Section 1: Introduction
Descriptive Statistics vs. Inferential Statistics 25m 31s
Intro
0:00Roadmap
0:10Roadmap
0:11
Statistics
0:35Statistics
0:36
Let's Think About High School Science
1:12Measurement and Find Patterns (Mathematical Formula)
1:13
Statistics = Math of Distributions
4:58Distributions
4:59Problematic… but also GREAT
5:58
Statistics
7:33How is It Different from Other Specializations in Mathematics?
7:34Statistics is Fundamental in Natural and Social Sciences
7:53
Two Skills of Statistics
8:20Description (Exploration)
8:21Inference
9:13
Descriptive Statistics vs. Inferential Statistics: Apply to Distributions
9:58Descriptive Statistics
9:59Inferential Statistics
11:05
Populations vs. Samples
12:19Populations vs. Samples: Is it the Truth?
12:20Populations vs. Samples: Pros & Cons
13:36Populations vs. Samples: Descriptive Values
16:12
Putting Together Descriptive/Inferential Stats & Populations/Samples
17:10Putting Together Descriptive/Inferential Stats & Populations/Samples
17:11
Example 1: Descriptive Statistics vs. Inferential Statistics
19:09Example 2: Descriptive Statistics vs. Inferential Statistics
20:47Example 3: Sample, Parameter, Population, and Statistic
21:40Example 4: Sample, Parameter, Population, and Statistic
23:28
Section 2: About Samples: Cases, Variables, Measurements
About Samples: Cases, Variables, Measurements 32m 14s
Intro
0:00Data
0:09Data, Cases, Variables, and Values
0:10Rows, Columns, and Cells
2:03Example: Aircrafts
3:52
How Do We Get Data?
5:38Research: Question and Hypothesis
5:39Research Design
7:11Measurement
7:29Research Analysis
8:33Research Conclusion
9:30
Types of Variables
10:03Discrete Variables
10:04Continuous Variables
12:07
Types of Measurements
14:17Types of Measurements
14:18
Types of Measurements (Scales)
17:22Nominal
17:23Ordinal
19:11Interval
21:33Ratio
24:24
Example 1: Cases, Variables, Measurements
25:20Example 2: Which Scale of Measurement is Used?
26:55Example 3: What Kind of a Scale of Measurement is This?
27:26Example 4: Discrete vs. Continuous Variables.
30:31
Section 3: Visualizing Distributions
Introduction to Excel 8m 9s
Intro
0:00Before Visualizing Distribution
0:10Excel
0:11
Excel: Organization
0:45Workbook
0:46Column x Rows
1:50Tools: Menu Bar, Standard Toolbar, and Formula Bar
3:00
Excel + Data
6:07Exce and Data
6:08
Frequency Distributions in Excel 39m 10s
Intro
0:00Roadmap
0:08Data in Excel and Frequency Distributions
0:09
Raw Data to Frequency Tables
0:42Raw Data to Frequency Tables
0:43Frequency Tables: Using Formulas and Pivot Tables
1:28
Example 1: Number of Births
7:17Example 2: Age Distribution
20:41Example 3: Height Distribution
27:45Example 4: Height Distribution of Males
32:19
Frequency Distributions and Features 25m 29s
Intro
0:00Roadmap
0:10Data in Excel, Frequency Distributions, and Features of Frequency Distributions
0:11
Example #1
1:35Uniform
1:36
Example #2
2:58Unimodal, Skewed Right, and Asymmetric
2:59
Example #3
6:29Bimodal
6:30
Example #4a
8:29Symmetric, Unimodal, and Normal
8:30Point of Inflection and Standard Deviation
11:13
Example #4b
12:43Normal Distribution
12:44
Summary
13:56Uniform, Skewed, Bimodal, and Normal
13:57
Sketch Problem 1: Driver's License
17:34Sketch Problem 2: Life Expectancy
20:01Sketch Problem 3: Telephone Numbers
22:01Sketch Problem 4: Length of Time Used to Complete a Final Exam
23:43
Dotplots and Histograms in Excel 42m 42s
Intro
0:00Roadmap
0:06Roadmap
0:07
Previously
1:02Data, Frequency Table, and visualization
1:03
Dotplots
1:22Dotplots Excel Example
1:23
Dotplots: Pros and Cons
7:22Pros and Cons of Dotplots
7:23Dotplots Excel Example Cont.
9:07
Histograms
12:47Histograms Overview
12:48Example of Histograms
15:29
Histograms: Pros and Cons
31:39Pros
31:40Cons
32:31
Frequency vs. Relative Frequency
32:53Frequency
32:54Relative Frequency
33:36
Example 1: Dotplots vs. Histograms
34:36Example 2: Age of Pennies Dotplot
36:21Example 3: Histogram of Mammal Speeds
38:27Example 4: Histogram of Life Expectancy
40:30
Intro
0:00Roadmap
0:05Roadmap
0:06
What Sets Stemplots Apart?
0:46Data Sets, Dotplots, Histograms, and Stemplots
0:47
Example 1: What Do Stemplots Look Like?
1:58Example 2: Back-to-Back Stemplots
5:00Example 3: Quiz Grade Stemplot
7:46Example 4: Quiz Grade & Afterschool Tutoring Stemplot
9:56
Intro
0:00Roadmap
0:05Roadmap
0:08
Review of Frequency Distributions
0:44Y-axis and X-axis
0:45Types of Frequency Visualizations Covered so Far
2:16Introduction to Bar Graphs
4:07
Example 1: Bar Graph
5:32Example 1: Bar Graph
5:33
Do Shapes, Center, and Spread of Distributions Apply to Bar Graphs?
11:07Do Shapes, Center, and Spread of Distributions Apply to Bar Graphs?
11:08
Example 2: Create a Frequency Visualization for Gender
14:02Example 3: Cases, Variables, and Frequency Visualization
16:34Example 4: What Kind of Graphs are Shown Below?
