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A.P. Statistics

Review Outline

Exploration of Data

A) One Sample

i. Numerical Analysis

1) Center (Mean, Median)

2) Spread (Variance, Standard Deviation, Range, IQR)

3) When to use each measure, resistance, comparison

ii. Graphical Display (Histogram, Stem-Plot, Box-Plot, Modified Box-Plot)

1) Center and Spread

2) Shape (Symmetry and Skewness, # of peaks, gaps and outliers)

iii. Theoretical Model

1) Normal Distribution

a. Characteristics (Single peak, symmetric, bell shaped)

b. 68, 95, 99.7 Rule

c. Central Limit Theorem

d. Calculations (CDF and Inverse CDF)

B) Two Sample

i. Comparing Distributions

1) Graphs (side by side Histograms, side by side box-plots, back-to-back stem-plots)

2) Numbers (Compare center and spread, compare Normal Distributions with z-scores.)

ii. Association of Quantitative Variables

1) Graphs (Scatterplot, Residual Plot)

2) Numbers (Correlation Coefficient, r-squared, Residuals)

3) Model (Least-Squares Regression, interpretation of slope, exponential regression)

iii. Comparing Categorical Data

1) Bar-Graphs, Marginal Distributions, Chi-Squared

Collecting Data and Design

C) Designing Samples

i. Reading Table of Digits, Using calculator random # generator

ii. Taking Samples (SRS, stratified random sample, multi-stage sample)

iii. Awareness of Bad sample designs, recognizing an SRS.

D) Designing Experiments

i. Completely Randomized Design

ii. Matched Pairs

iii. Randomized Block

iv. Benefits of experiments over observational studies

v. Control, Randomization, Replication

vi. Bias, Confounding, Common Response, Variability

E) Designing Simulation

i. Why, how, and when?

ii. Allocating digits to outcomes

iii. Assumptions

iv. Analysis

Probability

F) Basic Probability Laws

i. Disjointness and Independence

ii. Union and Intersection of events

iii. Conditional Probability

G) Random Variables

i. Discrete Random Variables

1) Calculate Probabilities, Means, and Variances

2) Binomial and Geometric Distributions

ii. Continuous Random Variables

1) Normal, Uniform, t, Chi-Squared

iii. Law of Large Numbers

iv. Rules of Means and Variances

H) Sampling Distributions

i. Sampling Distribution of p-hat

ii. Sampling Distribution of x-bar

iii. Central Limit Theorem

Statistical Inference

I) General Concepts

i. Construction of confidence intervals and Hypothesis tests

ii. Unbiased Estimators, Critical Values, Standard Deviation of estimates

iii. Test Statistics, P-Values, Significance levels, Conclusions

iv. Assumptions and checking assumptions

J) One Sample

i. Z test for population mean

ii. T-test for population mean

iii. Z-test for population proportion

iv. Matched Pairs t-test

K) Two Sample

i. Z and T tests for a difference between two population means

ii. Z test for a difference between two population proportions

iii. Linear Regression t-test for association between two variables

L) Inference for tables

i. Chi-Square test for Goodness-of-Fit for a distribution of counts

ii. Chi-Square test for association of two categorical variables

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