  General Statistics
Open course on descriptive and inferential statistics with theory and interactive exercises.
Offered by the Teaching and Learning Centre of FNWI.
Available languages: Course content
0. The Basics of R
Starting-up
THEORY
T
1.
Introduction
THEORY
T
2.
Setting-up online access
THEORY
T
3.
THEORY
T
4.
THEORY
T
5.
Getting Help
Using R
THEORY
T
1.
Making calculations
THEORY
T
2.
Working with vectors
THEORY
T
3.
Working with data frames
Practical 0
THEORY
T
1.
Introducing the gapminder data set
THEORY
T
2.
Exploring the data
THEORY
T
3.
Selecting subsets
PRACTICE
P
4.
Exploring the gapminder data
9
1. Descriptive Statistics
Types of Data and Measurement
THEORY
T
1.
Qualitative and Quantitative Variables
PRACTICE
P
2.
Qualitative and Quantitative Variables
9
THEORY
T
3.
The Hierarchy of Measurement Scales
PRACTICE
P
4.
The Hierarchy of Measurement Scales
2
THEORY
T
5.
Nominal Scale
PRACTICE
P
6.
Nominal Scale
5
THEORY
T
7.
Ordinal Scale
PRACTICE
P
8.
Ordinal Scale
5
THEORY
T
9.
Interval Scale
PRACTICE
P
10.
Interval Scale
5
THEORY
T
11.
Ratio Scale
PRACTICE
P
12.
Ratio Scale
5
Frequency Distributions
THEORY
T
1.
Frequency Distributions
THEORY
T
2.
Frequency Distribution Tables
PRACTICE
P
3.
Frequency Distribution Tables
3
THEORY
T
4.
Frequency Distribution Graphs
PRACTICE
P
5.
Frequency Distribution Graphs
7
THEORY
T
6.
Shape of a Distribution
PRACTICE
P
7.
Shape of a Distribution
8
THEORY
T
8.
Measures of Location I: Quantiles
PRACTICE
P
9.
Measures of Location I: Quantiles
6
Measures of Central Tendency
THEORY
T
1.
Introduction to Central Tendency
THEORY
T
2.
Mode
PRACTICE
P
3.
Mode
6
THEORY
T
4.
Median
PRACTICE
P
5.
Median
6
THEORY
T
6.
Mean
PRACTICE
P
7.
Mean
9
THEORY
T
8.
Central Tendency and the Shape of a Distribution
PRACTICE
P
9.
Central Tendency and the Shape of a Distribution
2
THEORY
T
10.
Sensitivity to Outliers
PRACTICE
P
11.
Sensitivity to Outliers
1
Measures of Variability
THEORY
T
1.
Range, Interquartile Range, and the Five-Number Summary
PRACTICE
P
2.
Range, Interquartile Range, and the Five-Number Summary
5
THEORY
T
3.
Interquartile Range Rule for Identifying Outliers
PRACTICE
P
4.
Interquartile Range Rule for Identifying Outliers
2
THEORY
T
5.
Deviation from the Mean and the Sum of Squares
PRACTICE
P
6.
Deviation from the Mean and the Sum of Squares
5
THEORY
T
7.
Variance and Standard Deviation
PRACTICE
P
8.
Variance and Standard Deviation
6
Measures of Location II: Z-scores
THEORY
T
1.
Z-scores
PRACTICE
P
2.
Z-scores
14
Practical 1
THEORY
T
1.
Introduction
THEORY
T
2.
Measures of Central Tendency
PRACTICE
P
3.
Measures of Central Tendency
6
THEORY
T
4.
PRACTICE
P
5.
2
THEORY
T
6.
Keypoints
2. Association and Correlation
Correlation
THEORY
T
1.
Introduction to Correlation
THEORY
T
2.
Displaying the Relationship Between Two Variables
PRACTICE
P
3.
Displaying the Relationship Between Two Variables
3
THEORY
T
4.
Measuring the Relationship Between Two Variables
PRACTICE
P
5.
Measuring the Relationship Between Two Variables
7
THEORY
T
6.
Direction of a Linear Relationship: Covariance
PRACTICE
P
7.
Direction of a Linear Relationship: Covariance
2
THEORY
T
8.
Strength of a Linear Relationship: Pearson Correlation Coefficient
PRACTICE
P
9.
Strength of a Linear Relationship: Pearson Correlation Coefficient
3
THEORY
T
10.
