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Dr. Ji Son

Dr. Ji Son

Between and Within Treatment Variability

Slide Duration:

Table of Contents

I. Introduction
Descriptive Statistics vs. Inferential Statistics

25m 31s

Intro
0:00
Roadmap
0:10
Roadmap
0:11
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
II. About Samples: Cases, Variables, Measurements
About Samples: Cases, Variables, Measurements

32m 14s

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
III. Visualizing Distributions
Introduction to Excel

8m 9s

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

39m 10s

Intro
0:00
Roadmap
0:08
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

25m 29s

Intro
0:00
Roadmap
0:10
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

42m 42s

Intro
0:00
Roadmap
0:06
Roadmap
0:07
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

12m 23s

Intro
0:00
Roadmap
0:05
Roadmap
0:06
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

22m 49s

Intro
0:00
Roadmap
0:05
Roadmap
0:08
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
IV. Summarizing Distributions
Central Tendency: Mean, Median, Mode

38m 50s

Intro
0:00
Roadmap
0:07
Roadmap
0:08
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

42m 40s

Intro
0:00
Roadmap
0:05
Roadmap
0:06
Variability (or Spread)
0:45
Variability (or Spread)
0:46
Things to Think About
5:45
Things to Think About
5:46
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

57m 15s

Intro
0:00
Roadmap
0:06
Roadmap
0:07
Summarizing Distributions
0:37
Shape, Center, and Spread
0:38
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

41m 51s

Intro
0:00
Roadmap
0:16
Roadmap
0:17
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

34m 33s

Intro
0:00
Roadmap
0:13
Roadmap
0:14
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

41m 44s

Intro
0:00
Roadmap
0:06
Roadmap
0:07
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

55m 44s

Intro
0:00
Roadmap
0:15
Roadmap
0:16
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
V. Linear Regression
Scatterplots

47m 19s

Intro
0:00
Roadmap
0:04
Roadmap
0:05
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
Spread & Strength
8:22
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

32m 2s

Intro
0:00
Roadmap
0:05
Roadmap
0:06
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

56m 36s

Intro
0:00
Roadmap
0:13
Roadmap
0:14
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

43m 58s

Intro
0:00
Roadmap
0:05
Roadmap
0:06
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

52m 52s

Intro
0:00
Roadmap
0:07
Roadmap
0:08
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

27m 8s

Intro
0:00
Roadmap
0:05
Roadmap
0:06
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
VI. Collecting Data in an Experiment
Sampling & Bias

54m 44s

Intro
0:00
Roadmap
0:05
Roadmap
0:06
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
Inadequate Sample Frame
25:40
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

14m 25s

Intro
0:00
Roadmap
0:05
Roadmap
0:06
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 1: Which Type(s) of Sampling was this?
8:33
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

53m 54s

Intro
0:00
Roadmap
0:06
Roadmap
0:07
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

41m 31s

Intro
0:00
Roadmap
0:06
Roadmap
0:07
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
VII. Review of Probability Axioms
Sample Spaces

37m 52s

Intro
0:00
Roadmap
0:07
Roadmap
0:08
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

20m 29s

Intro
0:00
Roadmap
0:08
Roadmap
0:09
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
General Addition Rule
5:41
General Addition Rule
5:42
Generalized Addition Rule
8:31
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 Party
15:17
Example 4: Home Owner's Insurance
18:30
Conditional Probability

57m 19s

Intro
0:00
Roadmap
0:05
Roadmap
0:06
'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

24m 27s

Intro
0:00
Roadmap
0:05
Roadmap
0:06
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
VIII. Probability Distributions
Introduction to Probability Distributions

56m 45s

Intro
0:00
Roadmap
0:08
Roadmap
0:09
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

53m 41s

Intro
0:00
Roadmap
0:06
Roadmap
0:07
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

55m 15s

Intro
0:00
Roadmap
0:05
Roadmap
0:06
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 2: College Graduates
38:03
Example 3: Types of Blood and Probability
45:39
Example 4: Expected Number and Standard Deviation
51:11
IX. Sampling Distributions of Statistics
Introduction to Sampling Distributions

