Readings for MTH107
Preface
1
Why Statistics is Important
1.1
Introductory Example
1.2
Major Goals of Statistics
1.3
Why Does Statistics (as a tool) Exist?
1.4
Definition of Statistics
2
Foundational Definitions
2.1
Definitions
2.2
Performing an IVPPSS
2.3
Variable Types
3
Data Production
3.1
Experiments
3.2
Observational Studies – Sampling
4
Univariate Summaries
4.1
Quantitative Variable
4.2
Categorical Variable
5
Univariate EDA
5.1
Quantitative Variable
5.2
Categorical Variable
6
Normal Distribution Introduction
6.1
Characteristics of a Normal Distribution
6.2
Area Under the Curve
6.3
68-95-99.7 (or Empirical) Rule
6.4
Example Calculations
6.5
Distinguish Calculation Types
7
Normal Distribution Calculations
7.1
Forward Calculations
7.2
Reverse Calculations
7.3
Example Calculations
7.4
Standardization and Z-Scores
8
Bivariate EDA - Quantitative
8.1
Response and Explanatory Variables
8.2
Summaries
8.3
Bivariate Items to Describe
8.4
Example Interpretations
8.5
Cautions About Correlation
9
Linear Regression
9.1
Response and Explanatory Variables
9.2
Slope and Intercept
9.3
Predictions
9.4
Residuals
9.5
Best-fit Criteria
9.6
Assumptions
9.7
Coefficient of Determination
9.8
Examples
10
Bivariate EDA - Categorical
10.1
Frequency Tables
10.2
Percentage Tables
10.3
Which Table to Use?
10.4
Example Calculations
10.5
Making an Overall Summary
11
Sampling Distributions
11.1
What is a Sampling Distribution?
11.2
Central Limit Theorem
11.3
Accuracy and Precision
12
Probability Introduction
12.1
Probability of Individuals
12.2
Probability of Statistics
12.3
A Process for Handling Probability Questions
12.4
Example Questions
13
Hypothesis Testing - Introduction
13.1
Hypothesis Testing & The Scientific Method
13.2
Statistical Hypotheses
13.3
Example p-value Calculations
13.4
Hypothesis Testing Concept Summary
14
Hypothesis Testing - Errors
14.1
Error Types
14.2
Error Rates
14.3
Test Statistics and Effect Sizes
15
Confidence Regions - Introduction
15.1
Confidence Concept
15.2
Constructing Confidence Regions
15.3
Example Confidence Region Calculations
16
Confidence Regions - Extension
16.1
Confidence Intervals and Precision
16.2
Sample Size Calculations
16.3
Inference Type Relationship
17
1-Sample Z-Test
17.1
11-Steps of Hypothesis Testing
17.2
1-Sample Z-Test Specifics
17.3
Examples
18
1-Sample t-Test
18.1
t-distribution
18.2
1-Sample t-Test Specifics
18.3
Examples
19
2-Sample t-Test
19.1
2-Sample t-Test Specifics
19.2
Testing for Equal Variances
19.3
Examples
20
Chi-Square Test
20.1
Chi-Square Distribution
20.2
Chi-Square Test Specifics
20.3
Examples
21
Goodness-of-Fit Test
21.1
Goodness-of-Fit Test Specifics
21.2
Examples
22
Getting Data into R
22.1
R Notebooks
22.2
Data in R
22.3
Viewing a Data Frame
22.4
Vectors
23
Filtering Data in R
23.1
Filtering a data frame
23.2
Selecting Entire Variables
23.3
Selecting Individuals
24
Univariate EDA in R
24.1
Quantitative
24.2
Quantitative for Multiple Groups
24.3
Categorical Data
25
Bivariate EDA in R
25.1
Quantitative
25.2
Categorical
26
Linear Regression in R
26.1
Fitted Line Plot
26.2
Fitting the Regression Model in R
26.3
Coefficient of Determination
26.4
Predicted Values
27
t-Tests in R
27.1
1-Sample t-Test
27.2
2-Sample t-Test
28
Chi-Square in R
28.1
Chi-Square Tests
28.2
Goodness-of-Fit Test in R
References
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Readings for MTH107
References