Monotonic Relationship: Spearman Correlation Coefficient
PRACTICE
P
11.
Monotonic Relationship: Spearman Correlation Coefficient
3
Practical 2
THEORY
T
1.
Introduction
PRACTICE
P
2.
Data Exploration
5
THEORY
T
3.
Visualising the Relationship Between Two Variables
PRACTICE
P
4.
Visualising the Relationship Between Two Variables
1
THEORY
T
5.
Pearson Correlcation Coefficient
PRACTICE
P
6.
Pearson Correlation Coefficient
9
THEORY
T
7.
Spearman Correlation Coefficient
PRACTICE
P
8.
Spearman Correlation Coefficient
6
3. Probability
Randomness
THEORY
T
1.
Sets, Subsets and Elements
PRACTICE
P
2.
Sets, Subsets and Elements
3
THEORY
T
3.
Random Experiments
THEORY
T
4.
Sample Space
PRACTICE
P
5.
Sample Space
5
THEORY
T
6.
Events
PRACTICE
P
7.
Events
2
THEORY
T
8.
Complement of an Event
PRACTICE
P
9.
Complement of an Event
2
Relationship between Events
THEORY
T
1.
Mutual Exclusivity
PRACTICE
P
2.
Mutual Exclusivity
2
THEORY
T
3.
Difference
PRACTICE
P
4.
Difference
8
THEORY
T
5.
Intersection
PRACTICE
P
6.
Intersection
5
THEORY
T
7.
Union
PRACTICE
P
8.
Union
1
Probability
THEORY
T
1.
Definition of Probability
PRACTICE
P
2.
Definition of Probability
5
THEORY
T
3.
Probability of the Complement
PRACTICE
P
4.
Probability of the Complement
4
THEORY
T
5.
Conditional Probability
PRACTICE
P
6.
Conditional Probability
2
THEORY
T
7.
Independence
PRACTICE
P
8.
Independence
4
THEORY
T
9.
Probability of the Intersection
PRACTICE
P
10.
Probability of the Intersection
2
THEORY
T
11.
Probability of the Union
PRACTICE
P
12.
Probability of the Union
5
THEORY
T
13.
Probability of the Difference
PRACTICE
P
14.
Probability of the Difference
2
THEORY
T
15.
Law of Total Probability
PRACTICE
P
16.
Law of Total Probability
1
THEORY
T
17.
Bayes' Theorem
PRACTICE
P
18.
Bayes' Theorem
3
Contingency Tables
THEORY
T
1.
Interpreting Contingency Tables
PRACTICE
P
2.
Interpreting Contingency Tables
7
Practical 3
THEORY
T
1.
Introduction
PRACTICE
P
2.
Data Exploration
3
THEORY
T
3.
Contingency Tables
PRACTICE
P
4.
Calculate Probabilities
7
THEORY
T
5.
Extention on Contingency Tables
PRACTICE
P
6.
Contingency Tables With 3 Variables
2
THEORY
T
7.
Probability Rules
PRACTICE
P
8.
Probability Rules
7
THEORY
T
9.
Keypoints
4. Probability Distributions
Probability Models
THEORY
T
1.
Discrete Probability Models
PRACTICE
P
2.
Discrete Probability Models
2
THEORY
T
3.
Continuous Probability Models
PRACTICE
P
4.
Continuous Probability Models
2
Random Variables
THEORY
T
1.
Random Variables
PRACTICE
P
2.
Random Variables
6
THEORY
T
3.
Probability Distributions
PRACTICE
P
4.
Probability Distributions
2
THEORY
T
5.
Expected Value of a Random Variable
PRACTICE
P
6.
Expected Value of a Random Variable
3
THEORY
T
7.
Variance of a Random Variable
PRACTICE
P
8.
Variance of a Random Variable
5
THEORY
T
9.
Sums of Random Variables
PRACTICE
P
10.
Sums of Random Variables
6
Common Distributions
THEORY
T
1.
The Binomial Distribution
PRACTICE
P
2.
The Binomial Distribution
14
THEORY
T
3.
Expected Value and Variance of a Binomial Random Variable
PRACTICE
P
4.
Expected Value and Variance of a Binomial Random Variable
3
THEORY
T
5.
The Normal Distribution
PRACTICE
P
6.
The Normal Distribution
6
THEORY
T
7.
The Normal Probability Distribution
PRACTICE
P
8.
