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Dr. Ji Son
Normal Distribution: PDF vs. CDF
Slide Duration:Table of Contents
I. Introduction
Descriptive Statistics vs. Inferential Statistics
25m 31s
 Intro0:00
 Roadmap0:10
 Roadmap0:11
 Statistics0:35
 Statistics0:36
 Let's Think About High School Science1:12
 Measurement and Find Patterns (Mathematical Formula)1:13
 Statistics = Math of Distributions4:58
 Distributions4:59
 Problematic… but also GREAT5:58
 Statistics7:33
 How is It Different from Other Specializations in Mathematics?7:34
 Statistics is Fundamental in Natural and Social Sciences7:53
 Two Skills of Statistics8:20
 Description (Exploration)8:21
 Inference9:13
 Descriptive Statistics vs. Inferential Statistics: Apply to Distributions9:58
 Descriptive Statistics9:59
 Inferential Statistics11:05
 Populations vs. Samples12:19
 Populations vs. Samples: Is it the Truth?12:20
 Populations vs. Samples: Pros & Cons13:36
 Populations vs. Samples: Descriptive Values16:12
 Putting Together Descriptive/Inferential Stats & Populations/Samples17:10
 Putting Together Descriptive/Inferential Stats & Populations/Samples17:11
 Example 1: Descriptive Statistics vs. Inferential Statistics19:09
 Example 2: Descriptive Statistics vs. Inferential Statistics20:47
 Example 3: Sample, Parameter, Population, and Statistic21:40
 Example 4: Sample, Parameter, Population, and Statistic23:28
II. About Samples: Cases, Variables, Measurements
About Samples: Cases, Variables, Measurements
32m 14s
 Intro0:00
 Data0:09
 Data, Cases, Variables, and Values0:10
 Rows, Columns, and Cells2:03
 Example: Aircrafts3:52
 How Do We Get Data?5:38
 Research: Question and Hypothesis5:39
 Research Design7:11
 Measurement7:29
 Research Analysis8:33
 Research Conclusion9:30
 Types of Variables10:03
 Discrete Variables10:04
 Continuous Variables12:07
 Types of Measurements14:17
 Types of Measurements14:18
 Types of Measurements (Scales)17:22
 Nominal17:23
 Ordinal19:11
 Interval21:33
 Ratio24:24
 Example 1: Cases, Variables, Measurements25:20
 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
III. Visualizing Distributions
Introduction to Excel
8m 9s
 Intro0:00
 Before Visualizing Distribution0:10
 Excel0:11
 Excel: Organization0:45
 Workbook0:46
 Column x Rows1:50
 Tools: Menu Bar, Standard Toolbar, and Formula Bar3:00
 Excel + Data6:07
 Exce and Data6:08
Frequency Distributions in Excel
39m 10s
 Intro0:00
 Roadmap0:08
 Data in Excel and Frequency Distributions0:09
 Raw Data to Frequency Tables0:42
 Raw Data to Frequency Tables0:43
 Frequency Tables: Using Formulas and Pivot Tables1:28
 Example 1: Number of Births7:17
 Example 2: Age Distribution20:41
 Example 3: Height Distribution27:45
 Example 4: Height Distribution of Males32:19
Frequency Distributions and Features
25m 29s
 Intro0:00
 Roadmap0:10
 Data in Excel, Frequency Distributions, and Features of Frequency Distributions0:11
 Example #11:35
 Uniform1:36
 Example #22:58
 Unimodal, Skewed Right, and Asymmetric2:59
 Example #36:29
 Bimodal6:30
 Example #4a8:29
 Symmetric, Unimodal, and Normal8:30
 Point of Inflection and Standard Deviation11:13
 Example #4b12:43
 Normal Distribution12:44
 Summary13:56
 Uniform, Skewed, Bimodal, and Normal13:57
 Sketch Problem 1: Driver's License17:34
 Sketch Problem 2: Life Expectancy20:01
 Sketch Problem 3: Telephone Numbers22:01
 Sketch Problem 4: Length of Time Used to Complete a Final Exam23:43
Dotplots and Histograms in Excel
42m 42s
 Intro0:00
 Roadmap0:06
 Roadmap0:07
 Previously1:02
 Data, Frequency Table, and visualization1:03
 Dotplots1:22
 Dotplots Excel Example1:23
 Dotplots: Pros and Cons7:22
 Pros and Cons of Dotplots7:23
 Dotplots Excel Example Cont.9:07
 Histograms12:47
 Histograms Overview12:48
 Example of Histograms15:29
 Histograms: Pros and Cons31:39
 Pros31:40
 Cons32:31
 Frequency vs. Relative Frequency32:53
 Frequency32:54
 Relative Frequency33:36
 Example 1: Dotplots vs. Histograms34:36
 Example 2: Age of Pennies Dotplot36:21
 Example 3: Histogram of Mammal Speeds38:27
 Example 4: Histogram of Life Expectancy40:30
Stemplots
12m 23s
 Intro0:00
 Roadmap0:05
 Roadmap0:06
 What Sets Stemplots Apart?0:46
 Data Sets, Dotplots, Histograms, and Stemplots0:47
 Example 1: What Do Stemplots Look Like?1:58
 Example 2: BacktoBack Stemplots5:00
 Example 3: Quiz Grade Stemplot7:46
 Example 4: Quiz Grade & Afterschool Tutoring Stemplot9:56
Bar Graphs
22m 49s
 Intro0:00
 Roadmap0:05
 Roadmap0:08
 Review of Frequency Distributions0:44
 Yaxis and Xaxis0:45
 Types of Frequency Visualizations Covered so Far2:16
 Introduction to Bar Graphs4:07
 Example 1: Bar Graph5:32
 Example 1: Bar Graph5:33
 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 Gender14:02
 Example 3: Cases, Variables, and Frequency Visualization16:34
 Example 4: What Kind of Graphs are Shown Below?19:29
IV. Summarizing Distributions
Central Tendency: Mean, Median, Mode
38m 50s
 Intro0:00