19:29
Section 4: Summarizing Distributions
Central Tendency: Mean, Median, Mode 38m 50s
Intro
0:00Roadmap
0:07Roadmap
0:08
Central Tendency 1
0:56Way to Summarize a Distribution of Scores
0:57Mode
1:32Median
2:02Mean
2:36
Central Tendency 2
3:47Mode
3:48Median
4:20Mean
5:25
Summation Symbol
6:11Summation Symbol
6:12
Population vs. Sample
10:46Population vs. Sample
10:47
Excel Examples
15:08Finding Mode, Median, and Mean in Excel
15:09
Median vs. Mean
21:45Effect of Outliers
21:46Relationship Between Parameter and Statistic
22:44Type of Measurements
24:00Which Distributions to Use With
24:55
Example 1: Mean
25:30Example 2: Using Summation Symbol
29:50Example 3: Average Calorie Count
32:50Example 4: Creating an Example Set
35:46
Intro
0:00Roadmap
0:05Roadmap
0:06
Variability (or Spread)
0:45Variability (or Spread)
0:46
Things to Think About
5:45Things to Think About
5:46
Range, Quartiles and Interquartile Range
6:37Range
6:38Interquartile Range
8:42
Interquartile Range Example
10:58Interquartile Range Example
10:59
Variance and Standard Deviation
12:27Deviations
12:28Sum of Squares
14:35Variance
16:55Standard Deviation
17:44
Sum of Squares (SS)
18:34Sum of Squares (SS)
18:35
Population vs. Sample SD
22:00Population vs. Sample SD
22:01
Population vs. Sample
23:20Mean
23:21SD
23:51
Example 1: Find the Mean and Standard Deviation of the Variable Friends in the Excel File
27:21Example 2: Find the Mean and Standard Deviation of the Tagged Photos in the Excel File
35:25Example 3: Sum of Squares
38:58Example 4: Standard Deviation
41:48
Five Number Summary & Boxplots 57m 15s
Intro
0:00Roadmap
0:06Roadmap
0:07
Summarizing Distributions
0:37Shape, Center, and Spread
0:385 Number Summary
1:14
Boxplot: Visualizing 5 Number Summary
3:37Boxplot: Visualizing 5 Number Summary
3:38
Boxplots on Excel
9:01Using 'Stocks' and Using Stacked Columns
9:02Boxplots on Excel Example
10:14
When are Boxplots Useful?
32:14Pros
32:15Cons
32:59
How to Determine Outlier Status
33:24Rule of Thumb: Upper Limit
33:25Rule of Thumb: Lower Limit
34:16Signal Outliers in an Excel Data File Using Conditional Formatting
34:52
Modified Boxplot
48:38Modified Boxplot
48:39
Example 1: Percentage Values & Lower and Upper Whisker
49:10Example 2: Boxplot
50:10Example 3: Estimating IQR From Boxplot
53:46Example 4: Boxplot and Missing Whisker
54:35
Shape: Calculating Skewness & Kurtosis 41m 51s
Intro
0:00Roadmap
0:16Roadmap
0:17
Skewness Concept
1:09Skewness Concept
1:10
Calculating Skewness
3:26Calculating Skewness
3:27
Interpreting Skewness
7:36Interpreting Skewness
7:37Excel Example
8:49
Kurtosis Concept
20:29Kurtosis Concept
20:30
Calculating Kurtosis
24:17Calculating Kurtosis
24:18
Interpreting Kurtosis
29:01Leptokurtic
29:35Mesokurtic
30:10Platykurtic
31:06Excel Example
32:04
Example 1: Shape of Distribution
38:28Example 2: Shape of Distribution
39:29Example 3: Shape of Distribution
40:14Example 4: Kurtosis
41:10
Normal Distribution 34m 33s
Intro
0:00Roadmap
0:13Roadmap
0:14
What is a Normal Distribution
0:44The Normal Distribution As a Theoretical Model
0:45
Possible Range of Probabilities
3:05Possible Range of Probabilities
3:06
What is a Normal Distribution
5:07Can Be Described By
5:08Properties
5:49
'Same' Shape: Illusion of Different Shape!
7:35'Same' Shape: Illusion of Different Shape!
7:36
Types of Problems
13:45Example: Distribution of SAT Scores
13:46
Shape Analogy
19:48Shape Analogy
19:49
Example 1: The Standard Normal Distribution and Z-Scores
22:34Example 2: The Standard Normal Distribution and Z-Scores
25:54Example 3: Sketching and Normal Distribution
28:55Example 4: Sketching and Normal Distribution
32:32
Standard Normal Distributions & Z-Scores 41m 44s
Intro
0:00Roadmap
0:06Roadmap
0:07
A Family of Distributions
0:28Infinite Set of Distributions
0:29Transforming Normal Distributions to 'Standard' Normal Distribution
1:04
Normal Distribution vs. Standard Normal Distribution
2:58Normal Distribution vs. Standard Normal Distribution
2:59
Z-Score, Raw Score, Mean, & SD
4:08Z-Score, Raw Score, Mean, & SD
4:09
Weird Z-Scores
9:40Weird Z-Scores
9:41
Excel
16:45For Normal Distributions
16:46For Standard Normal Distributions
19:11Excel Example
20:24
Types of Problems
25:18Percentage Problem: P(x)
25:19Raw Score and Z-Score Problems
26:28Standard Deviation Problems
27:01
Shape Analogy
27:44Shape Analogy
27:45
Example 1: Deaths Due to Heart Disease vs. Deaths Due to Cancer
28:24Example 2: Heights of Male College Students
33:15Example 3: Mean and Standard Deviation
37:14Example 4: Finding Percentage of Values in a Standard Normal Distribution
37:49
Normal Distribution: PDF vs. CDF 55m 44s
Intro
0:00Roadmap
0:15Roadmap
0:16
Frequency vs. Cumulative Frequency
0:56Frequency vs. Cumulative Frequency
0:57
Frequency vs. Cumulative Frequency
4:32Frequency vs. Cumulative Frequency Cont.
