Statistics - Study guide

1. Descriptive statistics
   1. Data types and levels of measurement
   2. Data collection and sampling methods
   3. Frequency distributions and histograms
   4. Measures of central tendency
   5. Measures of variability
   6. Measures of relative standing
   7. Box plots and outliers
2. Probability
   1. Basic concepts and rules of probability
   2. Conditional probability and independence
   3. Bayes' theorem and applications
   4. Counting techniques and combinatorics
   5. Random variables and probability distributions
   6. Binomial distribution and Bernoulli trials
   7. Poisson distribution and Poisson process
   8. Normal distribution and standard normal curve
   9. Sampling distribution and central limit theorem
3. Inferential statistics
   1. Point estimation and interval estimation
   2. Confidence intervals for means and proportions
   3. Hypothesis testing and significance levels
   4. Tests for means and proportions
   5. Type I and type II errors and power of a test
   6. P-values and decision rules
4. Regression and correlation
   1. Scatter plots and correlation coefficient
   2. Simple linear regression model and equation
   3. Least squares method and line of best fit
   4. Coefficient of determination and goodness of fit
   5. Inference for regression parameters
   6. Residual analysis and assumptions
5. Analysis of variance (ANOVA)
   1. One-way ANOVA and F-test
   2. ANOVA table and calculations
   3. Multiple comparisons and post-hoc tests
   4. Two-way ANOVA and interaction effects
6. Categorical data analysis
   1. Contingency tables and marginal distributions
   2. Chi-square test of independence
   3. Chi-square test of homogeneity
   4. Chi-square test of goodness-of-fit
7. Nonparametric statistics
   1. Advantages and disadvantages of nonparametric methods
   2. Sign test and Wilcoxon signed-rank test
   3. Mann-Whitney U test and Kruskal-Wallis test
   4. Spearman's rank correlation coefficient