The Normal Probability Distribution
13
Practical 4
THEORY
T
1.
Introduction
THEORY
T
2.
Normal random variables
PRACTICE
P
3.
The Normal Distribution
13
THEORY
T
4.
Binomial random variables
PRACTICE
P
5.
The Binomial Distribution
4
THEORY
T
6.
Random variables
PRACTICE
P
7.
Random variables
2
THEORY
T
8.
Combinations of random variables
PRACTICE
P
9.
Combinations of random variables
3
THEORY
T
10.
Keypoints
5. Sampling
Sampling and Sampling Methods
THEORY
T
1.
Sampling and Unbiased Sampling Methods
PRACTICE
P
2.
Sampling and Unbiased Sampling Methods
2
THEORY
T
3.
Biased Sampling Methods
PRACTICE
P
4.
Sampling Methods
6
Sampling Distributions
THEORY
T
1.
Sampling Distributions
PRACTICE
P
2.
Sampling Distributions
3
THEORY
T
3.
Sampling Distribution of the Sample Mean
PRACTICE
P
4.
Sampling Distribution of the Sample Mean
17
THEORY
T
5.
Sampling Distribution of the Sample Proportion
PRACTICE
P
6.
Sampling Distribution of the Sample Proportion
8
Practical 5a
THEORY
T
1.
Introduction
PRACTICE
P
2.
Data Exploration
6
THEORY
T
3.
Simple Random Sampling
PRACTICE
P
4.
Simple Random Sampling
2
THEORY
T
5.
Stratified Sampling
PRACTICE
P
6.
Stratified Sampling
4
THEORY
T
7.
Cluster Sampling
PRACTICE
P
8.
Cluster Sampling
3
THEORY
T
9.
Keypoints
Practical 5b
THEORY
T
1.
Introduction
PRACTICE
P
2.
Data Exploration
2
THEORY
T
3.
Construct the Sampling Distribution of any Statistic
PRACTICE
P
4.
Sampling Distribution
4
THEORY
T
5.
Central Limit Theorem
THEORY
T
6.
Keypoints
6. Parameter Estimation and Confidence Intervals
Estimation
THEORY
T
1.
Parameter Estimation
PRACTICE
P
2.
Parameter Estimation
3
THEORY
T
3.
Constructing a 95% Confidence Interval for the Population Mean
PRACTICE
P
4.
Constructing a 95% Confidence Interval for the Population Mean
5
THEORY
T
5.
Confidence Interval for the Population Mean
PRACTICE
P
6.
Confidence Interval for the Population Mean
13
THEORY
T
7.
Confidence Interval for the Population Proportion
PRACTICE
P
8.
Confidence Interval for the Population Proportion
10
Practical 6
THEORY
T
1.
Introduction
THEORY
T
2.
Recap: Sample Versus Population
THEORY
T
3.
Sample Mean and Confidence Interval
PRACTICE
P
4.
Confidence Interval
5
THEORY
T
5.
Multiple Samples
PRACTICE
P
6.
Multiple samples
2
THEORY
T
7.
Varying the Confidence Level
PRACTICE
P
8.
Varying the Confidence Level
3
THEORY
T
9.
Confidence Intervals for Proportions
PRACTICE
P
10.
Confidence intervals for proportions
3
THEORY
T
11.
Keypoints
7. Hypothesis Testing
Introduction to Hypothesis Testing
THEORY
T
1.
Hypothesis Testing Procedure
PRACTICE
P
2.
Hypothesis Testing Procedure
1
THEORY
T
3.
Formulating the Research Hypotheses
PRACTICE
P
4.
Formulating the Research Hypotheses
4
THEORY
T
5.
Two-tailed vs. One-tailed Testing
PRACTICE
P
6.
Two-tailed vs. One-tailed Testing
7
THEORY
T
7.
Setting the Criteria for a Decision
PRACTICE
P
8.
Setting the Criteria for a Decision
2
THEORY
T
9.
Computing the Test Statistic and Making a Decision
PRACTICE
P
10.
Computing the Test Statistic and Making a Decision
4
THEORY
T
11.
Computing the p-value and Making a Decision
PRACTICE
P
12.
Computing the p-value and Making a Decision
12
THEORY
T
13.
Assumptions of the z-test
PRACTICE
P
14.
Assumptions of the z-test
1
THEORY
T
15.