4:33
Calculus in Brief
6:21Derivative-Integral Continuum
6:22
PDF
10:08PDF for Standard Normal Distribution
10:09PDF for Normal Distribution
14:32
Integral of PDF = CDF
21:27Integral of PDF = CDF
21:28
Example 1: Cumulative Frequency Graph
23:31Example 2: Mean, Standard Deviation, and Probability
24:43Example 3: Mean and Standard Deviation
35:50Example 4: Age of Cars
49:32
Section 5: Linear Regression
Intro
0:00Roadmap
0:04Roadmap
0:05
Previous Visualizations
0:30Frequency Distributions
0:31
Compare & Contrast
2:26Frequency Distributions Vs. Scatterplots
2:27
Summary Values
4:53Shape
4:54Center & Trend
6:41Spread & Strength
8:22Univariate & Bivariate
10:25
Example Scatterplot
10:48Shape, Trend, and Strength
10:49
Positive and Negative Association
14:05Positive and Negative Association
14:06
Linearity, Strength, and Consistency
18:30Linearity
18:31Strength
19:14Consistency
20:40
Summarizing a Scatterplot
22:58Summarizing a Scatterplot
22:59
Example 1: Gapminder.org, Income x Life Expectancy
26:32Example 2: Gapminder.org, Income x Infant Mortality
36:12Example 3: Trend and Strength of Variables
40:14Example 4: Trend, Strength and Shape for Scatterplots
43:27
Intro
0:00Roadmap
0:05Roadmap
0:06
Linear Equations
0:34Linear Equations: y = mx + b
0:35
Rough Line
5:16Rough Line
5:17
Regression - A 'Center' Line
7:41Reasons for Summarizing with a Regression Line
7:42Predictor and Response Variable
10:04
Goal of Regression
12:29Goal of Regression
12:30
Prediction
14:50Example: Servings of Mile Per Year Shown By Age
14:51Intrapolation
17:06Extrapolation
17:58
Error in Prediction
20:34Prediction Error
20:35Residual
21:40
Example 1: Residual
23:34Example 2: Large and Negative Residual
26:30Example 3: Positive Residual
28:13Example 4: Interpret Regression Line & Extrapolate
29:40
Least Squares Regression 56m 36s
Intro
0:00Roadmap
0:13Roadmap
0:14
Best Fit
0:47Best Fit
0:48
Sum of Squared Errors (SSE)
1:50Sum of Squared Errors (SSE)
1:51
Why Squared?
3:38Why Squared?
3:39
Quantitative Properties of Regression Line
4:51Quantitative Properties of Regression Line
4:52
So How do we Find Such a Line?
6:49SSEs of Different Line Equations & Lowest SSE
6:50Carl Gauss' Method
8:01
How Do We Find Slope (b1)
11:00How Do We Find Slope (b1)
11:01
Hoe Do We Find Intercept
15:11Hoe Do We Find Intercept
15:12
Example 1: Which of These Equations Fit the Above Data Best?
17:18Example 2: Find the Regression Line for These Data Points and Interpret It
26:31Example 3: Summarize the Scatterplot and Find the Regression Line.
34:31Example 4: Examine the Mean of Residuals
43:52
Intro
0:00Roadmap
0:05Roadmap
0:06
Summarizing a Scatterplot Quantitatively
0:47Shape
0:48Trend
1:11Strength: Correlation ®
1:45
Correlation Coefficient ( r )
2:30Correlation Coefficient ( r )
2:31
Trees vs. Forest
11:59Trees vs. Forest
12:00
Calculating r
15:07Average Product of z-scores for x and y
15:08
Relationship between Correlation and Slope
21:10Relationship between Correlation and Slope
21:11
Example 1: Find the Correlation between Grams of Fat and Cost
24:11Example 2: Relationship between r and b1
30:24Example 3: Find the Regression Line
33:35Example 4: Find the Correlation Coefficient for this Set of Data
37:37
Correlation: r vs. r-squared 52m 52s
Intro
0:00Roadmap
0:07Roadmap
0:08
R-squared
0:44What is the Meaning of It? Why Squared?
0:45
Parsing Sum of Squared (Parsing Variability)
2:25SST = SSR + SSE
2:26
What is SST and SSE?
7:46What is SST and SSE?
7:47
r-squared
18:33Coefficient of Determination
18:34
If the Correlation is Strong…
20:25If the Correlation is Strong…
20:26
If the Correlation is Weak…
22:36If the Correlation is Weak…
22:37
Example 1: Find r-squared for this Set of Data
23:56Example 2: What Does it Mean that the Simple Linear Regression is a 'Model' of Variance?
33:54Example 3: Why Does r-squared Only Range from 0 to 1
37:29Example 4: Find the r-squared for This Set of Data
39:55
Transformations of Data 27m 8s
Intro
0:00Roadmap
0:05Roadmap
0:06
Why Transform?
0:26Why Transform?
0:27
Shape-preserving vs. Shape-changing Transformations
5:14Shape-preserving = Linear Transformations
5:15Shape-changing Transformations = Non-linear Transformations
6:20
Common Shape-Preserving Transformations
7:08Common Shape-Preserving Transformations
7:09
Common Shape-Changing Transformations
8:59Powers
9:00Logarithms
9:39
Change Just One Variable? Both?
10:38Log-log Transformations
10:39Log Transformations
14:38
Example 1: Create, Graph, and Transform the Data Set
15:19Example 2: Create, Graph, and Transform the Data Set
20:08Example 3: What Kind of Model would You Choose for this Data?
22:44Example 4: Transformation of Data
25:46
Section 6: Collecting Data in an Experiment
Intro
0:00Roadmap
0:05Roadmap
0:06
Descriptive vs. Inferential Statistics
1:04Descriptive Statistics: Data Exploration
1:05Example
2:03
To tackle Generalization…
4:31Generalization
4:32Sampling
6:06'Good' Sample
6:40
Defining Samples and Populations
8:55Population
8:56Sample
11:16
Why Use Sampling?
13:09Why Use Sampling?
