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 measurement
    1. Qualitative and quantitative variables
    2. The hierarchy of measurement scales
    3. Nominal scale
    4. Ordinal scale
    5. Interval scale
    6. Ratio scale
  • Frequency distributions
    1. Frequency distributions
    2. Frequency distribution tables
    3. Frequency distribution graphs
    4. Shape of a distribution
    5. Measures of location I: Quantiles
  • Measures of central tendency
    1. Mode
    2. Median
    3. Mean
    4. Central tendency and the shape of a distribution
    5. Sensitivity to outliers
  • Measures of variability
    1. Range, interquartile range , and the five-number summary
    2. Interquartile range rule for identifying outliers
    3. Deviation from the mean and the sum of squares
    4. Variance and standard deviation
  • Measures of location II: Z-scores
    1. Z-scores

Chapter 2: Correlation

  • Correlation
    1. Displaying the relationship between two variables
    2. Measuring the relationship between two variables
    3. Direction of a linear relationship: Covariance
    4. Strength of a linear relationship: Pearson

Chapter 3: Probability

  • Randomness
    1. Sets, subsets and elements
    2. Random experiments
    3. Sample space
    4. Events
    5. Complement of an event
  • Relationship between events
    1. Mutual exclusivity
    2. Difference
    3. Intersection
    4. Union
  • Probability
    1. Definition of probability
    2. Probability of the complement
    3. Conditional probability
    4. Independence
    5. Probability of the intersection
    6. Probability of the union
    7. Probability of the difference
    8. Law of total probability
    9. Bayes’ theorem
  • Contingency tables
    1. Interpreting contingency tables

Chapter 4: Probability distributions

  • Probability models
    1. Discrete probability models
    2. Continuous probability models
  • Random variables
    1. Random variables
    2. Probability distributions
    3. Expected value of the random variable
    4. Variance of a random variable
    5. Sums of random variables
  • Common distributions
    1. The binomial distribution
    2. Expected value and variance of a binomial random variable
    3. The normal distribution
    4. The normal probability distribution

Chapter 5: Sampling

  • Sampling and sampling methods
    1. Sampling and unbiased sampling methods
    2. Biased sampling methods
  • Sampling distributions
    1. Sampling distributions
    2. Sampling distribution of the sample mean
    3. Sampling distribution of the sample proportion

Chapter 6: Parameter estimation confidence intervals

  • Parameter estimation and the confidence intervals
    1. Parameter estimation
    2. Constructing a 95% confidence interval for the population mean
    3. Confidence interval for the population mean
    4. Confidence interval for the population proportion

Chapter 7: Hypothesis testing

  • Hypothesis testing
    1. Hypothesis testing procedure
    2. Formulating the research hypothesis
    3. Two-tailed vs one-tailed testing
    4. Setting the criteria for a decision
    5. Computing the test statistic
    6. Computing the p-value and making a decision
    7. Assumptions of the Z-test
    8. Connection between hypothesis testing and confidence intervals
    9. Errors in decision making
    10. Statistical power
  • Hypothesis test for a population proportion
    1. Hypotheses of a population proportion test
    2. Large-sample proportion test: Test statistic and p-value
    3. Small-sample proportion test: Test statistic and p-value
    4. Hypothesis test for a proportion and confidence intervals
  • One-sample t-test
    1. One-sample t-test: Purpose, hypotheses, and assumptions
    2. One-sample t-test: Test statistic and p-value
    3. Confidence interval for μ when σ is unkown

Chapter 8: Testing for differences in mean and proportion

  • Paired samples t-test
    1. Paired samples t-test: Purpose, hypotheses and assumptions
    2. Paired samples t-test: Test statistic and p-value
    3. Confidence interval for a mean difference
  • Independent samples t-test
    1. Independent samples t-test: Purpose, hypotheses and assumptions
    2. Independent samples t-test: Test statistic and p-value
    3. Confidence interval for the difference between two independent means
  • Independent proportions z-test
    1. Independent proportion z-test: Purpose, hypotheses and assumptions
    2. Independent proportion z-test: Test statistic and p-value
    3. Confidence interval for the difference between two independent proportions

Chapter 9: Regression analysis

  • Simple linear regression
    1. Introduction to regression analysis
    2. Residuals and total squared error
    3. Finding the regression equation
    4. The coefficient of determination
    5. Regression analysis and causality
  • Multiple linear regression
    1. Multiple linear regression
    2. Overfitting and multicollinearity
    3. Dummy variables

Chapter 10: Categorical association

  • Chi-square godness of fit test
    1. Chi-square goodness of fit test: Purpose, hypotheses and assumptions
    2. Chi-square goodness of fit test: Test statistic and p-value
  • Chi-square test for independence
    1. Chi-square test for independence: Purpose, hypotheses and assumptions
    2. Chi-square test for independence: Test statistic and p-value

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