48m 17s

Intro
0:00
Roadmap
0:08
Roadmap
0:09
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

1h 8m 48s

Intro
0:00
Roadmap
0:05
Roadmap
0:06
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
SPREAD
39:52
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
1:01:04
Sampling Distribution of Sample Proportions

54m 37s

Intro
0:00
Roadmap
0:06
Roadmap
0:07
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
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
SDoM vs. SDoSP: Spread
15:34
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
X. Inferential Statistics
Introduction to Confidence Intervals

42m 53s

Intro
0:00
Roadmap
0:06
Roadmap
0:07
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

1h 2m 6s

Intro
0:00
Roadmap
0:04
Roadmap
0:05
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

1h 6m 33s

Intro
0:00
Roadmap
0:06
Roadmap
0:07
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
Example: Average Facebook Friends
26:09
Step1
27:08
Step 2
27:58
Step 3
28:17
Step 4
32:18
Single Sample HT (When Sigma Not Available)
36:33
Example: Average Facebook Friends
36:34
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
1:03:23
Confidence Intervals for the Difference of Two Independent Means

55m 14s

Intro
0:00
Roadmap
0:14
Roadmap
0:15
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

50m

Intro
0:00
Roadmap
0:06
Roadmap
0:07
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

1h 14m 11s

Intro
0:00
Roadmap
0:09
Roadmap
0:10
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

31m 27s

Intro
0:00
Roadmap
0:18
Roadmap
0:19
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 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

44m 41s

Intro
0:00
Roadmap
0:05
Roadmap
0:06
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
XI. Analysis of Variance
F-distributions

24m 46s

Intro
0:00
Roadmap
0:04
Roadmap
0:05
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

1h 9m 25s

Intro
0:00
Roadmap
0:05
Roadmap
0:06
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

1h 15m 13s

Intro
0:00
Roadmap
0:05
Roadmap
0:06
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?
1:13:59
XII. Chi-square Test
Chi-Square Goodness-of-Fit Test

58m 23s

Intro
0:00
Roadmap
0:05
Roadmap
0:06
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
Hypotheses about Proportions
12:17
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

51m 36s

Intro
0:00
Roadmap
0:09
Roadmap
0:10
Goodness-of-Fit vs. Homogeneity
1:13
Goodness-of-Fit HT
1:14
Homogeneity
2:00
Analogy
2:38
Hypotheses About Proportions
5:00
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
XIII. Overview of Statistics
Overview of Statistics

18m 11s

Intro
0:00
Roadmap
0:07
Roadmap
0:08
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
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Between and Within Treatment Variability

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  • Intro 0:00
  • Roadmap 0:06
    • Roadmap
  • Experimental Designs 0:51
    • Experimental Designs: Manipulation & Control
  • Two Types of Variability 2:09
    • Between Treatment Variability
    • Within Treatment Variability
  • Updated Goal of Experimental Design 5:47
    • Updated Goal of Experimental Design
  • Example: Drugs and Driving 6:56
    • Example: Drugs and Driving
  • Different Types of Random Assignment 11:27
    • All Experiments
    • Completely Random Design
    • Randomized Block Design
  • Randomized Block Design 15:48
    • Matched Pairs Design
    • Repeated Measures Design
  • Between-subject Variable vs. Within-subject Variable 22:43
    • Completely Randomized Design
    • Repeated Measures Design
  • 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

Transcription: Between and Within Treatment Variability

Hi and welcome to www.educator.com.0000

Today we are going to be talking about between and within treatment variability.0002

Here is how we are going to do this.0006

First we are going to talk about all experiments have in common, just recap and then we are going to talk about 2 types of variability within experiments.0010

That is going to be between treatment variability and within treatment variability.0020

Then we are going to reframe the goal of all experiments in terms of variability.0025

We are going to talk about different types of random assignment or different types of control and that will help us control certain kind of variability.0031

Those three different kinds of random assignment IV are completely randomized design, matched pairs design, and repeated measures design.0041