13:10
Goal of Sampling: Avoiding Bias
15:04What is Bias?
15:05Where does Bias Come from: Sampling Bias
17:53Where does Bias Come from: Response Bias
18:27
Sampling Bias: Bias from Bas Sampling Methods
19:34Size Bias
19:35Voluntary Response Bias
21:13Convenience Sample
22:22Judgment Sample
23:58Inadequate Sample Frame
25:40
Response Bias: Bias from 'Bad' Data Collection Methods
28:00Nonresponse Bias
29:31Questionnaire Bias
31:10Incorrect Response or Measurement Bias
37:32
Example 1: What Kind of Biases?
40:29Example 2: What Biases Might Arise?
44:46Example 3: What Kind of Biases?
48:34Example 4: What Kind of Biases?
51:43
Intro
0:00Roadmap
0:05Roadmap
0:06
Biased vs. Unbiased Sampling Methods
0:32Biased Sampling
0:33Unbiased Sampling
1:13
Probability Sampling Methods
2:31Simple Random
2:54Stratified Random Sampling
4:06Cluster Sampling
5:24Two-staged Sampling
6:22Systematic Sampling
7:25
Example 1: Which Type(s) of Sampling was this?
8:33Example 2: Describe How to Take a Two-Stage Sample from this Book
10:16Example 3: Sampling Methods
11:58Example 4: Cluster Sample Plan
12:48
Intro
0:00Roadmap
0:06Roadmap
0:07
Descriptive vs. Inferential Statistics
0:51Descriptive Statistics: Data Exploration
0:52Inferential Statistics
1:02
Variables and Relationships
1:44Variables
1:45Relationships
2:49
Not Every Type of Study is an Experiment…
4:16Category I - Descriptive Study
4:54Category II - Correlational Study
5:50Category III - Experimental, Quasi-experimental, Non-experimental
6:33
Category III
7:42Experimental, Quasi-experimental, and Non-experimental
7:43
Why CAN'T the Other Strategies Determine Causation?
10:18Third-variable Problem
10:19Directionality Problem
15:49
What Makes Experiments Special?
17:54Manipulation
17:55Control (and Comparison)
21:58
Methods of Control
26:38Holding Constant
26:39Matching
29:11Random Assignment
31:48
Experiment Terminology
34:09'true' Experiment vs. Study
34:10Independent Variable (IV)
35:16Dependent Variable (DV)
35:45Factors
36:07Treatment Conditions
36:23Levels
37:43Confounds or Extraneous Variables
38:04
Blind
38:38Blind Experiments
38:39Double-blind Experiments
39:29
How Categories Relate to Statistics
41:35Category I - Descriptive Study
41:36Category II - Correlational Study
42:05Category III - Experimental, Quasi-experimental, Non-experimental
42:43
Example 1: Research Design
43:50Example 2: Research Design
47:37Example 3: Research Design
50:12Example 4: Research Design
52:00
Between and Within Treatment Variability 41m 31s
Intro
0:00Roadmap
0:06Roadmap
0:07
Experimental Designs
0:51Experimental Designs: Manipulation & Control
0:52
Two Types of Variability
2:09Between Treatment Variability
2:10Within Treatment Variability
3:31
Updated Goal of Experimental Design
5:47Updated Goal of Experimental Design
5:48
Example: Drugs and Driving
6:56Example: Drugs and Driving
6:57
Different Types of Random Assignment
11:27All Experiments
11:28Completely Random Design
12:02Randomized Block Design
13:19
Randomized Block Design
15:48Matched Pairs Design
15:49Repeated Measures Design
19:47
Between-subject Variable vs. Within-subject Variable
22:43Completely Randomized Design
22:44Repeated Measures Design
25:03
Example 1: Design a Completely Random, Matched Pair, and Repeated Measures Experiment
26:16Example 2: Block Design
31:41Example 3: Completely Randomized Designs
35:11Example 4: Completely Random, Matched Pairs, or Repeated Measures Experiments?
39:01
Section 7: Review of Probability Axioms
Intro
0:00Roadmap
0:07Roadmap
0:08
Why is Probability Involved in Statistics
0:48Probability
0:49Can People Tell the Difference between Cheap and Gourmet Coffee?
2:08
Taste Test with Coffee Drinkers
3:37If No One can Actually Taste the Difference
3:38If Everyone can Actually Taste the Difference
5:36
Creating a Probability Model
7:09Creating a Probability Model
7:10
D'Alembert vs. Necker
9:41D'Alembert vs. Necker
9:42
Problem with D'Alembert's Model
13:29Problem with D'Alembert's Model
13:30
Covering Entire Sample Space
15:08Fundamental Principle of Counting
15:09
Where Do Probabilities Come From?
22:54Observed Data, Symmetry, and Subjective Estimates
22:55
Checking whether Model Matches Real World
24:27Law of Large Numbers
24:28
Example 1: Law of Large Numbers
27:46Example 2: Possible Outcomes
30:43Example 3: Brands of Coffee and Taste
33:25Example 4: How Many Different Treatments are there?
35:33
Addition Rule for Disjoint Events 20m 29s
Intro
0:00Roadmap
0:08Roadmap
0:09
Disjoint Events
0:41Disjoint Events
0:42
Meaning of 'or'
2:39In Regular Life
2:40In Math/Statistics/Computer Science
3:10
Addition Rule for Disjoin Events
3:55If A and B are Disjoint: P (A and B)
3:56If A and B are Disjoint: P (A or B)
5:15
General Addition Rule
5:41General Addition Rule
5:42
Generalized Addition Rule
8:31If A and B are not Disjoint: P (A or B)
8:32
Example 1: Which of These are Mutually Exclusive?
10:50Example 2: What is the Probability that You will Have a Combination of One Heads and Two Tails?
