Download I) Exploration of Data

A.P. Statistics
Review Outline
I)
II)
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
A) 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.
B) 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
C) Designing Simulation
i. Why, how, and when?
ii. Allocating digits to outcomes
iii. Assumptions
iv. Analysis
III)
Probability
A) Basic Probability Laws
i. Disjointness and Independence
ii. Union and Intersection of events
iii. Conditional Probability
B) 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
C) Sampling Distributions
i. Sampling Distribution of p-hat
ii. Sampling Distribution of x-bar
iii. Central Limit Theorem
IV)
Statistical Inference
A) 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
B) 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
C) 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
D) 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