Section 1: Introduction |
|
Descriptive Statistics vs. Inferential Statistics |
25:31 |
| |
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 | |
Section 2: About Samples: Cases, Variables, Measurements |
|
About Samples: Cases, Variables, Measurements |
32:14 |
| |
Intro |
0:00 | |
| |
Data |
0:09 | |
| |
| Data, Cases, Variables, and Values |
0:10 | |
| |
| Rows, Columns, and Cells |
2:03 | |
| |
| Example: Aircrafts |
3:52 | |
| |
How Do We Get Data? |
5:38 | |
| |
| Research: Question and Hypothesis |
5:39 | |
| |
| Research Design |
7:11 | |
| |
| Measurement |
7:29 | |
| |
| Research Analysis |
8:33 | |
| |
| Research Conclusion |
9:30 | |
| |
Types of Variables |
10:03 | |
| |
| Discrete Variables |
10:04 | |
| |
| Continuous Variables |
12:07 | |
| |
Types of Measurements |
14:17 | |
| |
| Types of Measurements |
14:18 | |
| |
Types of Measurements (Scales) |
17:22 | |
| |
| Nominal |
17:23 | |
| |
| Ordinal |
19:11 | |
| |
| Interval |
21:33 | |
| |
| Ratio |
24:24 | |
| |
Example 1: Cases, Variables, Measurements |
25:20 | |
| |
Example 2: Which Scale of Measurement is Used? |
26:55 | |
| |
Example 3: What Kind of a Scale of Measurement is This? |
27:26 | |
| |
Example 4: Discrete vs. Continuous Variables. |
30:31 | |
Section 3: Visualizing Distributions |
|
Introduction to Excel |
8:09 |
| |
Intro |
0:00 | |
| |
Before Visualizing Distribution |
0:10 | |
| |
| Excel |
0:11 | |
| |
Excel: Organization |
0:45 | |
| |
| Workbook |
0:46 | |
| |
| Column x Rows |
1:50 | |
| |
| Tools: Menu Bar, Standard Toolbar, and Formula Bar |
3:00 | |
| |
Excel + Data |
6:07 | |
| |
| Exce and Data |
6:08 | |
|
Frequency Distributions in Excel |
39:10 |
| |
Intro |
0:00 | |
| |
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 |
25:29 |
| |
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 |
42:42 |
| |
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 |
12:23 |
| |
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 |
22:49 |
| |
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 | |
Section 4: Summarizing Distributions |
|
Central Tendency: Mean, Median, Mode |
38:50 |
| |
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 |
42:40 |
| |
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 |
57:15 |
| |
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 |
41:51 |
| |
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 |
34:33 |
| |
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 |
41:44 |
| |
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 |
55:44 |
| |
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 | |
Section 5: Linear Regression |
|
Scatterplots |
47:19 |
| |
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 |
32:02 |
| |
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 |
56:36 |
| |
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 |
43:58 |
| |
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 |
52:52 |
| |
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 |
27:08 |
| |
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 | |
Section 6: Collecting Data in an Experiment |
|
Sampling & Bias |
54:44 |
| |
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 |
14:25 |
| |
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 |
53:54 |
| |
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 |
41:31 |
| |
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 | |
Section 7: Review of Probability Axioms |
|
Sample Spaces |
37:52 |
| |
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 |
20:29 |
| |
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 |
57:19 |
| |
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 |
24:27 |
| |
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 | |
Section 8: Probability Distributions |
|
Introduction to Probability Distributions |
56:45 |
| |
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 |
53:41 |
| |
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 |
55:15 |
| |
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 | |
Section 9: Sampling Distributions of Statistics |
|
Introduction to Sampling Distributions |
48:17 |
| |
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 |
1:08:48 |
| |
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 |
61:04 | |
|
Sampling Distribution of Sample Proportions |
54:37 |
| |
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 | |
Section 10: Inferential Statistics |
|
Introduction to Confidence Intervals |
42:53 |
| |
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 |
1:02:06 |
| |
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 |
1:06:33 |
| |
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 |
63:23 | |
|
Confidence Intervals for the Difference of Two Independent Means |
55:14 |
| |
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 |
50:00 |
| |
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 |
1:14:11 |
| |
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 |
31:27 |
| |
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 |
44:41 |
| |
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 | |
Section 11: Analysis of Variance |
|
F-distributions |
24:46 |
| |
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 |
1:09:25 |
| |
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 |
1:15:13 |
| |
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? |
73:59 | |
Section 12: Chi-square Test |
|
Chi-Square Goodness-of-Fit Test |
58:23 |
| |
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 |
51:36 |
| |
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 | |
Section 13: Overview of Statistics |
|
Overview of Statistics |
18:11 |
| |
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 | |