 Roadmap0:07
 Roadmap0:08
 Central Tendency 10:56
 Way to Summarize a Distribution of Scores0:57
 Mode1:32
 Median2:02
 Mean2:36
 Central Tendency 23:47
 Mode3:48
 Median4:20
 Mean5:25
 Summation Symbol6:11
 Summation Symbol6:12
 Population vs. Sample10:46
 Population vs. Sample10:47
 Excel Examples15:08
 Finding Mode, Median, and Mean in Excel15:09
 Median vs. Mean21:45
 Effect of Outliers21:46
 Relationship Between Parameter and Statistic22:44
 Type of Measurements24:00
 Which Distributions to Use With24:55
 Example 1: Mean25:30
 Example 2: Using Summation Symbol29:50
 Example 3: Average Calorie Count32:50
 Example 4: Creating an Example Set35:46
Variability
42m 40s
 Intro0:00
 Roadmap0:05
 Roadmap0:06
 Variability (or Spread)0:45
 Variability (or Spread)0:46
 Things to Think About5:45
 Things to Think About5:46
 Range, Quartiles and Interquartile Range6:37
 Range6:38
 Interquartile Range8:42
 Interquartile Range Example10:58
 Interquartile Range Example10:59
 Variance and Standard Deviation12:27
 Deviations12:28
 Sum of Squares14:35
 Variance16:55
 Standard Deviation17:44
 Sum of Squares (SS)18:34
 Sum of Squares (SS)18:35
 Population vs. Sample SD22:00
 Population vs. Sample SD22:01
 Population vs. Sample23:20
 Mean23:21
 SD23:51
 Example 1: Find the Mean and Standard Deviation of the Variable Friends in the Excel File27:21
 Example 2: Find the Mean and Standard Deviation of the Tagged Photos in the Excel File35:25
 Example 3: Sum of Squares38:58
 Example 4: Standard Deviation41:48
Five Number Summary & Boxplots
57m 15s
 Intro0:00
 Roadmap0:06
 Roadmap0:07
 Summarizing Distributions0:37
 Shape, Center, and Spread0:38
 5 Number Summary1:14
 Boxplot: Visualizing 5 Number Summary3:37
 Boxplot: Visualizing 5 Number Summary3:38
 Boxplots on Excel9:01
 Using 'Stocks' and Using Stacked Columns9:02
 Boxplots on Excel Example10:14
 When are Boxplots Useful?32:14
 Pros32:15
 Cons32:59
 How to Determine Outlier Status33:24
 Rule of Thumb: Upper Limit33:25
 Rule of Thumb: Lower Limit34:16
 Signal Outliers in an Excel Data File Using Conditional Formatting34:52
 Modified Boxplot48:38
 Modified Boxplot48:39
 Example 1: Percentage Values & Lower and Upper Whisker49:10
 Example 2: Boxplot50:10
 Example 3: Estimating IQR From Boxplot53:46
 Example 4: Boxplot and Missing Whisker54:35
Shape: Calculating Skewness & Kurtosis
41m 51s
 Intro0:00
 Roadmap0:16
 Roadmap0:17
 Skewness Concept1:09
 Skewness Concept1:10
 Calculating Skewness3:26
 Calculating Skewness3:27
 Interpreting Skewness7:36
 Interpreting Skewness7:37
 Excel Example8:49
 Kurtosis Concept20:29
 Kurtosis Concept20:30
 Calculating Kurtosis24:17
 Calculating Kurtosis24:18
 Interpreting Kurtosis29:01
 Leptokurtic29:35
 Mesokurtic30:10
 Platykurtic31:06
 Excel Example32:04
 Example 1: Shape of Distribution38:28
 Example 2: Shape of Distribution39:29
 Example 3: Shape of Distribution40:14
 Example 4: Kurtosis41:10
Normal Distribution
34m 33s
 Intro0:00
 Roadmap0:13
 Roadmap0:14
 What is a Normal Distribution0:44
 The Normal Distribution As a Theoretical Model0:45
 Possible Range of Probabilities3:05
 Possible Range of Probabilities3:06
 What is a Normal Distribution5:07
 Can Be Described By5:08
 Properties5:49
 'Same' Shape: Illusion of Different Shape!7:35
 'Same' Shape: Illusion of Different Shape!7:36
 Types of Problems13:45
 Example: Distribution of SAT Scores13:46
 Shape Analogy19:48
 Shape Analogy19:49
 Example 1: The Standard Normal Distribution and ZScores22:34
 Example 2: The Standard Normal Distribution and ZScores25:54
 Example 3: Sketching and Normal Distribution28:55
 Example 4: Sketching and Normal Distribution32:32
Standard Normal Distributions & ZScores
41m 44s
 Intro0:00
 Roadmap0:06
 Roadmap0:07
 A Family of Distributions0:28
 Infinite Set of Distributions0:29
 Transforming Normal Distributions to 'Standard' Normal Distribution1:04
 Normal Distribution vs. Standard Normal Distribution2:58
 Normal Distribution vs. Standard Normal Distribution2:59
 ZScore, Raw Score, Mean, & SD4:08
 ZScore, Raw Score, Mean, & SD4:09
 Weird ZScores9:40
 Weird ZScores9:41
 Excel16:45
 For Normal Distributions16:46
 For Standard Normal Distributions19:11
 Excel Example20:24
 Types of Problems25:18
 Percentage Problem: P(x)25:19
 Raw Score and ZScore Problems26:28
 Standard Deviation Problems27:01
 Shape Analogy27:44
 Shape Analogy27:45
 Example 1: Deaths Due to Heart Disease vs. Deaths Due to Cancer28:24
 Example 2: Heights of Male College Students33:15
 Example 3: Mean and Standard Deviation37:14
 Example 4: Finding Percentage of Values in a Standard Normal Distribution37:49
Normal Distribution: PDF vs. CDF
55m 44s
 Intro0:00
 Roadmap0:15
 Roadmap0:16
 Frequency vs. Cumulative Frequency0:56
 Frequency vs. Cumulative Frequency0:57
 Frequency vs. Cumulative Frequency4:32
 Frequency vs. Cumulative Frequency Cont.4:33
 Calculus in Brief6:21
 DerivativeIntegral Continuum6:22
