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sowiso logo Basic Statistics

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

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Course content
Chapter 1. Descriptive Statistics
Types of Data and Measurements
THEORY
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1.
Qualitative and Quantitative Variables
PRACTICE
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2.
Qualitative and Quantitative Variables
9
THEORY
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3.
The Hierarchy of Measurement Scales
PRACTICE
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4.
The Hierarchy of Measurement Scales
2
THEORY
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5.
Nominal Scale
PRACTICE
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6.
Nominal Scale
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THEORY
T
7.
Ordinal Scale
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8.
Ordinal scale
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THEORY
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9.
Interval Scale
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10.
Interval scale
5
THEORY
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11.
Ratio Scale
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12.
Ratio Scale
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Frequency Distributions
THEORY
T
1.
Frequency Distributions
THEORY
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2.
Frequency Distribution Tables
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3.
Frequency Distribution Tables
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THEORY
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4.
Frequency Distribution Graphs
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5.
Frequency Distribution Graphs
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THEORY
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6.
Shape of a Distribution
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7.
Shape of a Distribution
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THEORY
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8.
Measures of Location I: Quantiles
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9.
Measures of Location I: Quantiles
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Measures of Central Tendency
THEORY
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1.
Introduction to Central Tendency
THEORY
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2.
Mode
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3.
Mode
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THEORY
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4.
Median
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5.
Median
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6.
Mean
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7.
Mean
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8.
Central Tendency and the Shape of a Distribution
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9.
Central Tendency and the Shape of a Distribution
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THEORY
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10.
Sensitivity to Outliers
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PRACTICE
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11.
Sensitivity to Outliers
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Measures of Variability
THEORY
T
1.
Range, Interquartile Range, and the Five-Number Summary
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2.
Range, Interquartile Range, and the Five-Number Summary
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3.
Interquartile Range Rule for Identifying Outliers
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4.
Interquartile Range Rule for Identifying Outliers
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THEORY
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5.
Deviation from the Mean and the Sum of Squares
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6.
Deviation from the Mean and Sum of Squares
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THEORY
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7.
Variance and Standard Deviation
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8.
Variance and Standard Deviation
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Measures of Location II: z-Scores
THEORY
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1.
Z-scores
PRACTICE
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2.
Z-scores
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Chapter 2. Correlation
THEORY
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1.
Introduction to Correlation
THEORY
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2.
Displaying the Relationship Between Two Variables
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3.
Displaying the Relationship Between Two Variables
3
THEORY
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4.
Measuring the Relationship Between Two Variables
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5.
Measuring the Relationship Between Two Variables
7
THEORY
T
6.
Direction of a Linear Relationship: Covariance
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7.
Direction of a Linear Relationship: Covariance
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THEORY
T
8.
Strength of a Linear Relationship: Pearson Correlation Coefficient
PRACTICE
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9.
Strength of a Linear Relationship: Pearson Correlation Coefficient
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THEORY
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10.
Hypothesis Test for the Pearson Correlation Coefficient
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PRACTICE
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11.
Hypothesis Test for the Pearson Correlation Coefficient
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Chapter 3. Probability
Randomness
THEORY
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1.
Sets, Subsets and Elements
PRACTICE
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2.
Sets, Subsets and Elements
3
THEORY
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3.
Random experiments
THEORY
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4.
Sample space
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5.
Sample space
3
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6.
Events
PRACTICE
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7.
Events
4
Relationships between Events
THEORY
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1.
Complement of an Event
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2.
Complement of an Event
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3.
Mutual Exclusivity
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4.
Mutual Exclusivity
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5.
Difference
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6.
Difference
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7.
Intersection
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8.
Intersection
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9.
Union
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10.
Union
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Probability
THEORY
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1.
Definition of Probability
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2.
Definition of Probability
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THEORY
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3.
Probability of the Complement
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4.
Probability of the Complement
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THEORY
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5.
Conditional Probability
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6.
Conditional Probability
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7.
Independence
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8.
Independence
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9.
Probability of the Intersection
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10.
Probability of the Intersection
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11.
Probability of the Union
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12.
Probability of the Union
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13.
Probability of the Difference
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14.
Probability of the Difference
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15.
Law of Total Probability
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16.
Law of Total Probability
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THEORY
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17.
