 4: Trend, Strength and Shape for Scatterplots 43:27
Regression 32:02
Intro 0:00
Linear Equations 0:34
Linear Equations: y = mx + b 0:35
Rough Line 5:16
Rough Line 5:17
Regression - A 'Center' Line 7:41
Reasons for Summarizing with a Regression Line 7:42
Predictor and Response Variable 10:04
Goal of Regression 12:29
Goal of Regression 12:30
Prediction 14:50
Example: Servings of Mile Per Year Shown By Age 14:51
Intrapolation 17:06
Extrapolation 17:58
Error in Prediction 20:34
Prediction Error 20:35
Residual 21:40
Example 1: Residual 23:34
Example 2: Large and Negative Residual 26:30
Example 3: Positive Residual 28:13
Example 4: Interpret Regression Line & Extrapolate 29:40
Least Squares Regression 56:36
Intro 0:00
Best Fit 0:47
Best Fit 0:48
Sum of Squared Errors (SSE) 1:50
Sum of Squared Errors (SSE) 1:51
Why Squared? 3:38
Why Squared? 3:39
Quantitative Properties of Regression Line 4:51
Quantitative Properties of Regression Line 4:52
So How do we Find Such a Line? 6:49
SSEs of Different Line Equations & Lowest SSE 6:50
Carl Gauss' Method 8:01
How Do We Find Slope (b1) 11:00
How Do We Find Slope (b1) 11:01
Hoe Do We Find Intercept 15:11
Hoe Do We Find Intercept 15:12
Example 1: Which of These Equations Fit the Above Data Best? 17:18
Example 2: Find the Regression Line for These Data Points and Interpret It 26:31
Example 3: Summarize the Scatterplot and Find the Regression Line. 34:31
Example 4: Examine the Mean of Residuals 43:52
Correlation 43:58
Intro 0:00
Summarizing a Scatterplot Quantitatively 0:47
Shape 0:48
Trend 1:11
Strength: Correlation ® 1:45
Correlation Coefficient ( r ) 2:30
Correlation Coefficient ( r ) 2:31
Trees vs. Forest 11:59
Trees vs. Forest 12:00
Calculating r 15:07
Average Product of z-scores for x and y 15:08
Relationship between Correlation and Slope 21:10
Relationship between Correlation and Slope 21:11
Example 1: Find the Correlation between Grams of Fat and Cost 24:11
Example 2: Relationship between r and b1 30:24
Example 3: Find the Regression Line 33:35
Example 4: Find the Correlation Coefficient for this Set of Data 37:37
Correlation: r vs. r-squared 52:52
Intro 0:00
R-squared 0:44
What is the Meaning of It? Why Squared? 0:45
Parsing Sum of Squared (Parsing Variability) 2:25
SST = SSR + SSE 2:26
What is SST and SSE? 7:46
What is SST and SSE? 7:47
r-squared 18:33
Coefficient of Determination 18:34
If the Correlation is Strong… 20:25
If the Correlation is Strong… 20:26
If the Correlation is Weak… 22:36
If the Correlation is Weak… 22:37
Example 1: Find r-squared for this Set of Data 23:56
Example 2: What Does it Mean that the Simple Linear Regression is a 'Model' of Variance? 33:54
Example 3: Why Does r-squared Only Range from 0 to 1 37:29
Example 4: Find the r-squared for This Set of Data 39:55
Transformations of Data 27:08
Intro 0:00
Why Transform? 0:26
Why Transform? 0:27
Shape-preserving vs. Shape-changing Transformations 5:14
Shape-preserving = Linear Transformations 5:15
Shape-changing Transformations = Non-linear Transformations 6:20
Common Shape-Preserving Transformations 7:08
Common Shape-Preserving Transformations 7:09
Common Shape-Changing Transformations 8:59
Powers 9:00
Logarithms 9:39
Change Just One Variable? Both? 10:38
Log-log Transformations 10:39
Log Transformations 14:38
Example 1: Create, Graph, and Transform the Data Set 15:19
Example 2: Create, Graph, and Transform the Data Set 20:08
Example 3: What Kind of Model would You Choose for this Data? 22:44
Example 4: Transformation of Data 25:46

