Chp 4-5: Contrasts & Post hoc Means Comparisons

Question 1

What is the definition of contrast?

Answer 1

A linear combination of parameters

Question 2

What is a Type I error?

Answer 2

Reject H_0 when H_0 is true

Question 3

What is the Type I error rate?

Answer 3

/alpha = P{reject H_0 | H_0 true}

Question 4

What is a Type II error?

Answer 4

Fail to reject H_0 when H_0 is false

Question 5

What is the Type II error rate?

Answer 5

ß=P{fail to reject H_0 | H_0 false}

Question 6

What is power?

Answer 6

1-ß = P{reject H_0 | H_0 false}

The opposite of the Type II error rate!

Question 7

We want our ________ to be low and our ________ to be high

Answer 7

Type I error rate

Power

Question 8

What is our error rate when we test H_0?

Answer 8

/alpha

Question 9

We want to control the error rate so that…

Answer 9

P(Type I error) ≤ /alpha

Question 10

Type I error rates of interest:

Answer 10

1. PCER = P(reject H_0i | H_0i true) for single i
   (per-comparison error rate)
2. FWER = P(reject at least one H_0i | H_01;… ;H_0K true)
   (family-wise error rate, or experiment-wise error rate)
3. FDR = (# wrongly-rejected H0i’s ) = (total # rejected H0i’s )
   (false discovery rate)
4. SFWER = P(# wrongly-rejected H0i’s 1)
   (strong family-wise error rate) (no condition that they are all true)
5. Simultaneous Condence Intervals
   (set confidence level for family of all K intervals)

Question 11

Tests in SAS for error rates:

Answer 11

Error Rate All Pairwise Comparisons
PCER LSD (don’t use this)
FWER pLSD
FDR SNK
SFWER REGWQ (Use this!)
Simult. CI Bonferroni, Tukey (also use this!)

Question 12

Specialized Comparison Tests

Answer 12

• Scheffé (test all possible contrasts)

- Dunnet (for testing “control” vs. all other tests)

Question 13

What does the REGWQ approach require?

Answer 13

Balance, and a single factor model.

Question 14

When asking many questions of data from an experiment, the honest thing to do is…

Answer 14

adjust for multiple testing.