Bayes' Theorem
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PRACTICE
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18.
Bayes' Theorem
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Contingency Tables
THEORY
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1.
Interpreting Contingency Tables
PRACTICE
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2.
Interpreting Contingency Tables
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Chapter 4. Probability Distributions
Probability Models
THEORY
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1.
Discrete Probability Models
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2.
Discrete Probability Models
2
THEORY
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3.
Continuous Probability Models
PRACTICE
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4.
Continuous Probability Models
2
Random Variables
THEORY
T
1.
Random Variables
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2.
Random Variables
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THEORY
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3.
Probability Distributions
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4.
Probability Distributions
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THEORY
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5.
Expected Value of a Random Variable
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6.
Expected Value of a Random Variable
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7.
Variance of a Random Variable
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8.
Variance of a Random Variable
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9.
Sums of Random Variables
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10.
Sum of Random Variables
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Discrete Probability Distributions
THEORY
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1.
The Bernoulli Probability Distribution
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2.
The Bernoulli Probability Distribution
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3.
The Binomial Probability Distribution
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4.
The Binomial Probability Distribution
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5.
The Geometric Probability Distribution
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6.
The Geometric Probability Distribution
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7.
The Poisson Probability Distribution
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8.
The Poisson Probability Distribution
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Continuous Probability Distributions
THEORY
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1.
The Normal Distribution
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2.
The Normal Distribution
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3.
The Normal Probability Distribution
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4.
The Normal Probability Distribution
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Chapter 5. Sampling
Sampling and Sampling Methods
THEORY
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1.
Sampling and Unbiased Sampling Methods
PRACTICE
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2.
Sampling and Unbiased Sampling Methods
2
THEORY
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3.
Biased Sampling Methods
PRACTICE
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4.
Sampling Methods
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Sampling Distributions
THEORY
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1.
Sampling Distributions
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2.
Sampling Distributions
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3.
Sampling Distribution of the Sample Mean
PRACTICE
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4.
Sampling Distribution of the Sample Mean
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5.
Sampling Distribution of the Sample Proportion
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6.
Sampling Distribution of the Sample Proportion
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Chapter 6. Parameter Estimation and Confidence Intervals
THEORY
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1.
Parameter Estimation
PRACTICE
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2.
Parameter Estimation
3
THEORY
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3.
Constructing a 95% Confidence Interval for the Population Mean
PRACTICE
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4.
Constructing a 95% Confidence Interval for the Population Mean
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THEORY
T
5.
Confidence Interval for the Population Mean
PRACTICE
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6.
Confidence Interval for the Population Mean
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7.
Confidence Interval for the Population Proportion
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PRACTICE
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8.
Confidence Interval for the Population Proportion
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Chapter 7. Hypothesis Testing
Introduction to Hypothesis Testing (p-value Approach)
THEORY
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1.
Hypothesis Testing Procedure
PRACTICE
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2.
Hypothesis Testing Procedure
1
THEORY
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3.
Formulating the Research Hypotheses
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4.
Formulating the Research Hypotheses
4
THEORY
T
5.
Two-tailed vs. One-tailed Testing
PRACTICE
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6.
Two-tailed vs. One-tailed Testing
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THEORY
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7.
Setting the Criteria for a Decision
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8.
Setting the Criteria for a Decision
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9.
Computing the Test Statistic
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10.
Computing the Test Statistic
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11.
Computing the p-value and Making a Decision
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12.
Computing the p-value and Making a Decision
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T
13.
Assumptions of the Z-test
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14.
Assumptions of the Z-test
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15.
Connection between Hypothesis Testing and Confidence Intervals
PRACTICE
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16.
Connection between Hypothesis Testing and Confidence Intervals
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THEORY
T
17.
Errors in Decision Making
PRACTICE
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18.
Errors in Decision Making
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THEORY
T
19.
Statistical Power
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20.
Statistical Power
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Introduction to Hypothesis Testing (Critical Region Approach
THEORY
T
1.
Hypothesis Testing Procedure
PRACTICE
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2.
Hypothesis Testing Procedure
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THEORY
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3.
Formulating the Research Hypotheses
PRACTICE
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4.
Formulating the Research Hypotheses
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5.
Determining the Critical Region
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6.
Determining the Critical Region
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7.