## Section 6: Collecting Data in an Experiment

Sampling & Bias 54:44
Intro 0:00
Descriptive vs. Inferential Statistics 1:04
Descriptive Statistics: Data Exploration 1:05
Example 2:03
To tackle Generalization… 4:31
Generalization 4:32
Sampling 6:06
'Good' Sample 6:40
Defining Samples and Populations 8:55
Population 8:56
Sample 11:16
Why Use Sampling? 13:09
Why Use Sampling? 13:10
Goal of Sampling: Avoiding Bias 15:04
What is Bias? 15:05
Where does Bias Come from: Sampling Bias 17:53
Where does Bias Come from: Response Bias 18:27
Sampling Bias: Bias from Bas Sampling Methods 19:34
Size Bias 19:35
Voluntary Response Bias 21:13
Convenience Sample 22:22
Judgment Sample 23:58
Response Bias: Bias from 'Bad' Data Collection Methods 28:00
Nonresponse Bias 29:31
Questionnaire Bias 31:10
Incorrect Response or Measurement Bias 37:32
Example 1: What Kind of Biases? 40:29
Example 2: What Biases Might Arise? 44:46
Example 3: What Kind of Biases? 48:34
Example 4: What Kind of Biases? 51:43
Sampling Methods 14:25
Intro 0:00
Biased vs. Unbiased Sampling Methods 0:32
Biased Sampling 0:33
Unbiased Sampling 1:13
Probability Sampling Methods 2:31
Simple Random 2:54
Stratified Random Sampling 4:06
Cluster Sampling 5:24
Two-staged Sampling 6:22
Systematic Sampling 7:25
Example 2: Describe How to Take a Two-Stage Sample from this Book 10:16
Example 3: Sampling Methods 11:58
Example 4: Cluster Sample Plan 12:48
Research Design 53:54
Intro 0:00
Descriptive vs. Inferential Statistics 0:51
Descriptive Statistics: Data Exploration 0:52
Inferential Statistics 1:02
Variables and Relationships 1:44
Variables 1:45
Relationships 2:49
Not Every Type of Study is an Experiment… 4:16
Category I - Descriptive Study 4:54
Category II - Correlational Study 5:50
Category III - Experimental, Quasi-experimental, Non-experimental 6:33
Category III 7:42
Experimental, Quasi-experimental, and Non-experimental 7:43
Why CAN'T the Other Strategies Determine Causation? 10:18
Third-variable Problem 10:19
Directionality Problem 15:49
What Makes Experiments Special? 17:54
Manipulation 17:55
Control (and Comparison) 21:58
Methods of Control 26:38
Holding Constant 26:39
Matching 29:11
Random Assignment 31:48
Experiment Terminology 34:09
'true' Experiment vs. Study 34:10
Independent Variable (IV) 35:16
Dependent Variable (DV) 35:45
Factors 36:07
Treatment Conditions 36:23
Levels 37:43
Confounds or Extraneous Variables 38:04
Blind 38:38
Blind Experiments 38:39
Double-blind Experiments 39:29
How Categories Relate to Statistics 41:35
Category I - Descriptive Study 41:36
Category II - Correlational Study 42:05
Category III - Experimental, Quasi-experimental, Non-experimental 42:43
Example 1: Research Design 43:50
Example 2: Research Design 47:37
Example 3: Research Design 50:12
Example 4: Research Design 52:00
Between and Within Treatment Variability 41:31
Intro 0:00
Experimental Designs 0:51
Experimental Designs: Manipulation & Control 0:52
Two Types of Variability 2:09
Between Treatment Variability 2:10
Within Treatment Variability 3:31
Updated Goal of Experimental Design 5:47
Updated Goal of Experimental Design 5:48
Example: Drugs and Driving 6:56
Example: Drugs and Driving 6:57
Different Types of Random Assignment 11:27
All Experiments 11:28
Completely Random Design 12:02
Randomized Block Design 13:19
Randomized Block Design 15:48
Matched Pairs Design 15:49
Repeated Measures Design 19:47
Between-subject Variable vs. Within-subject Variable 22:43
Completely Randomized Design 22:44
Repeated Measures Design 25:03
Example 1: Design a Completely Random, Matched Pair, and Repeated Measures Experiment 26:16
Example 2: Block Design 31:41
Example 3: Completely Randomized Designs 35:11
Example 4: Completely Random, Matched Pairs, or Repeated Measures Experiments? 39:01