Okay the first thing about experimental designs is that all of them have two things in common.0051

One is that they have manipulation and control of the treatment variable or we call the IV or the independent variable.0058

They all have that in common.0072

Now concretely what that really translates to is that each experimental unit, whatever that unit is, would be a rat or cell or a CD or states or a person.0074

Each experimental unit or case gets assigned to some treatment.0089

This rat gets treatment A, this rat gets treatment B.0097

Everything in this experiment should be alike except for the treatment.0105

Everything else about these rats or states or schools or people should be roughly similar except for the treatment.0112

That is how we isolate the effect of that treatment.0124

Given that experimental overview, there are really 2 kinds of variability that we need to think about.0129

One is what we call between treatment variability and you can think of it as here are two groups that have 2 different treatments A and B.0138

We know what is the between group variability?0150

How are these two treatments different from each other or three treatments or parts of a treatment?0152

This variability is hopefully caused by the treatment.0158

The impact of the treatment is making on these two different cases were experimental units and that is really caused by the treatment.0164

This is what we think of as the good kind of variability.0178

This is what variability we are interested in.0182

We are looking for this type of variability because if we have a lot of between treatment variability this means they are manipulated variable is quite important.0187

It makes an impact.0209

That is one kind of variability.0210

The other kind of variability is within treatment variability.0215

That means within an experimental unit they all have the same treatment.0218

It all rats that were exposed to the same hours of sleep.0224

These rats had different hours of sleep.0229

These rats that all have the same hours of sleep there a still some little differences between them.0230

Some rats sleep a little bit more or the other one is active.0239

They have a little bit of within treatment variability that will just come along for the ride.0241

Despite the rigorous experimental methodology, no matter how good your manipulation and control is0252

They were this some variability that will exists even within a treatment group and that could come from lots of different sources.0260

Sometimes it does come from experimental mistakes and sloppiness,0268

Most of the time it just comes from noise or other variables that we are not accounting for.0275

This is what we think of as bad variability, but is not as bad like we want to or if you have it, then oh your terrible experimenter.0281

That is not what it means.0294

It just means that this gets in the way of seeing the good kind of seeing the between treatment variability.0296

Here is the problem.0315

Within treatment variability is very difficult to avoid.0318

They are some techniques to try and avoid it and minimize in as much as possible and we are going to learn about those0323

Overall even though you try and reduce it probably never completely goes away.0330

Here is the issue with it.0337

It prevents us from seeing the between treatment variability because sometimes it obscure it.0338

Let me show you what that means in the next slide.0346

Because of these two different kinds of variability we want to update one of the goals of the experimental design.0354

Not only do we need to have manipulation and control of the IV in order to determine causality.0363

We are very interested in causality and experimenter so this is all in order to causality.0375

All so we want to know where as much as possible within treatment variability as much as we possibly can.0381

There can be a couple of different methods for lowering within treatment variability as much as we can.0400

Because that can help us see between treatment differences and that is where we are really interested in, in order to determine causality.0407

Let us look at an example to look at how this variability might impact each other.0419

Here is an example of drugs and driving.0424

Some antihistamines like allergy medicine make people feel drowsy like Benadryl.0428

One danger is that drowsy people are crappy drivers.0433

To check whether an antihistamine makes people worse at driving we wanted to test an antihistamine against the placebo,0438

Just a sugar pill on people's driving performance in a videogame.0445

Here is the ideal case.0449

In the ideal case in order to determine whether antihistamines cause people to be like crappy drivers.0454

One thing you might want to look at is let us say the score on the driving performance.0462

Higher score means you are better at driving lower score mean you have more like crashes or swerves, or whatever is right.0468

Maybe we will see if the we draw like a dot plot of the antihistamine people right.0475

Maybe we will see them all having sort of you know low scores but maybe the placebo group will just tend to get high scores.0483

If we had something like this then we will see that even though there is within treatment variability, there is variability here.0513

There are some within treatment variability here and there are some within treatment variability here too.0521

Basically the means are probably far apart enough where we could probably say all of the antihistamine seems to be different than the placebo group.0527