12:57Example 3: Engagement Party
15:17Example 4: Home Owner's Insurance
18:30
Conditional Probability 57m 19s
Intro
0:00Roadmap
0:05Roadmap
0:06
'or' vs. 'and' vs. Conditional Probability
1:07'or' vs. 'and' vs. Conditional Probability
1:08
'and' vs. Conditional Probability
5:57P (M or L)
5:58P (M and L)
8:41P (M|L)
11:04P (L|M)
12:24
Tree Diagram
15:02Tree Diagram
15:03
Defining Conditional Probability
22:42Defining Conditional Probability
22:43
Common Contexts for Conditional Probability
30:56Medical Testing: Positive Predictive Value
30:57Medical Testing: Sensitivity
33:03Statistical Tests
34:27
Example 1: Drug and Disease
36:41Example 2: Marbles and Conditional Probability
40:04Example 3: Cards and Conditional Probability
45:59Example 4: Votes and Conditional Probability
50:21
Independent Events 24m 27s
Intro
0:00Roadmap
0:05Roadmap
0:06
Independent Events & Conditional Probability
0:26Non-independent Events
0:27Independent Events
2:00
Non-independent and Independent Events
3:08Non-independent and Independent Events
3:09
Defining Independent Events
5:52Defining Independent Events
5:53
Multiplication Rule
7:29Previously…
7:30But with Independent Evens
8:53
Example 1: Which of These Pairs of Events are Independent?
11:12Example 2: Health Insurance and Probability
15:12Example 3: Independent Events
17:42Example 4: Independent Events
20:03
Section 8: Probability Distributions
Introduction to Probability Distributions 56m 45s
Intro
0:00Roadmap
0:08Roadmap
0:09
Sampling vs. Probability
0:57Sampling
0:58Missing
1:30What is Missing?
3:06
Insight: Probability Distributions
5:26Insight: Probability Distributions
5:27What is a Probability Distribution?
7:29
From Sample Spaces to Probability Distributions
8:44Sample Space
8:45Probability Distribution of the Sum of Two Die
11:16
The Random Variable
17:43The Random Variable
17:44
Expected Value
21:52Expected Value
21:53
Example 1: Probability Distributions
28:45Example 2: Probability Distributions
35:30Example 3: Probability Distributions
43:37Example 4: Probability Distributions
47:20
Expected Value & Variance of Probability Distributions 53m 41s
Intro
0:00Roadmap
0:06Roadmap
0:07
Discrete vs. Continuous Random Variables
1:04Discrete vs. Continuous Random Variables
1:05
Mean and Variance Review
4:44Mean: Sample, Population, and Probability Distribution
4:45Variance: Sample, Population, and Probability Distribution
9:12
Example Situation
14:10Example Situation
14:11
Some Special Cases…
16:13Some Special Cases…
16:14
Linear Transformations
19:22Linear Transformations
19:23What Happens to Mean and Variance of the Probability Distribution?
20:12
n Independent Values of X
25:38n Independent Values of X
25:39
Compare These Two Situations
30:56Compare These Two Situations
30:57
Two Random Variables, X and Y
32:02Two Random Variables, X and Y
32:03
Example 1: Expected Value & Variance of Probability Distributions
35:35Example 2: Expected Values & Standard Deviation
44:17Example 3: Expected Winnings and Standard Deviation
48:18
Binomial Distribution 55m 15s
Intro
0:00Roadmap
0:05Roadmap
0:06
Discrete Probability Distributions
1:42Discrete Probability Distributions
1:43
Binomial Distribution
2:36Binomial Distribution
2:37
Multiplicative Rule Review
6:54Multiplicative Rule Review
6:55
How Many Outcomes with k 'Successes'
10:23Adults and Bachelor's Degree: Manual List of Outcomes
10:24
P (X=k)
19:37Putting Together # of Outcomes with the Multiplicative Rule
19:38
Expected Value and Standard Deviation in a Binomial Distribution
25:22Expected Value and Standard Deviation in a Binomial Distribution
25:23
Example 1: Coin Toss
33:42Example 2: College Graduates
38:03Example 3: Types of Blood and Probability
45:39Example 4: Expected Number and Standard Deviation
51:11
Section 9: Sampling Distributions of Statistics
Introduction to Sampling Distributions 48m 17s
Intro
0:00Roadmap
0:08Roadmap
0:09
Probability Distributions vs. Sampling Distributions
0:55Probability Distributions vs. Sampling Distributions
0:56
Same Logic
3:55Logic of Probability Distribution
3:56Example: Rolling Two Die
6:56
Simulating Samples
9:53To Come Up with Probability Distributions
9:54In Sampling Distributions
11:12
Connecting Sampling and Research Methods with Sampling Distributions
12:11Connecting Sampling and Research Methods with Sampling Distributions
12:12
Simulating a Sampling Distribution
14:14Experimental Design: Regular Sleep vs. Less Sleep
14:15
Logic of Sampling Distributions
23:08Logic of Sampling Distributions
23:09
General Method of Simulating Sampling Distributions
25:38General Method of Simulating Sampling Distributions
25:39
Questions that Remain
28:45Questions that Remain
28:46
Example 1: Mean and Standard Error of Sampling Distribution
30:57Example 2: What is the Best Way to Describe Sampling Distributions?
37:12Example 3: Matching Sampling Distributions
38:21Example 4: Mean and Standard Error of Sampling Distribution
41:51
Sampling Distribution of the Mean 1h 8m 48s
Intro
0:00Roadmap
0:05Roadmap
0:06
Special Case of General Method for Simulating a Sampling Distribution
1:53Special Case of General Method for Simulating a Sampling Distribution
1:54Computer Simulation
3:43
Using Simulations to See Principles behind Shape of SDoM
15:50Using Simulations to See Principles behind Shape of SDoM
15:51Conditions
17:38
Using Simulations to See Principles behind Center (Mean) of SDoM
20:15Using Simulations to See Principles behind Center (Mean) of SDoM
20:16Conditions: Does n Matter?
21:31Conditions: Does Number of Simulation Matter?
24:37
Using Simulations to See Principles behind Standard Deviation of SDoM
27:13Using Simulations to See Principles behind Standard Deviation of SDoM
27:14Conditions: Does n Matter?