## Section 7: Review of Probability Axioms

Sample Spaces 37:52
Intro 0:00
Why is Probability Involved in Statistics 0:48
Probability 0:49
Can People Tell the Difference between Cheap and Gourmet Coffee? 2:08
Taste Test with Coffee Drinkers 3:37
If No One can Actually Taste the Difference 3:38
If Everyone can Actually Taste the Difference 5:36
Creating a Probability Model 7:09
Creating a Probability Model 7:10
D'Alembert vs. Necker 9:41
D'Alembert vs. Necker 9:42
Problem with D'Alembert's Model 13:29
Problem with D'Alembert's Model 13:30
Covering Entire Sample Space 15:08
Fundamental Principle of Counting 15:09
Where Do Probabilities Come From? 22:54
Observed Data, Symmetry, and Subjective Estimates 22:55
Checking whether Model Matches Real World 24:27
Law of Large Numbers 24:28
Example 1: Law of Large Numbers 27:46
Example 2: Possible Outcomes 30:43
Example 3: Brands of Coffee and Taste 33:25
Example 4: How Many Different Treatments are there? 35:33
Addition Rule for Disjoint Events 20:29
Intro 0:00
Disjoint Events 0:41
Disjoint Events 0:42
Meaning of 'or' 2:39
In Regular Life 2:40
In Math/Statistics/Computer Science 3:10
Addition Rule for Disjoin Events 3:55
If A and B are Disjoint: P (A and B) 3:56
If A and B are Disjoint: P (A or B) 5:15
If A and B are not Disjoint: P (A or B) 8:32
Example 1: Which of These are Mutually Exclusive? 10:50
Example 2: What is the Probability that You will Have a Combination of One Heads and Two Tails? 12:57
Example 3: Engagement Party 15:17
Example 4: Home Owner's Insurance 18:30
Conditional Probability 57:19
Intro 0:00
'or' vs. 'and' vs. Conditional Probability 1:07
'or' vs. 'and' vs. Conditional Probability 1:08
'and' vs. Conditional Probability 5:57
P (M or L) 5:58
P (M and L) 8:41
P (M|L) 11:04
P (L|M) 12:24
Tree Diagram 15:02
Tree Diagram 15:03
Defining Conditional Probability 22:42
Defining Conditional Probability 22:43
Common Contexts for Conditional Probability 30:56
Medical Testing: Positive Predictive Value 30:57
Medical Testing: Sensitivity 33:03
Statistical Tests 34:27
Example 1: Drug and Disease 36:41
Example 2: Marbles and Conditional Probability 40:04
Example 3: Cards and Conditional Probability 45:59
Example 4: Votes and Conditional Probability 50:21
Independent Events 24:27
Intro 0:00
Independent Events & Conditional Probability 0:26
Non-independent Events 0:27
Independent Events 2:00
Non-independent and Independent Events 3:08
Non-independent and Independent Events 3:09
Defining Independent Events 5:52
Defining Independent Events 5:53
Multiplication Rule 7:29
Previously… 7:30
But with Independent Evens 8:53
Example 1: Which of These Pairs of Events are Independent? 11:12
Example 2: Health Insurance and Probability 15:12
Example 3: Independent Events 17:42
Example 4: Independent Events 20:03

