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# Statistics

### Syllabus

The Basics: Descriptive and Inferential Statistics.
Sampling Methods.
Types of Variables.
Independent and Dependent Variables.
Variable Measurement Scales.
Frequency Distributions and Cumulative Frequency Distributions.
Bar Graphs and Pie Charts.
Histograms and Stem & Leaf Plots.
Arithmetic Mean for Samples and Populations.
Central Tendency: Mean, Median, and Mode.
Variance and Standard Deviation of a Population.
Variance and Standard Deviation of a Sample.
Percentiles and Quartiles.
The Five Number Summary, Interquartile Range(IQR), and Boxplots.
The Effects of Outliers.
Skewness.
The Normal Curve and Empirical Rule.
Z-Scores (part one).
Z-Scores (part two).
Extra Z-Score Problems.
The Basics of Probability.
Multiplication Rule (Probability "and").
Permutations.
Combinations.
Discrete and Continuous Random Variables.
Discrete Probability Distributions.
Probability Histograms.
Mean and Expected Value of Discrete Random Variables.
Variance and Standard Deviation of Discrete Random Variables.
The Law of Large Numbers.
Binomial Distribution.
Mean and Standard Deviation of Binomial Random Variables.
Poisson Distribution/Process.
Mean and Standard Deviation of Poisson Random Variables.
Coordinate (Cartesian) Planes.
Scatter Plots.
Pearson's r Correlation.
Hypothesis Testing with Pearson's r.
Spearman Correlation.
Linear Regression.
Correlation vs. Causation.
Parameters, Statistics, and Sampling Error.
Distribution of the Sample Mean.
The Central Limit Theorem.
Sample Proportions.
Confidence Intervals about the Mean, Population Standard Deviation Known.
Calculating Required Sample Size to Estimate Population Mean.
Student's t-Distribution.
Confidence Intervals about the Mean, Population Standard Deviation Unknown.
Confidence Intervals for Population Proportions.
Null and Alternative Hypotheses.
Type I and Type II Errors.
One-Tailed and Two-Tailed Tests.
Effect Size.
Power.
Statistical vs. Practical Significance.
Independent and Dependent Samples.
One Sample z-Test.
One Sample z-Test for Proportions.
One Sample t-Test.
Independent Samples t-Test.
Confidence Intervals for Independent Samples t-Test.
Effect Size for Independent Samples t-Test.
Dependent Samples t-Test.
Confidence Intervals for Dependent Samples t-Test.
Effect Size for Dependent Samples t-Test.
z-Test for Proportions, Two Samples.
Confidence Intervals for the Difference of Two Proportions.
Introduction to ANOVA.
One-Way ANOVA.
Effect Size for One-Way ANOVA.
Post-Hoc Tests for One-Way ANOVA.
Repeated-Measures ANOVA.
Factorial ANOVA, Two Independent Factors.
Factorial ANOVA, Two Dependent Factors.
Factorial ANOVA, Two Mixed Factors.
Chi-Square Test for Goodness of Fit.
Chi-Square Test for Independence.
Mann-Whitney U-Test.
Wilcoxon Signed-Ranks Test.
The Kruskal-Wallis Test.
The Friedman Test.
Calculating Required Sample Size to Estimate Population Proportions.
User Submitted Question: Alpha Levels.

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