Course content

Types of data and measurement
- Quantitative and qualitative data
- The hierarchy of measurement scales
- Nominal scale
- Ordinal scale
- Interval scale
- Ratio scale
Frequency distributions
- Frequency distributions
- Frequency distribution tables
- Frequency distribution graphs
- Shape of a distribution
- Measures of location I: percentiles, quantiles, and quartiles
Measures of central tendency
- Mode
- Median
- Mean
- Sensitivity to outliers
- Central tendency and the shape of the distribution
Measures of variability
- Range, interquartile range, and the five-number summary
- Interquartile range rule for identifying outliers
- Deviation from the mean and the sum of squares
- Variance and standard deviation
The Normal Distribution
- Normal distribution
Measures of location II: Z-Scores
- Z-Scores
Chapter 2: Probability
Randomness
- Sets, subsets, and elements
- Random experiments
- Sample space
- Events
- Complement of an event
Relationship between events
- Mutual exclusivity
- Difference
- Intersection
- Union
Probability
- Definition of probability
- Probability of the complement
- Conditional probability
- Independence
- Probability of the intersection
- Probability of the union
- Probability of the difference
- Law of total probability
- Bayes' theorem
Chapter 3: Probability Distributions
Probability models
- Discrete probability models
- Continuous probability models
Random variables
- Random variables
- Probability distributions
- Expected value of a random variables
- Variance of a random variable
- Sum of random variables
Common distributions
- The Binomial distribution
- Expected value and variance of a binomial random variable
- The Normal distribution
- The Normal probability distribution
Chapter 4: Sampling
Sampling and sampling methods
- Sampling and unbiased sampling methods
- Biased sampling methods
Sampling distributions
- Sampling distributions
- Sampling distributions of the sample mean
- Sampling distributions of the sample proportion
Chapter 5: Inferential statistics
Estimation
- Parameter estimation
- Constructing of a 95% confidence interval for the population mean
- Confidence interval for the population mean
- Confidence interval for the population proportion
Introduction to hypothesis testing (p-value approach)
- Hypothesis testing procedure
- Formulating the research hypotheses
- Two-tailed vs. one-tailed testing
- Setting the criteria for a decision
- Computing the test statistic
- Computing the p-value and making a decision
- Assumptions of the z-test
- Connection between hypothesis testing and confidence intervals
- Errors in decision making
- Statistical power
Hypothesis test for a population proportion
- Hypotheses of a population proportion test
- Large-sample proportion test: test statistic and p-value
- Small-sample proportion test: test statistic and p-value
- Hypothesis test for a proportion and confidence intervals
One-sample t-test
- One-sample t-test: purpose, hypotheses, and assumptions
- One-sample t-test: test statistic and p-value
- Confidence interval for μ when σ is unknown
Chapter 6: Bivariate analysis
Paired samples t-test
- Paired samples t-test: purpose, hypotheses, and assumptions
- Paired samples t-test: test statistic and p-value
- Confidence interval for a mean difference
Independent samples t-test
- Independent samples t-test: purpose, hypotheses, and assumptions
- Independent samples t-test: test statistic and p-value
- Confidence interval for the difference between two independent means
Two-proportion z-test
- Two-proportion z-test: purpose, hypotheses, and assumptions
- Two-proportion z-test: test statistic and p-value
- Confidence interval for the difference between two independent proportions
Chi-square goodness of fit
- Chi-square goodness of fit test: purpose, hypotheses, and assumptions
- Chi-square goodness of fit test: test statistic and p-value
Chi-square test for independence
- Chi-square test for independence: purpose, hypotheses, and assumptions
- Chi-square test for independence: test statistic and p-value
Associative statistics: correlation
- Introduction to correlation
- Linear relationship: covariance
- Linear relationship: pearson correlation coefficient
Simple linear regression
- Introduction to regression analysis
- Residuals and total squared error
- Finding the regression equation
- The coefficient of determination
- Regression analysis and causality
Multiple linear regression
- Multiple linear regression
- Overfitting and multicollinearity
- Dummy variables

Statistics


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