## Section 8: Probability Distributions

Introduction to Probability Distributions 56:45
Intro 0:00
Sampling vs. Probability 0:57
Sampling 0:58
Missing 1:30
What is Missing? 3:06
Insight: Probability Distributions 5:26
Insight: Probability Distributions 5:27
What is a Probability Distribution? 7:29
From Sample Spaces to Probability Distributions 8:44
Sample Space 8:45
Probability Distribution of the Sum of Two Die 11:16
The Random Variable 17:43
The Random Variable 17:44
Expected Value 21:52
Expected Value 21:53
Example 1: Probability Distributions 28:45
Example 2: Probability Distributions 35:30
Example 3: Probability Distributions 43:37
Example 4: Probability Distributions 47:20
Expected Value & Variance of Probability Distributions 53:41
Intro 0:00
Discrete vs. Continuous Random Variables 1:04
Discrete vs. Continuous Random Variables 1:05
Mean and Variance Review 4:44
Mean: Sample, Population, and Probability Distribution 4:45
Variance: Sample, Population, and Probability Distribution 9:12
Example Situation 14:10
Example Situation 14:11
Some Special Cases… 16:13
Some Special Cases… 16:14
Linear Transformations 19:22
Linear Transformations 19:23
What Happens to Mean and Variance of the Probability Distribution? 20:12
n Independent Values of X 25:38
n Independent Values of X 25:39
Compare These Two Situations 30:56
Compare These Two Situations 30:57
Two Random Variables, X and Y 32:02
Two Random Variables, X and Y 32:03
Example 1: Expected Value & Variance of Probability Distributions 35:35
Example 2: Expected Values & Standard Deviation 44:17
Example 3: Expected Winnings and Standard Deviation 48:18
Binomial Distribution 55:15
Intro 0:00
Discrete Probability Distributions 1:42
Discrete Probability Distributions 1:43
Binomial Distribution 2:36
Binomial Distribution 2:37
Multiplicative Rule Review 6:54
Multiplicative Rule Review 6:55
How Many Outcomes with k 'Successes' 10:23
Adults and Bachelor's Degree: Manual List of Outcomes 10:24
P (X=k) 19:37
Putting Together # of Outcomes with the Multiplicative Rule 19:38
Expected Value and Standard Deviation in a Binomial Distribution 25:22
Expected Value and Standard Deviation in a Binomial Distribution 25:23
Example 1: Coin Toss 33:42
Example 3: Types of Blood and Probability 45:39
Example 4: Expected Number and Standard Deviation 51:11

## Section 9: Sampling Distributions of Statistics

Introduction to Sampling Distributions 48:17
Intro 0:00
Probability Distributions vs. Sampling Distributions 0:55
Probability Distributions vs. Sampling Distributions 0:56
Same Logic 3:55
Logic of Probability Distribution 3:56
Example: Rolling Two Die 6:56
Simulating Samples 9:53
To Come Up with Probability Distributions 9:54
In Sampling Distributions 11:12
Connecting Sampling and Research Methods with Sampling Distributions 12:11
Connecting Sampling and Research Methods with Sampling Distributions 12:12
Simulating a Sampling Distribution 14:14
Experimental Design: Regular Sleep vs. Less Sleep 14:15
Logic of Sampling Distributions 23:08
Logic of Sampling Distributions 23:09
General Method of Simulating Sampling Distributions 25:38
General Method of Simulating Sampling Distributions 25:39
Questions that Remain 28:45
Questions that Remain 28:46
Example 1: Mean and Standard Error of Sampling Distribution 30:57
Example 2: What is the Best Way to Describe Sampling Distributions? 37:12
Example 3: Matching Sampling Distributions 38:21
Example 4: Mean and Standard Error of Sampling Distribution 41:51
Sampling Distribution of the Mean 1:08:48
Intro 0:00
Special Case of General Method for Simulating a Sampling Distribution 1:53
Special Case of General Method for Simulating a Sampling Distribution 1:54
Computer Simulation 3:43
Using Simulations to See Principles behind Shape of SDoM 15:50
Using Simulations to See Principles behind Shape of SDoM 15:51
Conditions 17:38
Using Simulations to See Principles behind Center (Mean) of SDoM 20:15
Using Simulations to See Principles behind Center (Mean) of SDoM 20:16
Conditions: Does n Matter? 21:31
Conditions: Does Number of Simulation Matter? 24:37
Using Simulations to See Principles behind Standard Deviation of SDoM 27:13
Using Simulations to See Principles behind Standard Deviation of SDoM 27:14
Conditions: Does n Matter? 34:45
Conditions: Does Number of Simulation Matter? 36:24
Central Limit Theorem 37:13
SHAPE 38:08
CENTER 39:34
Comparing Population, Sample, and SDoM 43:10
Comparing Population, Sample, and SDoM 43:11
Answering the 'Questions that Remain' 48:24
What Happens When We Don't Know What the Population Looks Like? 48:25
Can We Have Sampling Distributions for Summary Statistics Other than the Mean? 49:42
How Do We Know whether a Sample is Sufficiently Unlikely? 53:36
Do We Always Have to Simulate a Large Number of Samples in Order to get a Sampling Distribution? 54:40
Example 1: Mean Batting Average 55:25
Example 2: Mean Sampling Distribution and Standard Error 59:07
Example 3: Sampling Distribution of the Mean 61:04
Sampling Distribution of Sample Proportions 54:37
Intro 0:00
Intro to Sampling Distribution of Sample Proportions (SDoSP) 0:51
Categorical Data (Examples) 0:52
Wish to Estimate Proportion of Population from Sample… 2:00
Notation 3:34
Population Proportion and Sample Proportion Notations 3:35
What's the Difference? 9:19
SDoM vs. SDoSP: Type of Data 9:20
SDoM vs. SDoSP: Shape 11:24
SDoM vs. SDoSP: Center 12:30
Binomial Distribution vs. Sampling Distribution of Sample Proportions 19:14
Binomial Distribution vs. SDoSP: Type of Data 19:17
Binomial Distribution vs. SDoSP: Shape 21:07
Binomial Distribution vs. SDoSP: Center 21:43
Binomial Distribution vs. SDoSP: Spread 24:08
Example 1: Sampling Distribution of Sample Proportions 26:07
Example 2: Sampling Distribution of Sample Proportions 37:58
Example 3: Sampling Distribution of Sample Proportions 44:42
Example 4: Sampling Distribution of Sample Proportions 45:57