Connection Between Hypothesis Testing and Confidence Intervals
PRACTICE
P
16.
Connection Between Hypothesis Testing and Confidence Intervals
5
THEORY
T
17.
Errors in Decision Making
PRACTICE
P
18.
Errors in Decision Making
5
THEORY
T
19.
Statistical Power
PRACTICE
P
20.
Statistical Power
9
Hypothesis Test for a Population Proportion
THEORY
T
1.
Hypotheses of a Population Proportion Test
PRACTICE
P
2.
Hypotheses of a Population Proportion Test
4
THEORY
T
3.
Large-sample Proportion Test: Test Statistic and p-value
PRACTICE
P
4.
Large-sample Proportion Test: Test Statistic and p-value
6
THEORY
T
5.
Small-sample Proportion Test: Test Statistic and p-value
PRACTICE
P
6.
Small-sample Proportion Test: Test Statistic and p-value
6
THEORY
T
7.
Hypothesis Test for a Proportion and Confidence Intervals
PRACTICE
P
8.
Hypothesis Test for a Proportion and Confidence Intervals
4
One-sample t-test
THEORY
T
1.
One-sample t-test: Purpose, Hypotheses, and Assumptions
PRACTICE
P
2.
One-sample t-test: Purpose, Hypotheses, and Assumptions
5
THEORY
T
3.
One-sample t-test: Test Statistic and p-value
PRACTICE
P
4.
One-sample t-test: Test Statistic and p-value
6
THEORY
T
5.
Confidence Interval for μ when σ is Unknown
PRACTICE
P
6.
Confidence Interval for μ when σ is Unknown
6
Practical 7
THEORY
T
1.
Introduction to Hypothesis Testing
PRACTICE
P
2.
Introduction to Hypothesis Testing
3
THEORY
T
3.
Introduction to Air Quality Case Study
PRACTICE
P
4.
Data Exploration
4
THEORY
T
5.
One-sample t-test
PRACTICE
P
6.
Hypothesis Testing on Means
3
THEORY
T
7.
Testing for Differences Between Proportions
PRACTICE
P
8.
Hypothesis Testing on Proportions
3
THEORY
T
9.
Keypoints
8. Testing for Differences in Means and Proportions
Paired Samples t-test
THEORY
T
1.
Paired Samples t-test: Purpose, Hypotheses, and Assumptions
PRACTICE
P
2.
Paired Samples t-test: Purpose, Hypotheses, and Assumptions
4
THEORY
T
3.
Paired Samples t-test: Test Statistic and p-value
PRACTICE
P
4.
Paired Samples t-test: Test Statistic and p-value
9
THEORY
T
5.
Confidence Interval for a Mean Difference
PRACTICE
P
6.
Confidence Interval for a Mean Difference
6
Independent Samples t-test
THEORY
T
1.
Independent Samples t-test: Purpose, Hypotheses, and Assumptions
PRACTICE
P
2.
Independent Samples t-test: Purpose, Hypotheses, and Assumptions
4
THEORY
T
3.
Independent Samples t-test: Test Statistic and p-value
PRACTICE
P
4.
Independent Samples t-test: Test Statistic and p-value
9
THEORY
T
5.
Confidence Interval for the Difference Between Two Independent Means
PRACTICE
P
6.
Confidence Interval for the Difference Between Two Independent Means
6
Independent Proportions Z-test
THEORY
T
1.
Independent Proportions Z-test: Purpose, Hypotheses, and Assumptions
PRACTICE
P
2.
Independent Proportions Z-test: Purpose, Hypotheses, and Assumptions
4
THEORY
T
3.
Independent Proportions Z-test: Test Statistic and p-value
PRACTICE
P
4.
Independent Proportions Z-test: Test Statistic and p-value
9
THEORY
T
5.
Confidence Interval for the Difference Between Two Independent Proportions
PRACTICE
P
6.
Confidence Interval for the Difference Between Two Independent Proportions
2
Practical 8
THEORY
T
1.
Introduction
THEORY
T
2.
Testing for Differences Between Means
PRACTICE
P
3.
Two-sample t-test
6
THEORY
T
4.
Testing for Differences Between Proportions
PRACTICE
P
5.
Two-sample proportions test
6
THEORY
T
6.
Keypoints
9. Simple Linear Regression
Simple Linear Regression
THEORY
T
1.
Introduction to Regression
THEORY
T
2.
Simple Linear Regression
PRACTICE
P
3.