34:45Conditions: Does Number of Simulation Matter?
36:24
Central Limit Theorem
37:13SHAPE
38:08CENTER
39:34SPREAD
39:52
Comparing Population, Sample, and SDoM
43:10Comparing Population, Sample, and SDoM
43:11
Answering the 'Questions that Remain'
48:24What Happens When We Don't Know What the Population Looks Like?
48:25Can We Have Sampling Distributions for Summary Statistics Other than the Mean?
49:42How Do We Know whether a Sample is Sufficiently Unlikely?
53:36Do We Always Have to Simulate a Large Number of Samples in Order to get a Sampling Distribution?
54:40
Example 1: Mean Batting Average
55:25Example 2: Mean Sampling Distribution and Standard Error
59:07Example 3: Sampling Distribution of the Mean
1:01:04
Sampling Distribution of Sample Proportions 54m 37s
Intro
0:00Roadmap
0:06Roadmap
0:07
Intro to Sampling Distribution of Sample Proportions (SDoSP)
0:51Categorical Data (Examples)
0:52Wish to Estimate Proportion of Population from Sample…
2:00
Notation
3:34Population Proportion and Sample Proportion Notations
3:35
What's the Difference?
9:19SDoM vs. SDoSP: Type of Data
9:20SDoM vs. SDoSP: Shape
11:24SDoM vs. SDoSP: Center
12:30SDoM vs. SDoSP: Spread
15:34
Binomial Distribution vs. Sampling Distribution of Sample Proportions
19:14Binomial Distribution vs. SDoSP: Type of Data
19:17Binomial Distribution vs. SDoSP: Shape
21:07Binomial Distribution vs. SDoSP: Center
21:43Binomial Distribution vs. SDoSP: Spread
24:08
Example 1: Sampling Distribution of Sample Proportions
26:07Example 2: Sampling Distribution of Sample Proportions
37:58Example 3: Sampling Distribution of Sample Proportions
44:42Example 4: Sampling Distribution of Sample Proportions
45:57
Section 10: Inferential Statistics
Introduction to Confidence Intervals 42m 53s
Intro
0:00Roadmap
0:06Roadmap
0:07
Inferential Statistics
0:50Inferential Statistics
0:51
Two Problems with This Picture…
3:20Two Problems with This Picture…
3:21Solution: Confidence Intervals (CI)
4:59Solution: Hypotheiss Testing (HT)
5:49
Which Parameters are Known?
6:45Which Parameters are Known?
6:46
Confidence Interval - Goal
7:56When We Don't Know m but know s
7:57
When We Don't Know
18:27When We Don't Know m nor s
18:28
Example 1: Confidence Intervals
26:18Example 2: Confidence Intervals
29:46Example 3: Confidence Intervals
32:18Example 4: Confidence Intervals
38:31
Intro
0:00Roadmap
0:04Roadmap
0:05
When to Use z vs. t?
1:07When to Use z vs. t?
1:08
What is z and t?
3:02 z-score and t-score: Commonality
3:03z-score and t-score: Formulas
3:34z-score and t-score: Difference
5:22
Why not z? (Why t?)
7:24Why not z? (Why t?)
7:25
But Don't Worry!
15:13Gossett and t-distributions
15:14
Rules of t Distributions
17:05t-distributions are More Normal as n Gets Bigger
17:06t-distributions are a Family of Distributions
18:55
Degrees of Freedom (df)
20:02Degrees of Freedom (df)
20:03
t Family of Distributions
24:07t Family of Distributions : df = 2 , 4, and 60
24:08df = 60
29:16df = 2
29:59
How to Find It?
31:01'Student's t-distribution' or 't-distribution'
31:02Excel Example
33:06
Example 1: Which Distribution Do You Use? Z or t?
45:26Example 2: Friends on Facebook
47:41Example 3: t Distributions
52:15Example 4: t Distributions , confidence interval, and mean
55:59
Introduction to Hypothesis Testing 1h 6m 33s
Intro
0:00Roadmap
0:06Roadmap
0:07
Issues to Overcome in Inferential Statistics
1:35Issues to Overcome in Inferential Statistics
1:36What Happens When We Don't Know What the Population Looks Like?
2:57How Do We Know whether a sample is Sufficiently Unlikely
3:43
Hypothesizing a Population
6:44Hypothesizing a Population
6:45Null Hypothesis
8:07Alternative Hypothesis
8:56
Hypotheses
11:58Hypotheses
11:59
Errors in Hypothesis Testing
14:22Errors in Hypothesis Testing
14:23
Steps of Hypothesis Testing
21:15Steps of Hypothesis Testing
21:16
Single Sample HT ( When Sigma Available)
26:08Example: Average Facebook Friends
26:09Step1
27:08Step 2
27:58Step 3
28:17Step 4
32:18
Single Sample HT (When Sigma Not Available)
36:33Example: Average Facebook Friends
36:34Step1: Hypothesis Testing
36:58Step 2: Significance Level
37:25Step 3: Decision Stage
37:40Step 4: Sample
41:36
Sigma and p-value
45:04Sigma and p-value
45:05On tailed vs. Two Tailed Hypotheses
45:51
Example 1: Hypothesis Testing
48:37Example 2: Heights of Women in the US
57:43Example 3: Select the Best Way to Complete This Sentence
1:03:23
Confidence Intervals for the Difference of Two Independent Means 55m 14s
Intro
0:00Roadmap
0:14Roadmap
0:15
One Mean vs. Two Means
1:17One Mean vs. Two Means
1:18
Notation
2:41A Sample! A Set!
2:42Mean of X, Mean of Y, and Difference of Two Means
3:56SE of X
4:34SE of Y
6:28
Sampling Distribution of the Difference between Two Means (SDoD)
7:48Sampling Distribution of the Difference between Two Means (SDoD)
7:49
Rules of the SDoD (similar to CLT!)
15:00Mean for the SDoD Null Hypothesis
15:01Standard Error
17:39
When can We Construct a CI for the Difference between Two Means?