 PDF10:08
 PDF for Standard Normal Distribution10:09
 PDF for Normal Distribution14:32
 Integral of PDF = CDF21:27
 Integral of PDF = CDF21:28
 Example 1: Cumulative Frequency Graph23:31
 Example 2: Mean, Standard Deviation, and Probability24:43
 Example 3: Mean and Standard Deviation35:50
 Example 4: Age of Cars49:32
V. Linear Regression
Scatterplots
47m 19s
 Intro0:00
 Roadmap0:04
 Roadmap0:05
 Previous Visualizations0:30
 Frequency Distributions0:31
 Compare & Contrast2:26
 Frequency Distributions Vs. Scatterplots2:27
 Summary Values4:53
 Shape4:54
 Center & Trend6:41
 Spread & Strength8:22
 Univariate & Bivariate10:25
 Example Scatterplot10:48
 Shape, Trend, and Strength10:49
 Positive and Negative Association14:05
 Positive and Negative Association14:06
 Linearity, Strength, and Consistency18:30
 Linearity18:31
 Strength19:14
 Consistency20:40
 Summarizing a Scatterplot22:58
 Summarizing a Scatterplot22:59
 Example 1: Gapminder.org, Income x Life Expectancy26:32
 Example 2: Gapminder.org, Income x Infant Mortality36:12
 Example 3: Trend and Strength of Variables40:14
 Example 4: Trend, Strength and Shape for Scatterplots43:27
Regression
32m 2s
 Intro0:00
 Roadmap0:05
 Roadmap0:06
 Linear Equations0:34
 Linear Equations: y = mx + b0:35
 Rough Line5:16
 Rough Line5:17
 Regression  A 'Center' Line7:41
 Reasons for Summarizing with a Regression Line7:42
 Predictor and Response Variable10:04
 Goal of Regression12:29
 Goal of Regression12:30
 Prediction14:50
 Example: Servings of Mile Per Year Shown By Age14:51
 Intrapolation17:06
 Extrapolation17:58
 Error in Prediction20:34
 Prediction Error20:35
 Residual21:40
 Example 1: Residual23:34
 Example 2: Large and Negative Residual26:30
 Example 3: Positive Residual28:13
 Example 4: Interpret Regression Line & Extrapolate29:40
Least Squares Regression
56m 36s
 Intro0:00
 Roadmap0:13
 Roadmap0:14
 Best Fit0:47
 Best Fit0:48
 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 Line4:51
 Quantitative Properties of Regression Line4:52
 So How do we Find Such a Line?6:49
 SSEs of Different Line Equations & Lowest SSE6:50
 Carl Gauss' Method8:01
 How Do We Find Slope (b1)11:00
 How Do We Find Slope (b1)11:01
 Hoe Do We Find Intercept15:11
 Hoe Do We Find Intercept15:12
 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 It26:31
 Example 3: Summarize the Scatterplot and Find the Regression Line.34:31
 Example 4: Examine the Mean of Residuals43:52
Correlation
43m 58s
 Intro0:00
 Roadmap0:05
 Roadmap0:06
 Summarizing a Scatterplot Quantitatively0:47
 Shape0:48
 Trend1:11
 Strength: Correlation ®1:45
 Correlation Coefficient ( r )2:30
 Correlation Coefficient ( r )2:31
 Trees vs. Forest11:59
 Trees vs. Forest12:00
 Calculating r15:07
 Average Product of zscores for x and y15:08
 Relationship between Correlation and Slope21:10
 Relationship between Correlation and Slope21:11
 Example 1: Find the Correlation between Grams of Fat and Cost24:11
 Example 2: Relationship between r and b130:24
 Example 3: Find the Regression Line33:35
 Example 4: Find the Correlation Coefficient for this Set of Data37:37
Correlation: r vs. rsquared
52m 52s
 Intro0:00
 Roadmap0:07
 Roadmap0:08
 Rsquared0:44
 What is the Meaning of It? Why Squared?0:45
 Parsing Sum of Squared (Parsing Variability)2:25
 SST = SSR + SSE2:26
 What is SST and SSE?7:46
 What is SST and SSE?7:47
 rsquared18:33
 Coefficient of Determination18:34
 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 rsquared for this Set of Data23:56
 Example 2: What Does it Mean that the Simple Linear Regression is a 'Model' of Variance?33:54
 Example 3: Why Does rsquared Only Range from 0 to 137:29
 Example 4: Find the rsquared for This Set of Data39:55
Transformations of Data
27m 8s
 Intro0:00
 Roadmap0:05
 Roadmap0:06
 Why Transform?0:26
 Why Transform?0:27
 Shapepreserving vs. Shapechanging Transformations5:14
 Shapepreserving = Linear Transformations5:15
 Shapechanging Transformations = Nonlinear Transformations6:20
 Common ShapePreserving Transformations7:08
 Common ShapePreserving Transformations7:09
 Common ShapeChanging Transformations8:59
 Powers9:00
 Logarithms9:39
 Change Just One Variable? Both?10:38
 Loglog Transformations10:39
 Log Transformations14:38
 Example 1: Create, Graph, and Transform the Data Set15:19
 Example 2: Create, Graph, and Transform the Data Set20:08
 Example 3: What Kind of Model would You Choose for this Data?22:44
 Example 4: Transformation of Data25:46
VI. Collecting Data in an Experiment
Sampling & Bias
54m 44s
 Intro0:00
 Roadmap0:05
 Roadmap0:06
 Descriptive vs. Inferential Statistics1:04
 Descriptive Statistics: Data Exploration1:05
 Example2:03
 To tackle Generalization…4:31
 Generalization4:32
 Sampling6:06
 'Good' Sample6:40
 Defining Samples and Populations8:55
 Population8:56
 Sample11:16
 Why Use Sampling?13:09
 Why Use Sampling?13:10
 Goal of Sampling: Avoiding Bias15:04
 What is Bias?15:05