Between treatment difference is still big enough that we can see it.0540

But the world is not an ideal place.0547

Most of the time we have a sort of noisy world because some people are just better at driving games0551

and some are better at video game than and some people do not react to antihistamines as strongly as other people.0562

There are lots of other variables that come into play for within treatment variability.0568

We might have been no differences.0576

Maybe we can a lot of spread.0580

We have a lot of spread here and among the placebo group we might also have a whole lot of spread.0591

In the case is hard see if there is a between treatment difference just because there is a lot of within treatment difference.0602

That is what we mean by a bad kind of variability that gets in our way of really being able to make conclusions from our experiment.0623

What we want to do is reduce that within treatment variability as much as we possibly can.0631

To conclude that a treatment, some experimental treatment makes a big enough impact,0639

what you really have to see is that the between treatment variability is overcoming the within treatment variability.0645

The between treatment variability have to come out strong and the within treatment variability have to be some of sort of smaller.0668

When we see that then we can maybe start to have some more confidence and say I think this treatment might make a difference.0677

In order to reduce within treatment variability as much as possible there are a couple of different types of design for random assignment that we could carry out.0686

All experiments have random assignment of treatments to experimental units or cases.0700

I'm calling them experimental units here because there are so many different things that you could do experiments on.0706

You could do experiments on whole companies and you could do experiments on individual people.0713

I will generally call them units or cases.0719

The one type that we have already talked about before is that we call a completely random design.0722

This means you randomly assigned a treatment to each little experimental unit, gets randomly assigned to a treatment.0729

The only requirement other than is that you keep a number of units that are given each treatment as equal as possible.0741

Treatment A, B, and C all have the same number of experimental units back at each of those.0751

That is the only requirement.0757

The way you can think about this is like that is let us say you have experimental units ABCDEF and you have two treatment groups, treatment 1 and 2.0758

When A comes in you think about it as flipping a coin and whatever they get heads for 1 and 2 for tails, it might be A, B, C, D, E, F.0773

You just randomly assigned them to different treatment groups.0791

That one is really pretty easy and straightforward.0794

The other kinds are what we call generally randomized block design.0799

What we do here is first we have the additional that we place similar units into groups and we call those units blocks.0805

Randomly assigned treatments to use the units within the blocks.0822

Here is the general idea.0826

Let us say A, B, C, and D are similar for some reason.0828

They are females.0841

Maybe we have E, F, G, H and those are all males.0846

First, we placed similar units into groups of blocks.0854

We have two blocks here.0859

Once we have those blocks, then you randomly assign treatments to the units within the block.0860

Maybe we might get A, B, C, D.0867

We get randomly assigned to the treatments and then also with F, G, H we might get randomly assigned to these treatment groups.0879

Then you roughly have 2 treatments that have an equal number of females and equal number of males.0892

Whatever similarity you are interested in, you can use that.0901

For instance, if you are interested in whether they are in the same grade level or they have the same major0908

or sometimes it might be maybe rocks from the same litter because those tend to be similar.0914

Or plants from the similar elevation level.0922

Whatever those similarities are you want to place them into groups first before assigning them to treatments0925

so that each group gets equal representation in the two treatments.0932

Actually, there are multiple different kinds of randomized block design.0940

I’m going to show you two of them.0945

Randomized block design have two different ones.0948

The reason that it is called randomized block design is Guy and Fisher, who did a lot of the groundwork for all of the statistics.0952

He wanted to do experiments on meat or some kind of farming thing.0961

What he would do is say I do not want it to be that like one treatment is on the edge, on the west side.0967

What he did was he separated all of the fields into blocks first.0981

Let us say there are like four different treatment what he would do is randomly assign different quadrants into those different treatments.0991

A little bit of each in a place on the field got treatment A.1011

A little bit of each place in the field got treatment B.1022

If you look at all the A, there is an A here, here, and here.1027

If you look at C, there is a C here, here, here, and here,1038

This way he make sure that every part of the field is represented in his little treatment group of C.1044