## Section 10: Inferential Statistics

Introduction to Confidence Intervals 42:53
Intro 0:00
Inferential Statistics 0:50
Inferential Statistics 0:51
Two Problems with This Picture… 3:20
Two Problems with This Picture… 3:21
Solution: Confidence Intervals (CI) 4:59
Solution: Hypotheiss Testing (HT) 5:49
Which Parameters are Known? 6:45
Which Parameters are Known? 6:46
Confidence Interval - Goal 7:56
When We Don't Know m but know s 7:57
When We Don't Know 18:27
When We Don't Know m nor s 18:28
Example 1: Confidence Intervals 26:18
Example 2: Confidence Intervals 29:46
Example 3: Confidence Intervals 32:18
Example 4: Confidence Intervals 38:31
t Distributions 1:02:06
Intro 0:00
When to Use z vs. t? 1:07
When to Use z vs. t? 1:08
What is z and t? 3:02
z-score and t-score: Commonality 3:03
z-score and t-score: Formulas 3:34
z-score and t-score: Difference 5:22
Why not z? (Why t?) 7:24
Why not z? (Why t?) 7:25
But Don't Worry! 15:13
Gossett and t-distributions 15:14
Rules of t Distributions 17:05
t-distributions are More Normal as n Gets Bigger 17:06
t-distributions are a Family of Distributions 18:55
Degrees of Freedom (df) 20:02
Degrees of Freedom (df) 20:03
t Family of Distributions 24:07
t Family of Distributions : df = 2 , 4, and 60 24:08
df = 60 29:16
df = 2 29:59
How to Find It? 31:01
'Student's t-distribution' or 't-distribution' 31:02
Excel Example 33:06
Example 1: Which Distribution Do You Use? Z or t? 45:26
Example 2: Friends on Facebook 47:41
Example 3: t Distributions 52:15
Example 4: t Distributions , confidence interval, and mean 55:59
Introduction to Hypothesis Testing 1:06:33
Intro 0:00
Issues to Overcome in Inferential Statistics 1:35
Issues to Overcome in Inferential Statistics 1:36
What Happens When We Don't Know What the Population Looks Like? 2:57
How Do We Know whether a sample is Sufficiently Unlikely 3:43
Hypothesizing a Population 6:44
Hypothesizing a Population 6:45
Null Hypothesis 8:07
Alternative Hypothesis 8:56
Hypotheses 11:58
Hypotheses 11:59
Errors in Hypothesis Testing 14:22
Errors in Hypothesis Testing 14:23
Steps of Hypothesis Testing 21:15
Steps of Hypothesis Testing 21:16
Single Sample HT ( When Sigma Available) 26:08
Step1 27:08
Step 2 27:58
Step 3 28:17
Step 4 32:18
Single Sample HT (When Sigma Not Available) 36:33
Step1: Hypothesis Testing 36:58
Step 2: Significance Level 37:25
Step 3: Decision Stage 37:40
Step 4: Sample 41:36
Sigma and p-value 45:04
Sigma and p-value 45:05
On tailed vs. Two Tailed Hypotheses 45:51
Example 1: Hypothesis Testing 48:37
Example 2: Heights of Women in the US 57:43
Example 3: Select the Best Way to Complete This Sentence 63:23
Confidence Intervals for the Difference of Two Independent Means 55:14
Intro 0:00
One Mean vs. Two Means 1:17
One Mean vs. Two Means 1:18
Notation 2:41
A Sample! A Set! 2:42
Mean of X, Mean of Y, and Difference of Two Means 3:56
SE of X 4:34
SE of Y 6:28
Sampling Distribution of the Difference between Two Means (SDoD) 7:48
Sampling Distribution of the Difference between Two Means (SDoD) 7:49
Rules of the SDoD (similar to CLT!) 15:00
Mean for the SDoD Null Hypothesis 15:01
Standard Error 17:39
When can We Construct a CI for the Difference between Two Means? 21:28
Three Conditions 21:29
Finding CI 23:56
One Mean CI 23:57
Two Means CI 25:45
Finding t 29:16
Finding t 29:17
Interpreting CI 30:25
Interpreting CI 30:26
Better Estimate of s (s pool) 34:15
Better Estimate of s (s pool) 34:16
Example 1: Confidence Intervals 42:32
Example 2: SE of the Difference 52:36
Hypothesis Testing for the Difference of Two Independent Means 50:00
Intro 0:00
The Goal of Hypothesis Testing 0:56
One Sample and Two Samples 0:57
Sampling Distribution of the Difference between Two Means (SDoD) 3:42
Sampling Distribution of the Difference between Two Means (SDoD) 3:43
