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

English

- Types of data and measurement
- Qualitative and quantitative variables
- 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: Quantiles

- Measures of central tendency
- Mode
- Median
- Mean
- Central tendency and the shape of a distribution
- Sensitivity to outliers

- 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

- Measures of location II: Z-scores
- Z-scores

- Correlation
- Displaying the relationship between two variables
- Measuring the relationship between two variables
- Direction of a linear relationship: Covariance
- Strength of a linear relationship: Pearson

- 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

- Contingency tables
- Interpreting contingency tables

- Probability models
- Discrete probability models
- Continuous probability models

- Random variables
- Random variables
- Probability distributions
- Expected value of the random variable
- Variance of a random variable
- Sums of random variables

- Common distributions
- The binomial distribution
- Expected value and variance of a binomial random variable
- The normal distribution
- The normal probability distribution

- Sampling and sampling methods
- Sampling and unbiased sampling methods
- Biased sampling methods

- Sampling distributions
- Sampling distributions
- Sampling distribution of the sample mean
- Sampling distribution of the sample proportion

- Parameter estimation and the confidence intervals
- Parameter estimation
- Constructing a 95% confidence interval for the population mean
- Confidence interval for the population mean
- Confidence interval for the population proportion

- Hypothesis testing
- Hypothesis testing procedure
- Formulating the research hypothesis
- 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 unkown

- 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

- Independent proportions z-test
- Independent proportion z-test: Purpose, hypotheses and assumptions
- Independent proportion z-test: Test statistic and p-value
- Confidence interval for the difference between two independent proportions

- 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

- Chi-square godness of fit test
- 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