Back to two different types of block design.1056

The first type of randomized block design you need to know is what we call matched pairs design.1063

Each block is a pair of similar units and it does not have to be pair.1068

These pairs could be all certain different things.1077

Maybe they are twins because but at least in different genes they are identical.1080

Once they have these pairs that are the same you randomly assign treatments within pairs.1091

In one entry gets to be in treatment A and one in treatment B.1097

Another example is may be similar companies.1102

If you have big soft drink company like Coca-Cola, maybe it is matched pair is Pepsi company1106

then you randomly assign Coca-Cola to other thing and Pepsi to another thing.1115

The idea is you have all these little pairs but one gets to be assigned to be in the blue group randomly and one is assigned to be in the red group randomly.1122

These two individuals inside the pair are similar in some important way.1137

You often see matched pairs design, especially in psychology when you have something like different age groups.1144

You want to have age matched controls.1152

For every 4/2-year-old you have here, you have a 4 ½ year old pair and they are both get assigned to different treatment groups.1155

You might also see this when people do studies with individuals have autism or some brain damage.1163

They might have IQ matched controls.1173

They might have this individual and find somebody who matches them on IQ to be in the control group.1176

That is what we call a matched pairs design.1183

The other type of randomized block design you need to know is what we call a repeated measures design.1188

This one is really nice for reducing within treatment variability because each block now is one case.1196

Like for instance, one person or one lot and each case gets all the different treatments, but in a different random order.1205

Maybe we have case ABCDE.1217

We have all these little people or rats or plants in our study.1225

Let us say plants and they get 3 different kinds of fertilizer, one for each year but in different orders.1231

Maybe A will get fertilizer 1, 2, then 3.1244

Maybe B will get 2, then 3, then 1.1249

Maybe C will get 3, then 1, then 2.1252

And D will get 3, then 2, then 1.1255

E will get 2, and 1, and 3.1258

In this case, each case or experimental unit gets assigned to all the treatment groups.1262

The nice thing about this as well as this design is that you can compare how A does in treatment 1, 2, and 3.1271

You can compare how B does itself in treatment 1, 2, and 3.1282

Also with the match pairs you can look at how their pair does and we could rule out the difference in ages.1286

That is not as important anymore because they're the same age.1299

The nice thing about these is that now we have data to do within treatment comparisons and be able to rule out that source of variability.1303

Let us say plant A just grows a lot faster than all the other plants then they would be different from B because B grows slower than A.1316

Even so does one fertilizer help A grow more even more faster than the other ones?1329

Maybe fertilizer 1 here and 1 here even though B only grows like 3 inches, that is a lot for B, but maybe for A, A grows like 12 inches and that is a lot for A.1337

You can make it relative to A’s performance in the other treatment groups.1355

Often times you might hear the term with between subject variable and within subject variable.1361

This is just a matter of terminology and instead of the word subject feel free to put in the word cases or experimental units.1371

Often times like in social science or medical sciences, you will have between subject persons within subject because we are talking about people and animals.1386

In a between subject variable it just means that this variable whatever it is, like medicine it is being administered between cases or between people.1399

The people who get medicine A do not get medicine B and the people who get medicine B they do not get medicine A.1412

That is what you see in a completely randomized design.1419

Sometimes you also see that in other designs that are not experiments as well, but when we are talking about experiments,1423

You will see that primarily in a completely randomized design.1435

You might also see it in a matched pairs designs but it actually depends on what the pairs are.1439

In a completely randomized design what you'll end up having is 2 treatment groups.1443

You will have in the treatment group 1 or however many treatment you have, you could have three or four.1452

Treatment group 2.1460

You have different people in each of those.1462

You know you will have ABCDEF and so A is only in treatment 1 when they are not in treatment 2.1465

This treatment variable treatment is a between subject variable because it occurs between subjects.1476

It is not like inside of one subject that you have the different values of that variable inside it is between subjects.1495

In a repeated measures design this is a case where we have ABCDEF.1504

We have the same subjects here, but instead they might get 2 treatments.1513

Here everybody gets both the treatment.1521

Within subject A they hold both the treatment 1 and treatment 2.1536

Because of that treatment in this case, treatment here is a within subject variable.1546