Rules of the SDoD (Similar to CLT!) 6:46
Shape 6:47
Mean for the Null Hypothesis 7:26
Standard Error for Independent Samples (When Variance is Homogenous) 8:18
Standard Error for Independent Samples (When Variance is not Homogenous) 9:25
Same Conditions for HT as for CI 10:08
Three Conditions 10:09
Steps of Hypothesis Testing 11:04
Steps of Hypothesis Testing 11:05
Formulas that Go with Steps of Hypothesis Testing 13:21
Step 1 13:25
Step 2 14:18
Step 3 15:00
Step 4 16:57
Example 1: Hypothesis Testing for the Difference of Two Independent Means 18:47
Example 2: Hypothesis Testing for the Difference of Two Independent Means 33:55
Example 3: Hypothesis Testing for the Difference of Two Independent Means 44:22
Confidence Intervals & Hypothesis Testing for the Difference of Two Paired Means 1:14:11
Intro 0:00
The Goal of Hypothesis Testing 1:27
One Sample and Two Samples 1:28
Independent Samples vs. Paired Samples 3:16
Independent Samples vs. Paired Samples 3:17
Which is Which? 5:20
Independent SAMPLES vs. Independent VARIABLES 7:43
independent SAMPLES vs. Independent VARIABLES 7:44
T-tests Always… 10:48
T-tests Always… 10:49
Notation for Paired Samples 12:59
Notation for Paired Samples 13:00
Steps of Hypothesis Testing for Paired Samples 16:13
Steps of Hypothesis Testing for Paired Samples 16:14
Rules of the SDoD (Adding on Paired Samples) 18:03
Shape 18:04
Mean for the Null Hypothesis 18:31
Standard Error for Independent Samples (When Variance is Homogenous) 19:25
Standard Error for Paired Samples 20:39
Formulas that go with Steps of Hypothesis Testing 22:59
Formulas that go with Steps of Hypothesis Testing 23:00
Confidence Intervals for Paired Samples 30:32
Confidence Intervals for Paired Samples 30:33
Example 1: Confidence Intervals & Hypothesis Testing for the Difference of Two Paired Means 32:28
Example 2: Confidence Intervals & Hypothesis Testing for the Difference of Two Paired Means 44:02
Example 3: Confidence Intervals & Hypothesis Testing for the Difference of Two Paired Means 52:23
Type I and Type II Errors 31:27
Intro 0:00
Errors and Relationship to HT and the Sample Statistic? 1:11
Errors and Relationship to HT and the Sample Statistic? 1:12
One Sample t-test: Friends on Facebook 7:01
Two Sample t-test: Friends on Facebook 13:46
Usually, Lots of Overlap between Null and Alternative Distributions 16:59
Overlap between Null and Alternative Distributions 17:00
How Distributions and 'Box' Fit Together 22:45
How Distributions and 'Box' Fit Together 22:46
Example 1: Types of Errors 25:54
Example 2: Types of Errors 27:30
Example 3: What is the Danger of the Type I Error? 29:38
Effect Size & Power 44:41
Intro 0:00
Distance between Distributions: Sample t 0:49
Distance between Distributions: Sample t 0:50
Problem with Distance in Terms of Standard Error 2:56
Problem with Distance in Terms of Standard Error 2:57
Test Statistic (t) vs. Effect Size (d or g) 4:38
Test Statistic (t) vs. Effect Size (d or g) 4:39
Rules of Effect Size 6:09
Rules of Effect Size 6:10
Why Do We Need Effect Size? 8:21
Tells You the Practical Significance 8:22
HT can be Deceiving… 10:25
Important Note 10:42
What is Power? 11:20
What is Power? 11:21
Why Do We Need Power? 14:19
Conditional Probability and Power 14:20
Power is: 16:27
Can We Calculate Power? 19:00
Can We Calculate Power? 19:01
How Does Alpha Affect Power? 20:36
How Does Alpha Affect Power? 20:37
How Does Effect Size Affect Power? 25:38
How Does Effect Size Affect Power? 25:39
How Does Variability and Sample Size Affect Power? 27:56
How Does Variability and Sample Size Affect Power? 27:57
How Do We Increase Power? 32:47
Increasing Power 32:48
Example 1: Effect Size & Power 35:40
Example 2: Effect Size & Power 37:38
Example 3: Effect Size & Power 40:55

