In Educator's General Statistics course, Dr. Ji Son covers information applicable for both high school and college statistics courses. She teaches through a combination of equations, diagrams, and relevant examples. Dr. Son also uses Excel to breakdown the difficult concepts of statistics into understandable and memorable ideas. Topics include everything from Central Tendency and Normal Distribution to Correlation, Probability, and Hypothesis Testing. Dr. Son has a Ph.D. in Psychology and Cognitive Science and is a published researcher on how people learn and apply abstract concepts. Excel files and data used in lessons are downloadable so students can follow along.
| I. Introduction |
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Descriptive Statistics vs. Inferential Statistics |
25:31 |
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Intro |
0:00 | |
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Roadmap |
0:10 | |
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| Roadmap |
0:11 | |
| | |
Statistics |
0:35 | |
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| Statistics |
0:36 | |
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Let's Think About High School Science |
1:12 | |
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| Measurement and Find Patterns (Mathematical Formula) |
1:13 | |
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Statistics = Math of Distributions |
4:58 | |
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| Distributions |
4:59 | |
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| Problematic
but also GREAT |
5:58 | |
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Statistics |
7:33 | |
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| How is It Different from Other Specializations in Mathematics? |
7:34 | |
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| Statistics is Fundamental in Natural and Social Sciences |
7:53 | |
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Two Skills of Statistics |
8:20 | |
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| Description (Exploration) |
8:21 | |
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| Inference |
9:13 | |
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Descriptive Statistics vs. Inferential Statistics: Apply to Distributions |
9:58 | |
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| Descriptive Statistics |
9:59 | |
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| Inferential Statistics |
11:05 | |
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Populations vs. Samples |
12:19 | |
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| Populations vs. Samples: Is it the Truth? |
12:20 | |
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| Populations vs. Samples: Pros & Cons |
13:36 | |
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| Populations vs. Samples: Descriptive Values |
16:12 | |
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Putting Together Descriptive/Inferential Stats & Populations/Samples |
17:10 | |
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| Putting Together Descriptive/Inferential Stats & Populations/Samples |
17:11 | |
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Example 1: Descriptive Statistics vs. Inferential Statistics |
19:09 | |
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Example 2: Descriptive Statistics vs. Inferential Statistics |
20:47 | |
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Example 3: Sample, Parameter, Population, and Statistic |
21:40 | |
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Example 4: Sample, Parameter, Population, and Statistic |
23:28 | |
| II. About Samples: Cases, Variables, Measurements |
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About Samples: Cases, Variables, Measurements |
32:14 |
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Intro |
0:00 | |
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Data |
0:09 | |
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| Data, Cases, Variables, and Values |
0:10 | |
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| Rows, Columns, and Cells |
2:03 | |
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| Example: Aircrafts |
3:52 | |
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How Do We Get Data? |
5:38 | |
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| Research: Question and Hypothesis |
5:39 | |
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| Research Design |
7:11 | |
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| Measurement |
7:29 | |
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| Research Analysis |
8:33 | |
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| Research Conclusion |
9:30 | |
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Types of Variables |
10:03 | |
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| Discrete Variables |
10:04 | |
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| Continuous Variables |
12:07 | |
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Types of Measurements |
14:17 | |
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| Types of Measurements |
14:18 | |
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Types of Measurements (Scales) |
17:22 | |
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| Nominal |
17:23 | |
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| Ordinal |
19:11 | |
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| Interval |
21:33 | |
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| Ratio |
24:24 | |
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Example 1: Cases, Variables, Measurements |
25:20 | |
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Example 2: Which Scale of Measurement is Used? |
26:55 | |
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Example 3: What Kind of a Scale of Measurement is This? |
27:26 | |
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Example 4: Discrete vs. Continuous Variables. |
30:31 | |
| III. Visualizing Distributions |
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Introduction to Excel |
8:09 |
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Intro |
0:00 | |
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Before Visualizing Distribution |
0:10 | |
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| Excel |
0:11 | |
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Excel: Organization |
0:45 | |
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| Workbook |
0:46 | |
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| Column x Rows |
1:50 | |
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| Tools: Menu Bar, Standard Toolbar, and Formula Bar |
3:00 | |
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Excel + Data |
6:07 | |
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| Exce and Data |
6:08 | |
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Frequency Distributions in Excel |
39:10 |
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Intro |
0:00 | |
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Roadmap |
0:08 | |
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| Data in Excel and Frequency Distributions |
0:09 | |
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Raw Data to Frequency Tables |
0:42 | |
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| Raw Data to Frequency Tables |
0:43 | |
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| Frequency Tables: Using Formulas and Pivot Tables |
1:28 | |
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Example 1: Number of Births |
7:17 | |
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Example 2: Age Distribution |
20:41 | |
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Example 3: Height Distribution |
27:45 | |
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Example 4: Height Distribution of Males |
32:19 | |
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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 | |
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| Uniform |
1:36 | |
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Example #2 |
2:58 | |
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| Unimodal, Skewed Right, and Asymmetric |
2:59 | |
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Example #3 |
6:29 | |
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| Bimodal |
6:30 | |
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Example #4a |
8:29 | |
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| Symmetric, Unimodal, and Normal |
8:30 | |
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| Point of Inflection and Standard Deviation |
11:13 | |
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Example #4b |
12:43 | |
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| Normal Distribution |
12:44 | |
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Summary |
13:56 | |
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| Uniform, Skewed, Bimodal, and Normal |
13:57 | |
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Sketch Problem 1: Driver's License |
17:34 | |
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Sketch Problem 2: Life Expectancy |
20:01 | |