 Where does Bias Come from: Sampling Bias17:53
 Where does Bias Come from: Response Bias18:27
 Sampling Bias: Bias from Bas Sampling Methods19:34
 Size Bias19:35
 Voluntary Response Bias21:13
 Convenience Sample22:22
 Judgment Sample23:58
 Inadequate Sample Frame25:40
 Response Bias: Bias from 'Bad' Data Collection Methods28:00
 Nonresponse Bias29:31
 Questionnaire Bias31:10
 Incorrect Response or Measurement Bias37:32
 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
14m 25s
 Intro0:00
 Roadmap0:05
 Roadmap0:06
 Biased vs. Unbiased Sampling Methods0:32
 Biased Sampling0:33
 Unbiased Sampling1:13
 Probability Sampling Methods2:31
 Simple Random2:54
 Stratified Random Sampling4:06
 Cluster Sampling5:24
 Twostaged Sampling6:22
 Systematic Sampling7:25
 Example 1: Which Type(s) of Sampling was this?8:33
 Example 2: Describe How to Take a TwoStage Sample from this Book10:16
 Example 3: Sampling Methods11:58
 Example 4: Cluster Sample Plan12:48
Research Design
53m 54s
 Intro0:00
 Roadmap0:06
 Roadmap0:07
 Descriptive vs. Inferential Statistics0:51
 Descriptive Statistics: Data Exploration0:52
 Inferential Statistics1:02
 Variables and Relationships1:44
 Variables1:45
 Relationships2:49
 Not Every Type of Study is an Experiment…4:16
 Category I  Descriptive Study4:54
 Category II  Correlational Study5:50
 Category III  Experimental, Quasiexperimental, Nonexperimental6:33
 Category III7:42
 Experimental, Quasiexperimental, and Nonexperimental7:43
 Why CAN'T the Other Strategies Determine Causation?10:18
 Thirdvariable Problem10:19
 Directionality Problem15:49
 What Makes Experiments Special?17:54
 Manipulation17:55
 Control (and Comparison)21:58
 Methods of Control26:38
 Holding Constant26:39
 Matching29:11
 Random Assignment31:48
 Experiment Terminology34:09
 'true' Experiment vs. Study34:10
 Independent Variable (IV)35:16
 Dependent Variable (DV)35:45
 Factors36:07
 Treatment Conditions36:23
 Levels37:43
 Confounds or Extraneous Variables38:04
 Blind38:38
 Blind Experiments38:39
 Doubleblind Experiments39:29
 How Categories Relate to Statistics41:35
 Category I  Descriptive Study41:36
 Category II  Correlational Study42:05
 Category III  Experimental, Quasiexperimental, Nonexperimental42:43
 Example 1: Research Design43:50
 Example 2: Research Design47:37
 Example 3: Research Design50:12
 Example 4: Research Design52:00
Between and Within Treatment Variability
41m 31s
 Intro0:00
 Roadmap0:06
 Roadmap0:07
 Experimental Designs0:51
 Experimental Designs: Manipulation & Control0:52
 Two Types of Variability2:09
 Between Treatment Variability2:10
 Within Treatment Variability3:31
 Updated Goal of Experimental Design5:47
 Updated Goal of Experimental Design5:48
 Example: Drugs and Driving6:56
 Example: Drugs and Driving6:57
 Different Types of Random Assignment11:27
 All Experiments11:28
 Completely Random Design12:02
 Randomized Block Design13:19
 Randomized Block Design15:48
 Matched Pairs Design15:49
 Repeated Measures Design19:47
 Betweensubject Variable vs. Withinsubject Variable22:43
 Completely Randomized Design22:44
 Repeated Measures Design25:03
 Example 1: Design a Completely Random, Matched Pair, and Repeated Measures Experiment26:16
 Example 2: Block Design31:41
 Example 3: Completely Randomized Designs35:11
 Example 4: Completely Random, Matched Pairs, or Repeated Measures Experiments?39:01
VII. Review of Probability Axioms
Sample Spaces
37m 52s
 Intro0:00
 Roadmap0:07
 Roadmap0:08
 Why is Probability Involved in Statistics0:48
 Probability0:49
 Can People Tell the Difference between Cheap and Gourmet Coffee?2:08
 Taste Test with Coffee Drinkers3:37
 If No One can Actually Taste the Difference3:38
 If Everyone can Actually Taste the Difference5:36
 Creating a Probability Model7:09
 Creating a Probability Model7:10
 D'Alembert vs. Necker9:41
 D'Alembert vs. Necker9:42
 Problem with D'Alembert's Model13:29
 Problem with D'Alembert's Model13:30
 Covering Entire Sample Space15:08
 Fundamental Principle of Counting15:09
 Where Do Probabilities Come From?22:54
 Observed Data, Symmetry, and Subjective Estimates22:55
 Checking whether Model Matches Real World24:27
 Law of Large Numbers24:28
 Example 1: Law of Large Numbers27:46
 Example 2: Possible Outcomes30:43
 Example 3: Brands of Coffee and Taste33:25
 Example 4: How Many Different Treatments are there?35:33
Addition Rule for Disjoint Events
20m 29s
 Intro0:00
 Roadmap0:08
 Roadmap0:09
 Disjoint Events0:41
 Disjoint Events0:42
 Meaning of 'or'2:39
 In Regular Life2:40
 In Math/Statistics/Computer Science3:10
 Addition Rule for Disjoin Events3:55
 If A and B are Disjoint: P (A and B)3:56
 If A and B are Disjoint: P (A or B)5:15
 General Addition Rule5:41
 General Addition Rule5:42
 Generalized Addition Rule8:31
 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 Party15:17
 Example 4: Home Owner's Insurance18:30
Conditional Probability
57m 19s
 Intro0:00
 Roadmap0:05