## Section 11: Analysis of Variance

F-distributions 24:46
Intro 0:00
Z- & T-statistic and Their Distribution 0:34
Z- & T-statistic and Their Distribution 0:35
F-statistic 4:55
The F Ration ( the Variance Ratio) 4:56
F-distribution 12:29
F-distribution 12:30
s and p-value 15:00
s and p-value 15:01
Example 1: Why Does F-distribution Stop At 0 But Go On Until Infinity? 18:33
Example 2: F-distributions 19:29
Example 3: F-distributions and Heights 21:29
ANOVA with Independent Samples 1:09:25
Intro 0:00
The Limitations of t-tests 1:12
The Limitations of t-tests 1:13
Two Major Limitations of Many t-tests 3:26
Two Major Limitations of Many t-tests 3:27
Ronald Fisher's Solution… F-test! New Null Hypothesis 4:43
Ronald Fisher's Solution… F-test! New Null Hypothesis (Omnibus Test - One Test to Rule Them All!) 4:44
Analysis of Variance (ANoVA) Notation 7:47
Analysis of Variance (ANoVA) Notation 7:48
Partitioning (Analyzing) Variance 9:58
Total Variance 9:59
Within-group Variation 14:00
Between-group Variation 16:22
Time out: Review Variance & SS 17:05
Time out: Review Variance & SS 17:06
F-statistic 19:22
The F Ratio (the Variance Ratio) 19:23
S²bet = SSbet / dfbet 22:13
What is This? 22:14
How Many Means? 23:20
So What is the dfbet? 23:38
So What is SSbet? 24:15
S²w = SSw / dfw 26:05
What is This? 26:06
How Many Means? 27:20
So What is the dfw? 27:36
So What is SSw? 28:18
Chart of Independent Samples ANOVA 29:25
Chart of Independent Samples ANOVA 29:26
Example 1: Who Uploads More Photos: Unknown Ethnicity, Latino, Asian, Black, or White Facebook Users? 35:52
Hypotheses 35:53
Significance Level 39:40
Decision Stage 40:05
Calculate Samples' Statistic and p-Value 44:10
Reject or Fail to Reject H0 55:54
Example 2: ANOVA with Independent Samples 58:21
Repeated Measures ANOVA 1:15:13
Intro 0:00
The Limitations of t-tests 0:36
Who Uploads more Pictures and Which Photo-Type is Most Frequently Used on Facebook? 0:37
ANOVA (F-test) to the Rescue! 5:49
Omnibus Hypothesis 5:50
Analyze Variance 7:27
Independent Samples vs. Repeated Measures 9:12
Same Start 9:13
Independent Samples ANOVA 10:43
Repeated Measures ANOVA 12:00
Independent Samples ANOVA 16:00
Same Start: All the Variance Around Grand Mean 16:01
Independent Samples 16:23
Repeated Measures ANOVA 18:18
Same Start: All the Variance Around Grand Mean 18:19
Repeated Measures 18:33
Repeated Measures F-statistic 21:22
The F Ratio (The Variance Ratio) 21:23
S²bet = SSbet / dfbet 23:07
What is This? 23:08
How Many Means? 23:39
So What is the dfbet? 23:54
So What is SSbet? 24:32
S² resid = SS resid / df resid 25:46
What is This? 25:47
So What is SS resid? 26:44
So What is the df resid? 27:36
SS subj and df subj 28:11
What is This? 28:12
How Many Subject Means? 29:43
So What is df subj? 30:01
So What is SS subj? 30:09
SS total and df total 31:42
What is This? 31:43
What is the Total Number of Data Points? 32:02
So What is df total? 32:34
so What is SS total? 32:47
Chart of Repeated Measures ANOVA 33:19
Chart of Repeated Measures ANOVA: F and Between-samples Variability 33:20
Chart of Repeated Measures ANOVA: Total Variability, Within-subject (case) Variability, Residual Variability 35:50
Example 1: Which is More Prevalent on Facebook: Tagged, Uploaded, Mobile, or Profile Photos? 40:25
Hypotheses 40:26
Significance Level 41:46
Decision Stage 42:09
Calculate Samples' Statistic and p-Value 46:18
Reject or Fail to Reject H0 57:55
Example 2: Repeated Measures ANOVA 58:57
Example 3: What's the Problem with a Bunch of Tiny t-tests? 73:59