Computing the Test Statistic and Making a Decision
PRACTICE
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8.
Computing the Test Statistic and Making a Decision
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T
9.
Assumptions of the z-test
PRACTICE
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10.
Assumptions of the z-test
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11.
Connection between Hypothesis Testing and Confidence Intervals
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12.
Connection between Hypothesis Testing and Confidence Intervals
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13.
Errors in Decision Making
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14.
Errors in Decision Making
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15.
Statistical Power
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16.
Statistical Power
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17.
One-tailed Tests
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18.
One-tailed Tests
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Hypothesis Test for a Population Proportion
THEORY
T
1.
Hypotheses of a Population Proportion Test
PRACTICE
P
2.
Hypotheses of a Population Proportion Test
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3.
Large-sample Proportion Test: Test Statistic and p-value
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4.
Large-sample Proportion Test: Test Statistic and p-value
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5.
Small-sample Proportion Test: Test Statistic and p-value
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6.
Small-sample Proportion Test: Test Statistic and p-value
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7.
Hypothesis Test for a Proportion and Confidence Intervals
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8.
Hypothesis Test for a Proportion and Confidence Intervals
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One-sample t-test
THEORY
T
1.
One-sample t-test: Purpose, Hypotheses, and Assumptions
PRACTICE
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2.
One-sample t-test: Purpose, Hypotheses, and Assumptions
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3.
One-sample t-test: Test Statistic and p-value
PRACTICE
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4.
One-sample t-test: Test Statistic and p-value
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5.
Confidence Interval for μ when σ is Unknown
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6.
Confidence Interval for μ when σ is Unknown
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Chapter 8. Testing for Differences in Mean and Proportion
Paired Samples t-test
THEORY
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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
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THEORY
T
5.
Confidence Interval for a Mean Difference
PRACTICE
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6.
Confidence Interval for a Mean Difference
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Independent Samples t-test
THEORY
T
1.
Independent Samples t-test: Purpose, Hypotheses, and Assumptions
PRACTICE
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2.
Independent Samples t-test: Purpose, Hypotheses, and Assumptions
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3.
Independent Samples t-test: Test Statistic and p-value
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4.
Independent Samples t-test: Test Statistic and p-value
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5.
Confidence Interval for the Difference Between Two Independent Means
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6.
Confidence Interval for the Difference Between Two Independent Means
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Independent Proportions Z-test
THEORY
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1.
Independent Proportions Z-test: Purpose, Hypotheses, and Assumptions
PRACTICE
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2.
Independent Proportions Z-test: Purpose, Hypotheses, and Assumptions
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3.
Independent Proportions Z-test: Test Statistic and p-value
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4.
Independent Proportions Z-test: Test Statistic and p-value
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5.
Confidence Interval for the Difference Between Two Independent Proportions
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6.
Confidence Interval for the Difference Between Two Independent Proportions
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Chapter 9: 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
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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
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4.
Chi-Square Test for Independence: Test Statistic and p-value
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Chapter 10: 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
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4.
One-way ANOVA: Hypotheses and Logic
8
THEORY
T
5.
One-way ANOVA: Test Statistic
PRACTICE
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6.
One-way ANOVA: Test Statistic
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7.
One-way ANOVA: Model and Assumptions
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8.
One-way ANOVA: Model and Assumptions
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9.
One-way ANOVA: Post Hoc Tests
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10.
One-way ANOVA: Post Hoc Tests
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11.
One-way ANOVA: Using R
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12.
One-way ANOVA: Using R
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Chapter 11: Regression Analysis
Simple Linear Regression
THEORY
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1.
Introduction to Regression Analysis
PRACTICE
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2.
Introduction to Regression Analysis
3
THEORY
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3.
Residuals and Total Squared Error
PRACTICE
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4.
Residuals and Total Squared Error
2
THEORY
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5.
Finding the Regression Equation
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6.
Finding the Regression Equation
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7.
The Coefficient of Determination
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8.
The Coefficient of Determination
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9.
Regression Analysis and Causality
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10.
Regression Analysis and Causality
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Multiple Linear Regression
THEORY
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1.
Multiple Linear Regression
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2.
Multiple Linear Regression
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3.
Overfitting and Multicollinearity
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4.
Overfitting and Multicollinearity
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5.
Dummy Variables
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6.
Dummy Variables
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