21:28Three Conditions
21:29
Finding CI
23:56One Mean CI
23:57Two Means CI
25:45
Finding t
29:16Finding t
29:17
Interpreting CI
30:25Interpreting CI
30:26
Better Estimate of s (s pool)
34:15Better Estimate of s (s pool)
34:16
Example 1: Confidence Intervals
42:32Example 2: SE of the Difference
52:36
Hypothesis Testing for the Difference of Two Independent Means 50m
Intro
0:00Roadmap
0:06Roadmap
0:07
The Goal of Hypothesis Testing
0:56One Sample and Two Samples
0:57
Sampling Distribution of the Difference between Two Means (SDoD)
3:42Sampling Distribution of the Difference between Two Means (SDoD)
3:43
Rules of the SDoD (Similar to CLT!)
6:46Shape
6:47Mean for the Null Hypothesis
7:26Standard Error for Independent Samples (When Variance is Homogenous)
8:18Standard Error for Independent Samples (When Variance is not Homogenous)
9:25
Same Conditions for HT as for CI
10:08Three Conditions
10:09
Steps of Hypothesis Testing
11:04Steps of Hypothesis Testing
11:05
Formulas that Go with Steps of Hypothesis Testing
13:21Step 1
13:25Step 2
14:18Step 3
15:00Step 4
16:57
Example 1: Hypothesis Testing for the Difference of Two Independent Means
18:47Example 2: Hypothesis Testing for the Difference of Two Independent Means
33:55Example 3: Hypothesis Testing for the Difference of Two Independent Means
44:22
Confidence Intervals & Hypothesis Testing for the Difference of Two Paired Means 1h 14m 11s
Intro
0:00Roadmap
0:09Roadmap
0:10
The Goal of Hypothesis Testing
1:27One Sample and Two Samples
1:28
Independent Samples vs. Paired Samples
3:16Independent Samples vs. Paired Samples
3:17Which is Which?
5:20
Independent SAMPLES vs. Independent VARIABLES
7:43independent SAMPLES vs. Independent VARIABLES
7:44
T-tests Always…
10:48T-tests Always…
10:49
Notation for Paired Samples
12:59Notation for Paired Samples
13:00
Steps of Hypothesis Testing for Paired Samples
16:13Steps of Hypothesis Testing for Paired Samples
16:14
Rules of the SDoD (Adding on Paired Samples)
18:03Shape
18:04Mean for the Null Hypothesis
18:31Standard Error for Independent Samples (When Variance is Homogenous)
19:25Standard Error for Paired Samples
20:39
Formulas that go with Steps of Hypothesis Testing
22:59Formulas that go with Steps of Hypothesis Testing
23:00
Confidence Intervals for Paired Samples
30:32Confidence Intervals for Paired Samples
30:33
Example 1: Confidence Intervals & Hypothesis Testing for the Difference of Two Paired Means
32:28Example 2: Confidence Intervals & Hypothesis Testing for the Difference of Two Paired Means
44:02Example 3: Confidence Intervals & Hypothesis Testing for the Difference of Two Paired Means
52:23
Type I and Type II Errors 31m 27s
Intro
0:00Roadmap
0:18Roadmap
0:19
Errors and Relationship to HT and the Sample Statistic?
1:11Errors and Relationship to HT and the Sample Statistic?
1:12
Instead of a Box…Distributions!
7:00One Sample t-test: Friends on Facebook
7:01Two Sample t-test: Friends on Facebook
13:46
Usually, Lots of Overlap between Null and Alternative Distributions
16:59Overlap between Null and Alternative Distributions
17:00
How Distributions and 'Box' Fit Together
22:45How Distributions and 'Box' Fit Together
22:46
Example 1: Types of Errors
25:54Example 2: Types of Errors
27:30Example 3: What is the Danger of the Type I Error?
29:38
Effect Size & Power 44m 41s
Intro
0:00Roadmap
0:05Roadmap
0:06
Distance between Distributions: Sample t
0:49Distance between Distributions: Sample t
0:50
Problem with Distance in Terms of Standard Error
2:56Problem with Distance in Terms of Standard Error
2:57
Test Statistic (t) vs. Effect Size (d or g)
4:38Test Statistic (t) vs. Effect Size (d or g)
4:39
Rules of Effect Size
6:09Rules of Effect Size
6:10
Why Do We Need Effect Size?
8:21Tells You the Practical Significance
8:22HT can be Deceiving…
10:25Important Note
10:42
What is Power?
11:20What is Power?
11:21
Why Do We Need Power?
14:19Conditional Probability and Power
14:20Power is:
16:27
Can We Calculate Power?
19:00Can We Calculate Power?
19:01
How Does Alpha Affect Power?
20:36How Does Alpha Affect Power?
20:37
How Does Effect Size Affect Power?
25:38How Does Effect Size Affect Power?
25:39
How Does Variability and Sample Size Affect Power?
27:56How Does Variability and Sample Size Affect Power?
27:57
How Do We Increase Power?
32:47Increasing Power
32:48
Example 1: Effect Size & Power
35:40Example 2: Effect Size & Power
37:38Example 3: Effect Size & Power
40:55
Section 11: Analysis of Variance
Intro
0:00Roadmap
0:04Roadmap
0:05
Z- & T-statistic and Their Distribution
0:34Z- & T-statistic and Their Distribution
0:35
F-statistic
4:55The F Ration ( the Variance Ratio)
4:56
F-distribution
12:29F-distribution
12:30
s and p-value
15:00s and p-value
15:01
Example 1: Why Does F-distribution Stop At 0 But Go On Until Infinity?
18:33Example 2: F-distributions
19:29Example 3: F-distributions and Heights
21:29
ANOVA with Independent Samples 1h 9m 25s
Intro
0:00Roadmap
0:05Roadmap
0:06
The Limitations of t-tests
1:12The Limitations of t-tests
1:13
Two Major Limitations of Many t-tests
3:26Two Major Limitations of Many t-tests
3:27
Ronald Fisher's Solution… F-test! New Null Hypothesis
4:43Ronald Fisher's Solution… F-test! New Null Hypothesis (Omnibus Test - One Test to Rule Them All!)
