2nd Half Review

1
2nd Half Review

• ANOVA (Ch. 11)
• Non-Parametric (7.11, 9.5)
• Regression (Ch. 12)
• ANCOVA
• Categorical (Ch. 10)
• Correlation (Ch. 12)

2
The Exam

• Thursday, April 27, 900am
• TC 348 ? Abdi to Middleton
• TC 348a ? Minto to Shetty
• TC 348b ? Siddiqui to Zdravic
• 50 Questions
• Not Cumulative
• 3hr
• Bring a calculator
• No formula Sheets

3
ANOVA

• Variance Partitions
• Total Among Within
• Grand Mean, Group Mean and associated Deviations
• When do we reject based on variance ratio???

4
ANOVA Table
5
ANOVA

• When do we use??
• Model I vs Model II vs Model III??
• Multi-Factors??
• Main Effects vs Interactions??

6
Example From Text

• Question 11.40, p. 518
• 10 women in an aerobic exercise class, 10 women
  in a modern dance class, and a control group of 9
  women were studied. One measurement made on each
  women was change in fat-free mass over the course
  of the 16-week training period. Summary
  statistics are given in the table. The ANOVA
  SS(between) is 2.465 and the SS(within) is 50.133.

• State the null hypothesis
• Construct the ANOVA table and test the null
  hypothesis (a 0.05)

7
Example From Text

• Question 11.57, p. 522
• A new investigational drug was given to 4 male
  and 4 female dogs, at doses 8 mg/kg and 25 mg/kg.
  The variable recorded was alkaline phosphatase
  level (U/Li).

• (SS(sex) 81, SS(dose) 81, SS(interaction)
  784, and SS(within) 12604
• Construct the ANOVA Table
• Carry out an F test for interactions use (a
  0.05).
• Test the null hypothesis that does has no effect
  on alkaline phosphatase level. (a 0.05)

8
Extra Questions from the Text

• 11.4-11.6
• 11.9-11.11
• 11.17, 11.19
• 11.42, 11.43, 11.50, 11.54

9
Non-Parametric

• When to use??
• Normality
• Homogenous of Variance
• Independent Observations
• What about Power??
• What do they use to compare data??

10
Mann-Whitney Test

• Compares two samples
• Replaces two-sample t-test

If either U or U is greater than the critical
value of U, then you should reject the Ho
11
Critical U
if n1 lt n2
if n1 gt n2
If either U or U is greater than the critical
value of U, then you should reject the Ho
12
One-tailed Mann-Whitney U test
Use U or U depending on whether you expect
sample 1 or sample 2 to be bigger
13
Wilcoxon paired sample test

• Compares two paired samples
• Replaces Paired t-test

14
Critical T
Sum the positive ranks - T Sum the negative
ranks - T-
If either T or T- is less than or equal to
T0.05, (2),n then reject Ho
Can also do these one tailed Ho Measurement 1
? Measurement 2 HA Measurement 1 gt Measurement
2 --gt reject Ho if T- ? T0.05, (1),n
Ho Measurement 1 ? Measurement 2 HA Measurement
1 lt Measurement 2 --gt reject Ho if T ? T0.05,
(1),n
15
Kruskal Wallis Test

• Test for three or more groups
• Replaces ANOVA

• Rank each individual sample across all groups
• Sum ranks within each group R
• Critical value -

16
Correction factor for tied ranks
17
Critical Value
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Practice Questions

• Mann-Whitney
• 7.79, 7.80, 7.82-7.84
• Wilcoxon
• 9.30 9.33
• Kruskal-Wallis
• 11.54, 11.57 ? use Kruskal-Wallis instead of ANOVA

19
Regression

• Two or more continuous variables
• Linear relationship between

Intercept
Slope
20
Least Squares

• Line with smallest residual sum of squares

as
21
ANOVA Table
Source of Variation SS DF MS F
1
Regression
n-2
Residual
Total
n-1
22
Coefficient of Determination
- proportion of variation explained
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Slope
Intercept
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Confidence Interval for Slope
25
Practice Questions

• 12.45
• 12.49-12.54

26
ANCOVA

• Continuous Dependent
• Continuous and Discrete Independents
• Compares relationship of two variables across two
  groups

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(No Transcript)
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Categorical Data

• Discrete Response variable
• Interested in Frequencies

29
Chi-Squared Test

• Observed vs Expected Frequencies

f expected is hypothesized ratio e.g. 5050 males
to females
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Contingency Table

• Test for independence among variables
• 2x2, 2x3, 3x3 etc.
• 2 variables with 2 levels, 2 variables with 3
  levels, 3 variables with 3 levels etc.

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R1 sum of observed in Row 1 R2 sum of
observed in Row 2 C1 sum of observed in Column
1 C2 sum of observed in Column 2 C3 sum of
observed in Column 3 Total sum of all observed
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Expected calculation
/
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Practice Questions

• 10.73-10.78
• 10.84-10.88

34
Logistic Regression

• Discrete dependent usually dichotomous
• Continuous independent