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Sketch Problem 3: Telephone Numbers |
22:01 | |
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Sketch Problem 4: Length of Time Used to Complete a Final Exam |
23:43 | |
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Dotplots and Histograms in Excel |
42:42 |
| | |
Intro |
0:00 | |
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Roadmap |
0:06 | |
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| Roadmap |
0:07 | |
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Previously |
1:02 | |
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| Data, Frequency Table, and visualization |
1:03 | |
| | |
Dotplots |
1:22 | |
| | |
| Dotplots Excel Example |
1:23 | |
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Dotplots: Pros and Cons |
7:22 | |
| | |
| Pros and Cons of Dotplots |
7:23 | |
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| Dotplots Excel Example Cont. |
9:07 | |
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Histograms |
12:47 | |
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| Histograms Overview |
12:48 | |
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| Example of Histograms |
15:29 | |
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Histograms: Pros and Cons |
31:39 | |
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| Pros |
31:40 | |
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| Cons |
32:31 | |
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Frequency vs. Relative Frequency |
32:53 | |
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| Frequency |
32:54 | |
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| Relative Frequency |
33:36 | |
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Example 1: Dotplots vs. Histograms |
34:36 | |
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Example 2: Age of Pennies Dotplot |
36:21 | |
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Example 3: Histogram of Mammal Speeds |
38:27 | |
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Example 4: Histogram of Life Expectancy |
40:30 | |
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Stemplots |
12:23 |
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Intro |
0:00 | |
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Roadmap |
0:05 | |
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| Roadmap |
0:06 | |
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What Sets Stemplots Apart? |
0:46 | |
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| Data Sets, Dotplots, Histograms, and Stemplots |
0:47 | |
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Example 1: What Do Stemplots Look Like? |
1:58 | |
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Example 2: Back-to-Back Stemplots |
5:00 | |
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Example 3: Quiz Grade Stemplot |
7:46 | |
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Example 4: Quiz Grade & Afterschool Tutoring Stemplot |
9:56 | |
| |
Bar Graphs |
22:49 |
| | |
Intro |
0:00 | |
| | |
Roadmap |
0:05 | |
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| Roadmap |
0:08 | |
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Review of Frequency Distributions |
0:44 | |
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| Y-axis and X-axis |
0:45 | |
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| Types of Frequency Visualizations Covered so Far |
2:16 | |
| | |
| Introduction to Bar Graphs |
4:07 | |
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Example 1: Bar Graph |
5:32 | |
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| Example 1: Bar Graph |
5:33 | |
| | |
Do Shapes, Center, and Spread of Distributions Apply to Bar Graphs? |
11:07 | |
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| Do Shapes, Center, and Spread of Distributions Apply to Bar Graphs? |
11:08 | |
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Example 2: Create a Frequency Visualization for Gender |
14:02 | |
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Example 3: Cases, Variables, and Frequency Visualization |
16:34 | |
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Example 4: What Kind of Graphs are Shown Below? |
19:29 | |
| IV. Summarizing Distributions |
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Central Tendency: Mean, Median, Mode |
38:50 |
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Intro |
0:00 | |
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Roadmap |
0:07 | |
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| Roadmap |
0:08 | |
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Central Tendency 1 |
0:56 | |
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| Way to Summarize a Distribution of Scores |
0:57 | |
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| Mode |
1:32 | |
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| Median |
2:02 | |
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| Mean |
2:36 | |
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Central Tendency 2 |
3:47 | |
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| Mode |
3:48 | |
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| Median |
4:20 | |
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| Mean |
5:25 | |
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Summation Symbol |
6:11 | |
| | |
| Summation Symbol |
6:12 | |
| | |
Population vs. Sample |
10:46 | |
| | |
| Population vs. Sample |
10:47 | |
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Excel Examples |
15:08 | |
| | |
| Finding Mode, Median, and Mean in Excel |
15:09 | |
| | |
Median vs. Mean |
21:45 | |
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| Effect of Outliers |
21:46 | |
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| Relationship Between Parameter and Statistic |
22:44 | |
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| Type of Measurements |
24:00 | |
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| Which Distributions to Use With |
24:55 | |
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Example 1: Mean |
25:30 | |
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Example 2: Using Summation Symbol |
29:50 | |
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Example 3: Average Calorie Count |
32:50 | |
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Example 4: Creating an Example Set |
35:46 | |
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Variability |
42:40 |
| | |
Intro |
0:00 | |
| | |
Roadmap |
0:05 | |
| | |
| Roadmap |
0:06 | |
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Variability (or Spread) |
0:45 | |
| | |
| Variability (or Spread) |
0:46 | |
| | |
Things to Think About |
5:45 | |
| | |
| Things to Think About |
5:46 | |
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Range, Quartiles and Interquartile Range |
6:37 | |
| | |
| Range |
6:38 | |
| | |
| Interquartile Range |
8:42 | |
| | |
Interquartile Range Example |
10:58 | |
| | |
| Interquartile Range Example |
10:59 | |
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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 | |
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Population vs. Sample |
23:20 | |
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| Mean |
23:21 | |
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| SD |
23:51 | |
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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 | |
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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 | |
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Summarizing Distributions |
0:37 | |
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| Shape, Center, and Spread |
0:38 | |
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| 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 | |
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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 | |
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| 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 | |
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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 | |
| V. 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 | |
| VI. 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 | |
| VII. 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 | |
| VIII. 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 | |
| IX. 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 |
68:48 |
| | |
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 | |
| X. 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 |
62:06 |
| | |
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 |
66:33 |
| | |
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 |
74:11 |
| | |
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 |
70:1 | |
| | |
| 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 | |
| XI. 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 |
69:25 |
| | |
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 |
75:13 |
| | |
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 | |
| XII. 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 | |
| XIII. 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 | |