Simple Linear Regression
3
THEORY
T
4.
Finding the Regression Equation
PRACTICE
P
5.
Finding the Regression Equation
3
THEORY
T
6.
Residuals
PRACTICE
P
7.
Residuals
2
THEORY
T
8.
Assessing the Quality of a Regression Model
PRACTICE
P
9.
Assessing the Quality of a Regression Model
6
THEORY
T
10.
Statistical Inference in Regression
PRACTICE
P
11.
Statistical Inference in Regression
3
THEORY
T
12.
Inference about the Slope of a Linear Model
PRACTICE
P
13.
Inference about the Slope of a Linear Model
5
Practical 9
THEORY
T
1.
Introduction
PRACTICE
P
2.
Data Exploration - Quality of Life
4
THEORY
T
3.
Sum of Squared Residuals
PRACTICE
P
4.
Sum of Squared Residuals
2
THEORY
T
5.
Regression Line
PRACTICE
P
6.
Simple Linear Regression
5
THEORY
T
7.
Prediction and Prediction Errors
PRACTICE
P
8.
Prediction
1
THEORY
T
9.
Model Reliability and Validity of the Inference
PRACTICE
P
10.
Practice
7
THEORY
T
11.
Keypoints
10. Categorical Association
Chi-Square Goodness of Fit Test
THEORY
T
1.
Chi-Square Goodness of Fit Test: Purpose, Hypotheses, and Assumptions
PRACTICE
P
2.
Chi-Square Goodness of Fit Test: Purpose, Hypotheses, and Assumptions
3
THEORY
T
3.
Chi-Square Goodness of Fit Test: Test Statistic and p-value
PRACTICE
P
4.
Chi-Square Goodness of Fit Test: Test Statistic and p-value
15
Chi-Square Test for Independence
THEORY
T
1.
Chi-Square Test for Independence: Purpose, Hypotheses, and Assumptions
PRACTICE
P
2.
Chi-Square Test for Independence: Purpose, Hypotheses, and Assumptions
2
THEORY
T
3.
Chi-Square Test for Independence: Test Statistic and p-value
PRACTICE
P
4.
Chi-Square Test for Independence: Test Statistic and p-value
12
Practical 10
THEORY
T
1.
Introduction to Cross Tables and Categorical Association
PRACTICE
P
2.
Data Exploration - Water Use
2
THEORY
T
3.
Cross Tables
PRACTICE
P
4.
Cross Tables
2
THEORY
T
5.
Chi-square Goodness of Fit Test
PRACTICE
P
6.
Chi-square Goodness of Fit Test
7
THEORY
T
7.
The Goodness of Fit Test on Repeat
PRACTICE
P
8.
Chi-square Goodness of Fit Test
1
THEORY
T
9.
Chi-square Test for Association
PRACTICE
P
10.
Chi-square Test for Association
6
THEORY
T
11.
Keypoints
Formulas, Statistical Tables and R Commands
Formulas
THEORY
T
1.
Formulas descriptive statistics
THEORY
T
2.
Formulas random variables
THEORY
T
3.
Formulas probability
THEORY
T
4.
Formulas regression
THEORY
T
5.
Formulas binomial distribution
THEORY
T
6.
Formulas normal distribution - z- and t-tests
THEORY
T
7.
Formulas analysis of variance (ANOVA)
THEORY
T
8.
Formulas cross tables
THEORY
T
9.
Formulas non-parametric tests
THEORY
T
10.
Formulas choosing tests
Statistical Tables
THEORY
T
1.
Table 1: Critical values z-distribution
THEORY
T
2.
Table 2: Critical values Student t-distribution
THEORY
T
3.
Table 3: Critical values chi-squared-distribution
THEORY
T
4.
Table 4: Critical values F-distribution
R commands
THEORY
T
1.
Overview of R commands
VVA Formula sheet
THEORY
T
1.
VVA Formula sheet I (Descriptive Statistics)
THEORY
T
2.
VVA Formula sheet II (Probability)
THEORY
T
3.
VVA Formula sheet III (Random Variables)
THEORY
T
4.
VVA Formula sheet IV (Probability and Sampling Distributions)
THEORY
T
5.
VVA Formula sheet V (Hypothesis Testing and Confidence Intervals)
THEORY
T
6.
VVA Formula sheet VI (Regression)
THEORY
T
7.
VVA overview R Commands