Courses
Contact
Unlock
Statistics

Statistics for college and university students. Contains descriptive statistics, probability theory, inferential statistics, hypothesis testing, data analysis and more.

Available languages:
Course content
Chapter 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 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
Chapter 2. 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
3
THEORY
T
8.
Strength of a Linear Relationship: Pearson Correlation Coefficient
PRACTICE
P
9.
Strength of a Linear Relationship: Pearson Correlation Coefficient
2
THEORY
T
10.
Hypothesis Test for the Pearson Correlation Coefficient
PRACTICE
P
11.
Hypothesis Test for the Pearson Correlation Coefficient
12
Chapter 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
3
THEORY
T
6.
Events
PRACTICE
P
7.
Events
2
Relationships between Events
THEORY
T
1.
Complement of an Event
PRACTICE
P
2.
Complement of an Event
2
THEORY
T
3.
Mutual Exclusivity
PRACTICE
P
4.
Mutual Exclusivity
2
THEORY
T
5.
Difference
PRACTICE
P
6.
Difference
8
THEORY
T
7.
Intersection
PRACTICE
P
8.
Intersection
5
THEORY
T
9.
Union
PRACTICE
P
10.
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
Chapter 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.
Sum 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
Chapter 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
Chapter 6. Parameter Estimation and Confidence Intervals
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
Chapter 7. Hypothesis Testing
Introduction to Hypothesis Testing (p-value Approach)
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
PRACTICE
P
10.
Computing the Test Statistic
3
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
Introduction to Hypothesis Testing (Critical Region Approach
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.
Determining the Critical Region
PRACTICE
P
6.
Determining the Critical Region
2
THEORY
T
7.
Computing the Test Statistic and Making a Decision
PRACTICE
P
8.
Computing the Test Statistic and Making a Decision
2
THEORY
T
9.
Assumptions of the z-test
PRACTICE
P
10.
Assumptions of the z-test
1
THEORY
T
11.
Connection between Hypothesis Testing and Confidence Intervals
PRACTICE
P
12.
Connection between Hypothesis Testing and Confidence Intervals
5
THEORY
T
13.
Errors in Decision Making
PRACTICE
P
14.
Errors in Decision Making
5
THEORY
T
15.
Statistical Power
PRACTICE
P
16.
Statistical Power
8
THEORY
T
17.
One-tailed Tests
PRACTICE
P
18.
One-tailed Tests
2
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
Chapter 8. Testing for Differences in Mean and Proportion
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
Chapter 9. Regression Analysis
Simple Linear Regression
THEORY
T
1.
Introduction to Regression Analysis
PRACTICE
P
2.
Introduction to Regression Analysis
3
THEORY
T
3.
Residuals and Total Squared Error
PRACTICE
P
4.
Residuals and Total Squared Error
2
THEORY
T
5.
Finding the Regression Equation
PRACTICE
P
6.
Finding the Regression Equation
1
THEORY
T
7.
The Coefficient of Determination
PRACTICE
P
8.
The Coefficient of Determination
1
THEORY
T
9.
Regression Analysis and Causality
PRACTICE
P
10.
Regression Analysis and Causality
2
Multiple Linear Regression
THEORY
T
1.
Multiple Linear Regression
PRACTICE
P
2.
Multiple Linear Regression
1
THEORY
T
3.
Overfitting and Multicollinearity
PRACTICE
P
4.
Overfitting and Multicollinearity
2
THEORY
T
5.
Dummy Variables
PRACTICE
P
6.
Dummy Variables
1
Chapter 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
Chapter 11: Analysis of Variance
One-way Analysis of Variance
THEORY
T
1.
Introduction to Analysis of Variance
PRACTICE
P
2.
Introduction to Analysis of Variance
5
THEORY
T
3.
One-way ANOVA: Hypotheses and Logic
PRACTICE
P
4.
One-way ANOVA: Hypotheses and Logic
8
THEORY
T
5.
One-way ANOVA: Test Statistic
PRACTICE
P
6.
One-way ANOVA: Test Statistic
16
THEORY
T
7.
One-way ANOVA: Model and Assumptions
PRACTICE
P
8.
One-way ANOVA: Model and Assumptions
9
THEORY
T
9.
One-way ANOVA: Post Hoc Tests
PRACTICE
P
10.
One-way ANOVA: Post Hoc Tests
14
THEORY
T
11.
One-way ANOVA: Using R
PRACTICE
P
12.
One-way ANOVA: Using R
14
Unlock full access
Teacher access
Request a demo account. We will help you get started with our digital learning environment.
Student access
Is your university not a partner? Get access to our courses via Pass Your Math independent of your university. See pricing and more.

# Request your teacher demo

First, we need some information to get you started.

Select one or more

* Required