STAT 503 Quiz V

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Author:
MRK
ID:
270224
Filename:
STAT 503 Quiz V
Updated:
2014-04-17 21:03:21
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Wilsons adjusted chi square
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Chapter 9 and 10
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  1. Sample proportion
    • p-hat = y/n
    • y = success
    • n = number of trials
  2. Wilson-adjusted proportion
    • p-tilda = (y+2)/(n+4)
    • to keep p-tilda from 0 or 1
  3. SE for p-hat
    √(p-hat (1-p-hat)/n)
  4. CI for p-hat (95%)
    • p-hat +/- z.025√(p-hat(1-p-hat)/n) =
    • p-hat +/- 1.96√(p-hat(1-p-hat)/n)
    • set upper limit to 1 and lower limit to 0 if surpass
    • unstable, sometimes over coverage, sometimes less (not always 95%)
  5. Wilson adjusted 95% CI
    • p-tilda +/- 1.96√(p-tilda(1-p-tilda)/(n+4))
    • set upper limit to 1 and lower limit to 0
    • Gives better coverage (closer to 95%)
  6. One sided confidence interval
    • (-∞,p-tilda + 1.65 * SEp-tilda)
    • (p-tilda - 1.65 * SEp-tilda, ∞)
    • Still between 0 or 1
  7. Wilson SE
    √(p-tilda(1 - p-tilda)/ (n + 4))
  8. Χ2 for more than 2
    • (Observed - Expected)2 / Expected + all values
    • Use df
    • All expected have to be greater than 5
    • Can just say if they are different than expected
    • Observed-expect2 will always be the same so
  9. X2 for 2
    • directional
    • could use binomial
    • H0: p = .75
    • HA: p ≠ .75
    • check with table
    • For one sided, ts has to be >/< than 2*alpha ts AND on the right side of expected
  10. Test for independence w/ contingency tables
    • p1 = (A|B)
    • p2 = (A|C)
    • H0: p1 = p2
    • HA: p1 = p2 (p1 >< p2)
  11. Expected values in 2x2 tables
    • row total * column total / Grand total
    • Make sure each is at least 5
  12. df in 2x2 tables
    (# rows - 1) * (# columns - 1)
  13. Directional test with X2 and 2x2
    • X2 > Xtablefor 2alpha
    • and
    • Alternate hypothesis was satisfied
    • Non-directional don't double
  14. Interpretation for X2
    • association not causal
    • maybe causal in controlled study
    • if one H0 is rejected, differently defined p will be also be rejected from same table
  15. What is significance level
    the likely-hood of making a type I error
  16. CI for p-tilda
    • p-tilda1 - p-tilda2 +/- ZApha/2 * SEp1-p2
    • If it contains 0 no differences
  17. SE for p-tilda
    • To keep it away from 0
  18. Assumptions for ANOVA
    • each population is normally distributed
    • samples are independent
    • samples are random
  19. For several categories why not pair-wise t-test?
    • Because chance of committing type I error is large for whole test
    • alpha for each pair
    • 1- (1-alpha)# colums
    • Problem of multiple comparisons
    • if lower alpha get higher type II

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