 Roadmap0:06
 'or' vs. 'and' vs. Conditional Probability1:07
 'or' vs. 'and' vs. Conditional Probability1:08
 'and' vs. Conditional Probability5:57
 P (M or L)5:58
 P (M and L)8:41
 P (ML)11:04
 P (LM)12:24
 Tree Diagram15:02
 Tree Diagram15:03
 Defining Conditional Probability22:42
 Defining Conditional Probability22:43
 Common Contexts for Conditional Probability30:56
 Medical Testing: Positive Predictive Value30:57
 Medical Testing: Sensitivity33:03
 Statistical Tests34:27
 Example 1: Drug and Disease36:41
 Example 2: Marbles and Conditional Probability40:04
 Example 3: Cards and Conditional Probability45:59
 Example 4: Votes and Conditional Probability50:21
Independent Events
24m 27s
 Intro0:00
 Roadmap0:05
 Roadmap0:06
 Independent Events & Conditional Probability0:26
 Nonindependent Events0:27
 Independent Events2:00
 Nonindependent and Independent Events3:08
 Nonindependent and Independent Events3:09
 Defining Independent Events5:52
 Defining Independent Events5:53
 Multiplication Rule7:29
 Previously…7:30
 But with Independent Evens8:53
 Example 1: Which of These Pairs of Events are Independent?11:12
 Example 2: Health Insurance and Probability15:12
 Example 3: Independent Events17:42
 Example 4: Independent Events20:03
VIII. Probability Distributions
Introduction to Probability Distributions
56m 45s
 Intro0:00
 Roadmap0:08
 Roadmap0:09
 Sampling vs. Probability0:57
 Sampling0:58
 Missing1:30
 What is Missing?3:06
 Insight: Probability Distributions5:26
 Insight: Probability Distributions5:27
 What is a Probability Distribution?7:29
 From Sample Spaces to Probability Distributions8:44
 Sample Space8:45
 Probability Distribution of the Sum of Two Die11:16
 The Random Variable17:43
 The Random Variable17:44
 Expected Value21:52
 Expected Value21:53
 Example 1: Probability Distributions28:45
 Example 2: Probability Distributions35:30
 Example 3: Probability Distributions43:37
 Example 4: Probability Distributions47:20
Expected Value & Variance of Probability Distributions
53m 41s
 Intro0:00
 Roadmap0:06
 Roadmap0:07
 Discrete vs. Continuous Random Variables1:04
 Discrete vs. Continuous Random Variables1:05
 Mean and Variance Review4:44
 Mean: Sample, Population, and Probability Distribution4:45
 Variance: Sample, Population, and Probability Distribution9:12
 Example Situation14:10
 Example Situation14:11
 Some Special Cases…16:13
 Some Special Cases…16:14
 Linear Transformations19:22
 Linear Transformations19:23
 What Happens to Mean and Variance of the Probability Distribution?20:12
 n Independent Values of X25:38
 n Independent Values of X25:39
 Compare These Two Situations30:56
 Compare These Two Situations30:57
 Two Random Variables, X and Y32:02
 Two Random Variables, X and Y32:03
 Example 1: Expected Value & Variance of Probability Distributions35:35
 Example 2: Expected Values & Standard Deviation44:17
 Example 3: Expected Winnings and Standard Deviation48:18
Binomial Distribution
55m 15s
 Intro0:00
 Roadmap0:05
 Roadmap0:06
 Discrete Probability Distributions1:42
 Discrete Probability Distributions1:43
 Binomial Distribution2:36
 Binomial Distribution2:37
 Multiplicative Rule Review6:54
 Multiplicative Rule Review6:55
 How Many Outcomes with k 'Successes'10:23
 Adults and Bachelor's Degree: Manual List of Outcomes10:24
 P (X=k)19:37
 Putting Together # of Outcomes with the Multiplicative Rule19:38
 Expected Value and Standard Deviation in a Binomial Distribution25:22
 Expected Value and Standard Deviation in a Binomial Distribution25:23
 Example 1: Coin Toss33:42
 Example 2: College Graduates38:03
 Example 3: Types of Blood and Probability45:39
 Example 4: Expected Number and Standard Deviation51:11
IX. Sampling Distributions of Statistics
Introduction to Sampling Distributions
48m 17s
 Intro0:00
 Roadmap0:08
 Roadmap0:09
 Probability Distributions vs. Sampling Distributions0:55
 Probability Distributions vs. Sampling Distributions0:56
 Same Logic3:55
 Logic of Probability Distribution3:56
 Example: Rolling Two Die6:56
 Simulating Samples9:53
 To Come Up with Probability Distributions9:54
 In Sampling Distributions11:12
 Connecting Sampling and Research Methods with Sampling Distributions12:11
 Connecting Sampling and Research Methods with Sampling Distributions12:12
 Simulating a Sampling Distribution14:14
 Experimental Design: Regular Sleep vs. Less Sleep14:15
 Logic of Sampling Distributions23:08
 Logic of Sampling Distributions23:09
 General Method of Simulating Sampling Distributions25:38
 General Method of Simulating Sampling Distributions25:39
 Questions that Remain28:45
 Questions that Remain28:46
 Example 1: Mean and Standard Error of Sampling Distribution30:57
 Example 2: What is the Best Way to Describe Sampling Distributions?37:12
 Example 3: Matching Sampling Distributions38:21
 Example 4: Mean and Standard Error of Sampling Distribution41:51
Sampling Distribution of the Mean
1h 8m 48s
 Intro0:00
