GSE Stat Methods I - Review Notes

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The following review is based on the indicated chapter and section of

Moore, D. S., McCabe, G. P., & Craig, B. A. (2012). Introduction to the practice of statistics (7th ed). New York: W. H. Freeman.

The questions and items for display are organized as a slide show. The sub-bullets for each point support discussion and content to be written out on the board.


Contents

Tests of Significance (6.2)

  1. Identify two opposing claims
    • student claims innocence (claim 1); instructor claims she cheated (claim 2).
    • claim 1 is challenged by claim 2
    • begin with assumption that claim 1 is true.
  2. Collect evidence
    • instructor provides evidence against claim 1
    • observations in sample will serve as evidence against claim 1
  3. Assess evidence
    • committee evaluates evidence: how likely (probability based) to observe this evidence if student is innocent
    • evaluate sample statistics in context of sampling distribution; determine how likely to observe this result if it were to have occurred by chance.
  4. Make a decision
    • If very unlikely that student could be innocent (claim 1) given evidence (strong evidence against claim 1), then reject claim 1 and decide for claim 2
    • If likely that student could be innocent (claim 1) given evidence (weak evidence against claim 1), then stay with claim 1 (cannot reject claim 1 in favor of claim 2). Note: we do not say we accept claim one, we just don't have anything better to conclude.

Estimating with Confidence (6.1)

Introduction to inference (intro)

Sampling distributions for counts and percents (5.2)

The sampling distribution of a sample mean (5.1)

Sampling distributions - intro

Means and variances of random variables (4.4)

Number of persons 2 3 4 5 6 7
Probability 0.44 0.22 0.20 0.09 0.03 0.02
Payoff X $0 $500
Probability 0.999 0.001
Number of persons 2 3 4 5 6 7
Probability 0.44 0.22 0.20 0.09 0.03 0.02
Math Reading
Mean 514 496
Stand dev 117 114

Random variables (4.3)

HH HT, TH TT
Value of X 0 1 2
Probability P(X=0) = 1/4 P(X=1) = 1/4 + 1/4 = 1/2 P(X=2) = 1/4
B GB GGB, GGG
Value of X 1 2 3
Probability P(X=1) = 1/2 P(X=2) = 1/4 P(X=3) = 1/8 + 1/8 = 1/4
Number of persons 2 3 4 5 6 7
Probability 0.44 0.22 0.20 0.09 0.03 0.02

Last bit of section 1.3

Probability models (4.2)

Randomness (4.1)

Ethics (3.4)

Toward statistical inference (3.3)

Sampling design (3.2)

Design of experiments (3.1)

Producing data (Chapt 3 intro)

The question of causation (2.6)

Data analysis for two-way tables (2.5)

Cautions about correlation and regression (2.4)

Least-squares regression (2.3)

Correlation (2.2)

Scatterplots (2.1)

Examining relationships (Chapt 2 intro)

Density curves and normal distributions (1.3, through 68-95-99.7 rule)

Displaying distributions with numbers (1.2)

Displaying distributions with graphs (1.1)

Chapt 1.Introduction


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