## Section 12: Chi-square Test

Chi-Square Goodness-of-Fit Test 58:23
Intro 0:00
Where Does the Chi-Square Test Belong? 0:50
Where Does the Chi-Square Test Belong? 0:51
A New Twist on HT: Goodness-of-Fit 7:23
HT in General 7:24
Goodness-of-Fit HT 8:26
Null Hypothesis 12:18
Alternative Hypothesis 13:23
Example 14:38
Chi-Square Statistic 17:52
Chi-Square Statistic 17:53
Chi-Square Distributions 24:31
Chi-Square Distributions 24:32
Conditions for Chi-Square 28:58
Condition 1 28:59
Condition 2 30:20
Condition 3 30:32
Condition 4 31:47
Example 1: Chi-Square Goodness-of-Fit Test 32:23
Example 2: Chi-Square Goodness-of-Fit Test 44:34
Example 3: Which of These Statements Describe Properties of the Chi-Square Goodness-of-Fit Test? 56:06
Chi-Square Test of Homogeneity 51:36
Intro 0:00
Goodness-of-Fit vs. Homogeneity 1:13
Goodness-of-Fit HT 1:14
Homogeneity 2:00
Analogy 2:38
Null Hypothesis 5:01
Alternative Hypothesis 6:11
Example 6:33
Chi-Square Statistic 10:12
Same as Goodness-of-Fit Test 10:13
Set Up Data 12:28
Setting Up Data Example 12:29
Expected Frequency 16:53
Expected Frequency 16:54
Chi-Square Distributions & df 19:26
Chi-Square Distributions & df 19:27
Conditions for Test of Homogeneity 20:54
Condition 1 20:55
Condition 2 21:39
Condition 3 22:05
Condition 4 22:23
Example 1: Chi-Square Test of Homogeneity 22:52
Example 2: Chi-Square Test of Homogeneity 32:10

## Section 13: Overview of Statistics

Overview of Statistics 18:11
Intro 0:00
The Statistical Tests (HT) We've Covered 0:28
The Statistical Tests (HT) We've Covered 0:29
Organizing the Tests We've Covered… 1:08
One Sample: Continuous DV and Categorical DV 1:09
Two Samples: Continuous DV and Categorical DV 5:41
More Than Two Samples: Continuous DV and Categorical DV 8:21
The Following Data: OK Cupid 10:10
The Following Data: OK Cupid 10:11
Example 1: Weird-MySpace-Angle Profile Photo 10:38
Example 2: Geniuses 12:30
Example 3: Promiscuous iPhone Users 13:37
Example 4: Women, Aging, and Messaging 16:07

Duration: 36 hours, 33 minutes

Number of Lessons: 49

This time-saving course covers information applicable for both high school and college statistics courses, as well as lifelong learners. Excel and downloadable files are used to highlight lecture examples and provide hands-on training of the popular program.

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Topics Include:

• Descriptive vs Inferential Statistics
• Frequency Distributions
• Central Tendency
• Normal Distribution
• Linear Regression
• Sampling Methods
• Probability Distributions
• Sampling Distributions
• Hypothesis Testing
• ANOVA
• Chi-Square Test

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