 Roadmap0:05
 Roadmap0:06
 Special Case of General Method for Simulating a Sampling Distribution1:53
 Special Case of General Method for Simulating a Sampling Distribution1:54
 Computer Simulation3:43
 Using Simulations to See Principles behind Shape of SDoM15:50
 Using Simulations to See Principles behind Shape of SDoM15:51
 Conditions17:38
 Using Simulations to See Principles behind Center (Mean) of SDoM20:15
 Using Simulations to See Principles behind Center (Mean) of SDoM20:16
 Conditions: Does n Matter?21:31
 Conditions: Does Number of Simulation Matter?24:37
 Using Simulations to See Principles behind Standard Deviation of SDoM27:13
 Using Simulations to See Principles behind Standard Deviation of SDoM27:14
 Conditions: Does n Matter?34:45
 Conditions: Does Number of Simulation Matter?36:24
 Central Limit Theorem37:13
 SHAPE38:08
 CENTER39:34
 SPREAD39:52
 Comparing Population, Sample, and SDoM43:10
 Comparing Population, Sample, and SDoM43:11
 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 Average55:25
 Example 2: Mean Sampling Distribution and Standard Error59:07
 Example 3: Sampling Distribution of the Mean01:04
Sampling Distribution of Sample Proportions
54m 37s
 Intro0:00
 Roadmap0:06
 Roadmap0:07
 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
 Notation3:34
 Population Proportion and Sample Proportion Notations3:35
 What's the Difference?9:19
 SDoM vs. SDoSP: Type of Data9:20
 SDoM vs. SDoSP: Shape11:24
 SDoM vs. SDoSP: Center12:30
 SDoM vs. SDoSP: Spread15:34
 Binomial Distribution vs. Sampling Distribution of Sample Proportions19:14
 Binomial Distribution vs. SDoSP: Type of Data19:17
 Binomial Distribution vs. SDoSP: Shape21:07
 Binomial Distribution vs. SDoSP: Center21:43
 Binomial Distribution vs. SDoSP: Spread24:08
 Example 1: Sampling Distribution of Sample Proportions26:07
 Example 2: Sampling Distribution of Sample Proportions37:58
 Example 3: Sampling Distribution of Sample Proportions44:42
 Example 4: Sampling Distribution of Sample Proportions45:57
X. Inferential Statistics
Introduction to Confidence Intervals
42m 53s
 Intro0:00
 Roadmap0:06
 Roadmap0:07
 Inferential Statistics0:50
 Inferential Statistics0:51
 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  Goal7:56
 When We Don't Know m but know s7:57
 When We Don't Know18:27
 When We Don't Know m nor s18:28
 Example 1: Confidence Intervals26:18
 Example 2: Confidence Intervals29:46
 Example 3: Confidence Intervals32:18
 Example 4: Confidence Intervals38:31
t Distributions
1h 2m 6s
 Intro0:00
 Roadmap0:04
 Roadmap0:05
 When to Use z vs. t?1:07
 When to Use z vs. t?1:08
 What is z and t?3:02
 zscore and tscore: Commonality3:03
 zscore and tscore: Formulas3:34
 zscore and tscore: Difference5:22
 Why not z? (Why t?)7:24
 Why not z? (Why t?)7:25
 But Don't Worry!15:13
 Gossett and tdistributions15:14
 Rules of t Distributions17:05
 tdistributions are More Normal as n Gets Bigger17:06
 tdistributions are a Family of Distributions18:55
 Degrees of Freedom (df)20:02
 Degrees of Freedom (df)20:03
 t Family of Distributions24:07
 t Family of Distributions : df = 2 , 4, and 6024:08
 df = 6029:16
 df = 229:59
 How to Find It?31:01
 'Student's tdistribution' or 'tdistribution'31:02
 Excel Example33:06
 Example 1: Which Distribution Do You Use? Z or t?45:26
 Example 2: Friends on Facebook47:41
 Example 3: t Distributions52:15
 Example 4: t Distributions , confidence interval, and mean55:59
Introduction to Hypothesis Testing
1h 6m 33s
 Intro0:00
 Roadmap0:06
 Roadmap0:07
 Issues to Overcome in Inferential Statistics1:35
 Issues to Overcome in Inferential Statistics1:36
 What Happens When We Don't Know What the Population Looks Like?2:57
 How Do We Know whether a sample is Sufficiently Unlikely3:43
 Hypothesizing a Population6:44
 Hypothesizing a Population6:45
 Null Hypothesis8:07
 Alternative Hypothesis8:56
 Hypotheses11:58
 Hypotheses11:59
 Errors in Hypothesis Testing14:22
 Errors in Hypothesis Testing14:23
 Steps of Hypothesis Testing21:15
 Steps of Hypothesis Testing21:16
 Single Sample HT ( When Sigma Available)26:08
 Example: Average Facebook Friends26:09
 Step127:08
 Step 227:58
 Step 328:17
 Step 432:18
 Single Sample HT (When Sigma Not Available)36:33
 Example: Average Facebook Friends36:34
 Step1: Hypothesis Testing36:58
 Step 2: Significance Level37:25
 Step 3: Decision Stage37:40
 Step 4: Sample41:36
 Sigma and pvalue45:04
 Sigma and pvalue45:05
 On tailed vs. Two Tailed Hypotheses45:51
 Example 1: Hypothesis Testing48:37
 Example 2: Heights of Women in the US57:43
 Example 3: Select the Best Way to Complete This Sentence03:23
Confidence Intervals for the Difference of Two Independent Means
55m 14s
 Intro0:00
 Roadmap0:14
 Roadmap0:15
 One Mean vs. Two Means1:17
 One Mean vs. Two Means1:18
 Notation2:41
 A Sample! A Set!2:42
 Mean of X, Mean of Y, and Difference of Two Means3:56
 SE of X4:34
 SE of Y6:28