4:44
Analysis of Variance (ANoVA) Notation
7:47Analysis of Variance (ANoVA) Notation
7:48
Partitioning (Analyzing) Variance
9:58Total Variance
9:59Within-group Variation
14:00Between-group Variation
16:22
Time out: Review Variance & SS
17:05Time out: Review Variance & SS
17:06
F-statistic
19:22The F Ratio (the Variance Ratio)
19:23
S²bet = SSbet / dfbet
22:13What is This?
22:14How Many Means?
23:20So What is the dfbet?
23:38So What is SSbet?
24:15
S²w = SSw / dfw
26:05What is This?
26:06How Many Means?
27:20So What is the dfw?
27:36So What is SSw?
28:18
Chart of Independent Samples ANOVA
29:25Chart of Independent Samples ANOVA
29:26
Example 1: Who Uploads More Photos: Unknown Ethnicity, Latino, Asian, Black, or White Facebook Users?
35:52Hypotheses
35:53Significance Level
39:40Decision Stage
40:05Calculate Samples' Statistic and p-Value
44:10Reject or Fail to Reject H0
55:54
Example 2: ANOVA with Independent Samples
58:21
Repeated Measures ANOVA 1h 15m 13s
Intro
0:00Roadmap
0:05Roadmap
0:06
The Limitations of t-tests
0:36Who Uploads more Pictures and Which Photo-Type is Most Frequently Used on Facebook?
0:37
ANOVA (F-test) to the Rescue!
5:49Omnibus Hypothesis
5:50Analyze Variance
7:27
Independent Samples vs. Repeated Measures
9:12Same Start
9:13Independent Samples ANOVA
10:43Repeated Measures ANOVA
12:00
Independent Samples ANOVA
16:00Same Start: All the Variance Around Grand Mean
16:01Independent Samples
16:23
Repeated Measures ANOVA
18:18Same Start: All the Variance Around Grand Mean
18:19Repeated Measures
18:33
Repeated Measures F-statistic
21:22The F Ratio (The Variance Ratio)
21:23
S²bet = SSbet / dfbet
23:07What is This?
23:08How Many Means?
23:39So What is the dfbet?
23:54So What is SSbet?
24:32
S² resid = SS resid / df resid
25:46What is This?
25:47So What is SS resid?
26:44So What is the df resid?
27:36
SS subj and df subj
28:11What is This?
28:12How Many Subject Means?
29:43So What is df subj?
30:01So What is SS subj?
30:09
SS total and df total
31:42What is This?
31:43What is the Total Number of Data Points?
32:02So What is df total?
32:34so What is SS total?
32:47
Chart of Repeated Measures ANOVA
33:19Chart of Repeated Measures ANOVA: F and Between-samples Variability
33:20Chart 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?
40:25Hypotheses
40:26Significance Level
41:46Decision Stage
42:09Calculate Samples' Statistic and p-Value
46:18Reject or Fail to Reject H0
57:55
Example 2: Repeated Measures ANOVA
58:57Example 3: What's the Problem with a Bunch of Tiny t-tests?
1:13:59
Section 12: Chi-square Test
Chi-Square Goodness-of-Fit Test 58m 23s
Intro
0:00Roadmap
0:05Roadmap
0:06
Where Does the Chi-Square Test Belong?
0:50Where Does the Chi-Square Test Belong?
0:51
A New Twist on HT: Goodness-of-Fit
7:23HT in General
7:24Goodness-of-Fit HT
8:26
Hypotheses about Proportions
12:17Null Hypothesis
12:18Alternative Hypothesis
13:23Example
14:38
Chi-Square Statistic
17:52Chi-Square Statistic
17:53
Chi-Square Distributions
24:31Chi-Square Distributions
24:32
Conditions for Chi-Square
28:58Condition 1
28:59Condition 2
30:20Condition 3
30:32Condition 4
31:47
Example 1: Chi-Square Goodness-of-Fit Test
32:23Example 2: Chi-Square Goodness-of-Fit Test
44:34Example 3: Which of These Statements Describe Properties of the Chi-Square Goodness-of-Fit Test?
56:06
Chi-Square Test of Homogeneity 51m 36s
Intro
0:00Roadmap
0:09Roadmap
0:10
Goodness-of-Fit vs. Homogeneity
1:13Goodness-of-Fit HT
1:14Homogeneity
2:00Analogy
2:38
Hypotheses About Proportions
5:00Null Hypothesis
5:01Alternative Hypothesis
6:11Example
6:33
Chi-Square Statistic
10:12Same as Goodness-of-Fit Test
10:13
Set Up Data
12:28Setting Up Data Example
12:29
Expected Frequency
16:53Expected Frequency
16:54
Chi-Square Distributions & df
19:26Chi-Square Distributions & df
19:27
Conditions for Test of Homogeneity
20:54Condition 1
20:55Condition 2
21:39Condition 3
22:05Condition 4
22:23
Example 1: Chi-Square Test of Homogeneity
22:52Example 2: Chi-Square Test of Homogeneity
32:10
Section 13: Overview of Statistics
Overview of Statistics 18m 11s
Intro
0:00Roadmap
0:07Roadmap
0:08
The Statistical Tests (HT) We've Covered
0:28The Statistical Tests (HT) We've Covered
0:29
Organizing the Tests We've Covered…
1:08One Sample: Continuous DV and Categorical DV
1:09Two Samples: Continuous DV and Categorical DV
5:41More Than Two Samples: Continuous DV and Categorical DV
8:21
The Following Data: OK Cupid
10:10The Following Data: OK Cupid
10:11
Example 1: Weird-MySpace-Angle Profile Photo
10:38Example 2: Geniuses
12:30Example 3: Promiscuous iPhone Users
13:37Example 4: Women, Aging, and Messaging
16:07
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