Because the variable varies within a subject inside of one subject.1565

Inside of one subject.1569

Let us go into some examples.1571

Here is example 1, We want to know whether sitting or standing affects our heart rate.1579

Design a completely random experiment, as well as a matched pair and repeated measures experiment.1584

In order to have a completely random experiment let us say we start off with 20 people, maybe in your statistics class1590

and maybe one thing you might do is assign 10 of those people random like to split the coin or something1603

and assigned 10 of those people to the sitting condition treatment and assign half of the people to the standing treatment.1612

Here is sit, stand, sit, stand, sit, stand.1622

Actually the other way I’m going to write it, let me write sit in red and stand in blue.1633

It might be sit, sit, sit, sit, sit, we will do 10 of those.1648

Maybe stand, stand, stand, stand, 10 of those.1656

Then you will get you know people ABCDEFGH and then the other half you might pu FGHIJ.1666

That will make it easier and make it 10 people because it makes me easier to draw.1684

In this way you might have 5 people standing, 5 people sitting, and they have been randomly assign and then you might get everybody's heart rate.1691

Whatever their heart rates are.1706

58, 52 so on and so forth.1710

That might be one experiment, and you will compare these numbers to these numbers.1714

A matched pair design might go something like this.1720

Let us say we have those same 10 people, but maybe we want to match them based on something.1726

Everybody already has a different heart rate.1733

Some people have faster heart rate and some people slower and so maybe we take everyone's heart rate first.1737

Everyone who has the same heart rate we will put them as a pair.1743

These people might have a resting heart rate of 58 and one person, one of these people gets to be in this standing condition.1748

And one of these people get to be in the sitting condition.1766

We might do that for 5 pairs.1770

A, B, C, D, E, F, G, H, I, J.1779

In this way they are paired according to their resting heart rate.1796

And then one person continues to sit and then one person to sit and take the heart rate again.1803

But one person stands up and they are now taking their heart rates standing up.1808

We could compare these two people because we know that they started off with the same resting heart rate.1815

This is the A matched pair design.1823

Finally the repeated measures design we might do something like this.1827

Let us say we have A, B, C, D, E, F, G, H, I, J.1832

We have our 10 people and some of them have to sit and take their heart rate first and then stand and take their heart rate.1842

Sit, sit, sit, sit, sit.1855

Stand, stand, stand, stand, stand.1860

In this way, person A will have to sit and take heart rate and then stand then take the heart rate.1866

Person B will have to stand first and take their heart rate and sit then take heart rate.1874

Everyone gets both treatments and the treatment is the within subject variable.1879

It is within each subject, but they each have in a different order.1885

So, roughly half of our participants should be in the sit- stand order and the other half should be in the stand-sit order.1891

Example 2, why is blocking sometimes a desirable feature of the design?1901

Given example where blocking might be better idea than completely randomized.1908

Blocking might be important if there's some variable that you know of ahead of time that might impact your dependent variable.1912

Like standing heart rate might be influenced by your sitting heart rate.1922

For whatever your baseline is it is going to affect what your standing heart rate is.1930

Sometimes you want to like rule out variation that comes from that variable that you know might be important.1936

Let us think of an example.1946

Maybe we want to see how fast people learn to play tennis.1950

How quickly people learn to play tennis?1956

What are some things that might affect their ability to learn to play tennis?1967

Maybe our racquet ball experience?1972

Maybe, previous tennis experience.1975

Maybe their age.1988

Maybe younger people might be able to learn faster than older people.1992

Anyone of these variables might be important.1996

Let us just pick one athletic experience.2001

We will just ask people how many years of athletic experience.2003

We might want to the experienced athletes in one block and the less experienced athletes in another block.2007

We have a whole bunch of experience.2015

Maybe we have moderately experienced.2018

A little bit experienced and then little to no experience and within each block, maybe we give them two different ways of learning tennis.2022