 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 Hypothesis15:01
 Standard Error17:39
 When can We Construct a CI for the Difference between Two Means?21:28
 Three Conditions21:29
 Finding CI23:56
 One Mean CI23:57
 Two Means CI25:45
 Finding t29:16
 Finding t29:17
 Interpreting CI30:25
 Interpreting CI30:26
 Better Estimate of s (s pool)34:15
 Better Estimate of s (s pool)34:16
 Example 1: Confidence Intervals42:32
 Example 2: SE of the Difference52:36
Hypothesis Testing for the Difference of Two Independent Means
50m
 Intro0:00
 Roadmap0:06
 Roadmap0:07
 The Goal of Hypothesis Testing0:56
 One Sample and Two Samples0:57
 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
 Shape6:47
 Mean for the Null Hypothesis7:26
 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 CI10:08
 Three Conditions10:09
 Steps of Hypothesis Testing11:04
 Steps of Hypothesis Testing11:05
 Formulas that Go with Steps of Hypothesis Testing13:21
 Step 113:25
 Step 214:18
 Step 315:00
 Step 416:57
 Example 1: Hypothesis Testing for the Difference of Two Independent Means18:47
 Example 2: Hypothesis Testing for the Difference of Two Independent Means33:55
 Example 3: Hypothesis Testing for the Difference of Two Independent Means44:22
Confidence Intervals & Hypothesis Testing for the Difference of Two Paired Means
1h 14m 11s
 Intro0:00
 Roadmap0:09
 Roadmap0:10
 The Goal of Hypothesis Testing1:27
 One Sample and Two Samples1:28
 Independent Samples vs. Paired Samples3:16
 Independent Samples vs. Paired Samples3:17
 Which is Which?5:20
 Independent SAMPLES vs. Independent VARIABLES7:43
 independent SAMPLES vs. Independent VARIABLES7:44
 Ttests Always…10:48
 Ttests Always…10:49
 Notation for Paired Samples12:59
 Notation for Paired Samples13:00
 Steps of Hypothesis Testing for Paired Samples16:13
 Steps of Hypothesis Testing for Paired Samples16:14
 Rules of the SDoD (Adding on Paired Samples)18:03
 Shape18:04
 Mean for the Null Hypothesis18:31
 Standard Error for Independent Samples (When Variance is Homogenous)19:25
 Standard Error for Paired Samples20:39
 Formulas that go with Steps of Hypothesis Testing22:59
 Formulas that go with Steps of Hypothesis Testing23:00
 Confidence Intervals for Paired Samples30:32
 Confidence Intervals for Paired Samples30:33
 Example 1: Confidence Intervals & Hypothesis Testing for the Difference of Two Paired Means32:28
 Example 2: Confidence Intervals & Hypothesis Testing for the Difference of Two Paired Means44:02
 Example 3: Confidence Intervals & Hypothesis Testing for the Difference of Two Paired Means52:23
Type I and Type II Errors
31m 27s
 Intro0:00
 Roadmap0:18
 Roadmap0:19
 Errors and Relationship to HT and the Sample Statistic?1:11
 Errors and Relationship to HT and the Sample Statistic?1:12
 Instead of a Box…Distributions!7:00
 One Sample ttest: Friends on Facebook7:01
 Two Sample ttest: Friends on Facebook13:46
 Usually, Lots of Overlap between Null and Alternative Distributions16:59
 Overlap between Null and Alternative Distributions17:00
 How Distributions and 'Box' Fit Together22:45
 How Distributions and 'Box' Fit Together22:46
 Example 1: Types of Errors25:54
 Example 2: Types of Errors27:30
 Example 3: What is the Danger of the Type I Error?29:38
Effect Size & Power
44m 41s
 Intro0:00
 Roadmap0:05
 Roadmap0:06
 Distance between Distributions: Sample t0:49
 Distance between Distributions: Sample t0:50
 Problem with Distance in Terms of Standard Error2:56
 Problem with Distance in Terms of Standard Error2:57
 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 Size6:09
 Rules of Effect Size6:10
 Why Do We Need Effect Size?8:21
 Tells You the Practical Significance8:22
 HT can be Deceiving…10:25
 Important Note10:42
 What is Power?11:20
 What is Power?11:21
 Why Do We Need Power?14:19
 Conditional Probability and Power14:20
 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 Power32:48
 Example 1: Effect Size & Power35:40
 Example 2: Effect Size & Power37:38
 Example 3: Effect Size & Power40:55
XI. Analysis of Variance
Fdistributions
24m 46s
 Intro0:00
 Roadmap0:04
 Roadmap0:05
 Z & Tstatistic and Their Distribution0:34
 Z & Tstatistic and Their Distribution0:35
 Fstatistic4:55
 The F Ration ( the Variance Ratio)4:56
 Fdistribution12:29
 Fdistribution12:30
 s and pvalue15:00
 s and pvalue15:01
 Example 1: Why Does Fdistribution Stop At 0 But Go On Until Infinity?18:33
 Example 2: Fdistributions19:29
 Example 3: Fdistributions and Heights21:29
ANOVA with Independent Samples
1h 9m 25s
 Intro0:00
 Roadmap0:05
 Roadmap0:06
 The Limitations of ttests1:12
 The Limitations of ttests1:13
 Two Major Limitations of Many ttests3:26
 Two Major Limitations of Many ttests3:27
 Ronald Fisher's Solution… Ftest! New Null Hypothesis4:43
 Ronald Fisher's Solution… Ftest! New Null Hypothesis (Omnibus Test  One Test to Rule Them All!)4:44
 Analysis of Variance (ANoVA) Notation7:47
 Analysis of Variance (ANoVA) Notation7:48
