# STAT 503 Quiz VI

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 Author: MRK ID: 272014 Filename: STAT 503 Quiz VI Updated: 2014-05-08 13:48:17 Tags: ANOVA REgression Folders: Description: ANOVA and Regression Show Answers:

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1. Limits to ANOVA
• population must be normally distributed
• samples are independent and random
• sd of sample = sd of larger population therefore pooled SE
2. ANOVA Hypothesis
• H0: u1 = u2 = u3
• HA: at lease one u is different
3. n dot
total number of observations
4. yij
observation in j position from group i
5. SSW
• sum of squares within
• (yij - meani)2 + (yij - meani)2 + all js
6. df within
n dot - number of categories
7. MSW
• mean squares within
• = SSW/dfW
8. SSB
• sum of squares between
• ni(yi - ygrand)2 + ...
• Will go up if one mean is higher (reject)
9. y- double bar
• overall mean
• (ni * group mean) + (ni * group mean) / n dot
10. df between
I - 1
11. MSB
• Mean Squares between
• = SSB/dfB
12. SS(total)
• SS(total) = SSW + SSB
• df = total observations -1
13. distance of yij from grand mean
(yij - yi mean) + (yi mean - grand mean)
14. Values in ANOVA table
• df (w & b) total
• SS (w & b) total
• MS (w & b) no total
• Fs
15. Fs
• test statistic for ANOVA
• MSB/MSW
• High = reject
• distribution like X2
16. relationship btw F-test and t-test
• F2 = ts2
• using pooled SE
• Falpha = talpha/22
• df = n1 + n2 -2
• non-directional
• will have same decision
17. eg
F(4,20).05
• F(dfB, dfW)alpha
• can get I and n-dot from
18. Conditions of validity for ANOVA
• Population sds are equal
• within each group the samples are from normal populations are large n
• independent and random samples
19. how to check if sd's are similar
• residuals:
• add/subract average - to center on zero
• want parallel lines
20. checking for normality?
plot qq in straight line
21. response variable
explanatory variable (controlled)
• Y
• X, predictor, co-variate
22. r
23. measures strength of relationship X and Y
24. Hypothosis for correlation btw X and Y
• H0: rho = 0
• HA: rho ≠ 0
25. ts for X, Y correlation
• t-test
• = r* √(n-2)/(1-r2)
• df = n - 2
26. ei
• residuals
• = (yi - bo - mxi)
• want them to be smallest

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