Method A and method B.2036

Here some people get method A in red.2039

Some people get method A.2047

For each of these people there is another person in their group that gets method B.2053

In this way, we have a mix of people who have experience who get method A and less experienced people who have a lot experience get method B.2067

That is the same across all these different levels of experience.2087

That might be an example if blocking is better because then you reduce the within treatment variability2092

so that you could maybe see more clearly between treatment variabilities.2098

The real difference between treatment A and treatment B.2108

Why our completely randomized designs, also called between subjects designs popular?2109

Given example where this is a better design than randomized block design.2118

One of the real problems with randomized block design is that sometimes you do not know you what might be important.2122

There might be a lot of variables that you need to control for and it is probably really hard to control for all of those things.2132

Maybe in something like grade at school.2139

Many things important grades at school that it might be better off to have a completely randomized design than to have a randomized block design.2145

Or if you do have a randomized block design maybe you could only do it with a limited number of variables like one variable.2158

In that case, our completely randomized design might be more important.2165

In example of something like this and you know, let us also modify this question to why it might be better than with subjective design.2170

The one kind we learned about is the repeated measures design.2188

Sometimes it is hard to assign one single experimental unit to multiple treatments.2200

For example, some medications last in your body for a long time and so it would be really hard to give one group of rats the medication2207

and then give them a placebo later because that medication is still in their body.2221

Sometimes it might be very difficult to assign different treatment levels to the same individual.2227

And there might be some carryover effects.2236

Things like the drugs staying in their body or maybe we are looking at two different teaching methods for statistics.2239

Maybe we are trying within treatment A versus treatment B or teaching method A versus B.2248

And they might have learned a lot from whatever teaching method came first.2256

And because of that the second one may not look as effective, but maybe it is just that whichever one came first.2260

Sometimes it is going to be really hard to deal within subject design, but you have to do between subjects design.2268

In a completely randomized design this actually a sort of easier.2275

It is an easy way of doing experiments because you do not have to do as much planning ahead of time.2281

In the case where maybe you do not know who your subjects or cases might be.2289

Maybe it is good to have a completely randomized design.2296

That is it.2300

An example might be maybe we are looking at how volunteers at a supermarket case test some jams.2307

Maybe where looking at if they taste it plastic spoons versus metal spoons.2316

Does it make an impact?2326

We do not know who's coming at.2327

We can randomly assign them to blocks first.2329

We might just a clever confident and randomly assign them to one group or the other.2333

That might be an example.2339

Example 4, are the following designs completely random?2342

Matched pairs or repeated measures experiments?2346

A college health service wanted to test whether putting antibacterial soap in the dorm bathrooms will reduce visits to the infirmary.2351

They kept track of how many students from which dorms visited the infirmary per semester.2359

They assigned 10 randomly picked alarms to get antibacterial soap and the other 10 get regular soap.2364

It is helpful to know what are the experimental units here.2370

You might think it is the people, the students going to the infirmary.2376

Actually, that is not.2380

That is the dependent variable.2382

How many students?2384

The case is the experimental units are actually the dorms.2385

The dorms had been randomly selected into one group or the other.2389

The antibacterial soap group or the regular soap group.2395

This one looks like a completely random design.2398

The other way they could have done that is that five large dorms that have 200 students2406

and 5 small dorms only have 40 students received antibacterial soap.2413

Then another 5 large dorms and 5 small dorms received regular soap.2418

The largeness of the dorms might matter because maybe in a larger dorms things are crazier and messier.2423

Maybe it is easier to cast disease in a larger dorm.2431

Maybe they wanted to make sure half of the time that the size of the dorm isn't what causing the difference in the variability.2437

In order to control for that day they have an equal number of large dorms and small dorms in each of the treatment conditions,2448

the antibacterial soap and regular soap groups.2456

That looks like sort of a matched pairs.2460

It is a block design.2462

For every large dorm you have another large dorm here and it is like a pair on the other side.2464

For every small dorms you have a small dorm, on the other side. So they have a matched pair.2477

That is the end of within and between treatment variability.2482

Thanks for using www.educator.com.2489

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