 Partitioning (Analyzing) Variance9:58
 Total Variance9:59
 Withingroup Variation14:00
 Betweengroup Variation16:22
 Time out: Review Variance & SS17:05
 Time out: Review Variance & SS17:06
 Fstatistic19:22
 The F Ratio (the Variance Ratio)19:23
 S²bet = SSbet / dfbet22:13
 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 / dfw26:05
 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 ANOVA29:25
 Chart of Independent Samples ANOVA29:26
 Example 1: Who Uploads More Photos: Unknown Ethnicity, Latino, Asian, Black, or White Facebook Users?35:52
 Hypotheses35:53
 Significance Level39:40
 Decision Stage40:05
 Calculate Samples' Statistic and pValue44:10
 Reject or Fail to Reject H055:54
 Example 2: ANOVA with Independent Samples58:21
Repeated Measures ANOVA
1h 15m 13s
 Intro0:00
 Roadmap0:05
 Roadmap0:06
 The Limitations of ttests0:36
 Who Uploads more Pictures and Which PhotoType is Most Frequently Used on Facebook?0:37
 ANOVA (Ftest) to the Rescue!5:49
 Omnibus Hypothesis5:50
 Analyze Variance7:27
 Independent Samples vs. Repeated Measures9:12
 Same Start9:13
 Independent Samples ANOVA10:43
 Repeated Measures ANOVA12:00
 Independent Samples ANOVA16:00
 Same Start: All the Variance Around Grand Mean16:01
 Independent Samples16:23
 Repeated Measures ANOVA18:18
 Same Start: All the Variance Around Grand Mean18:19
 Repeated Measures18:33
 Repeated Measures Fstatistic21:22
 The F Ratio (The Variance Ratio)21:23
 S²bet = SSbet / dfbet23:07
 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 resid25:46
 What is This?25:47
 So What is SS resid?26:44
 So What is the df resid?27:36
 SS subj and df subj28:11
 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 total31:42
 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 ANOVA33:19
 Chart of Repeated Measures ANOVA: F and Betweensamples Variability33:20
 Chart of Repeated Measures ANOVA: Total Variability, Withinsubject (case) Variability, Residual Variability35:50
 Example 1: Which is More Prevalent on Facebook: Tagged, Uploaded, Mobile, or Profile Photos?40:25
 Hypotheses40:26
 Significance Level41:46
 Decision Stage42:09
 Calculate Samples' Statistic and pValue46:18
 Reject or Fail to Reject H057:55
 Example 2: Repeated Measures ANOVA58:57
 Example 3: What's the Problem with a Bunch of Tiny ttests?13:59
XII. Chisquare Test
ChiSquare GoodnessofFit Test
58m 23s
 Intro0:00
 Roadmap0:05
 Roadmap0:06
 Where Does the ChiSquare Test Belong?0:50
 Where Does the ChiSquare Test Belong?0:51
 A New Twist on HT: GoodnessofFit7:23
 HT in General7:24
 GoodnessofFit HT8:26
 Hypotheses about Proportions12:17
 Null Hypothesis12:18
 Alternative Hypothesis13:23
 Example14:38
 ChiSquare Statistic17:52
 ChiSquare Statistic17:53
 ChiSquare Distributions24:31
 ChiSquare Distributions24:32
 Conditions for ChiSquare28:58
 Condition 128:59
 Condition 230:20
 Condition 330:32
 Condition 431:47
 Example 1: ChiSquare GoodnessofFit Test32:23
 Example 2: ChiSquare GoodnessofFit Test44:34
 Example 3: Which of These Statements Describe Properties of the ChiSquare GoodnessofFit Test?56:06
ChiSquare Test of Homogeneity
51m 36s
 Intro0:00
 Roadmap0:09
 Roadmap0:10
 GoodnessofFit vs. Homogeneity1:13
 GoodnessofFit HT1:14
 Homogeneity2:00
 Analogy2:38
 Hypotheses About Proportions5:00
 Null Hypothesis5:01
 Alternative Hypothesis6:11
 Example6:33
 ChiSquare Statistic10:12
 Same as GoodnessofFit Test10:13
 Set Up Data12:28
 Setting Up Data Example12:29
 Expected Frequency16:53
 Expected Frequency16:54
 ChiSquare Distributions & df19:26
 ChiSquare Distributions & df19:27
 Conditions for Test of Homogeneity20:54
 Condition 120:55
 Condition 221:39
 Condition 322:05
 Condition 422:23
 Example 1: ChiSquare Test of Homogeneity22:52
 Example 2: ChiSquare Test of Homogeneity32:10
XIII. Overview of Statistics
Overview of Statistics
18m 11s
 Intro0:00
 Roadmap0:07
 Roadmap0:08
 The Statistical Tests (HT) We've Covered0:28
 The Statistical Tests (HT) We've Covered0:29
 Organizing the Tests We've Covered…1:08
 One Sample: Continuous DV and Categorical DV1:09
 Two Samples: Continuous DV and Categorical DV5:41
 More Than Two Samples: Continuous DV and Categorical DV8:21
 The Following Data: OK Cupid10:10
 The Following Data: OK Cupid10:11
 Example 1: WeirdMySpaceAngle Profile Photo10:38
 Example 2: Geniuses12:30
 Example 3: Promiscuous iPhone Users13:37
 Example 4: Women, Aging, and Messaging16:07
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0 answers
Post by Mohammed Alam on August 6, 2014
Useful lecture series. Good instructor.
0 answers
Post by Manoj Joseph on June 17, 2013
I am finding difficult to make sense this session.
0 answers
Post by Robin Dorsey on October 20, 2012
This example assumes that quarterly results with have a normal distribution...why is this a reasonable assumption?
0 answers
Post by Kamal Almarzooq on January 23, 2012
too much depend on excel makes your teachings less useful to me :(