Flashcards in Quiz 2 Deck (31):
1
What are the null hypotheses (one-way)?
-Ex:
-H(sub o): There is no statistically significant difference between the population means of males and females with regard to their GPAs.
-H(sub o): u(sub m) = u(sub f)
-With null hypothesis, you always state that there is no statistically significant difference.
2
What are the characteristics of Orthogonal Comparisons?
1. A priori hypotheses
2. ∑a(sub i) = 0 (valid comparison)
∑a(sub i)b(sub i) = 0 (independence)
3. Each comparison is on 1 degree of freedom
4. You get as many comparisons as g-1 degrees of freedom
5. Most powerful test of the three
6. Significance level = alpha
3
What are the characteristics of Bonferroni?
1. A priori hypotheses
2. ∑a(sub i) = 0 (valid comparison)
Don’t need independence, so ∑a(sub i)b(sub i) does not have to equal 0
3. Each comparison is on 1 degree of freedom
4. You get as many comparisons as you want, but you lose power with each subsequent comparison
5. Moderate power of the three
6. Significance level = alpha/c (c is the number of comparisons)
4
What are characteristics of Scheffe?
1. A posteriori or post hoc hypotheses
2. ∑a(sub i) = 0 (valid comparison)
Don’t need independence, so ∑a(sub i)b(sub i)does not have to equal 0
3. Each comparison is on the among degrees of freedom
4. You can make as many comparisons as you want
5. Lowest power of the three tests
6. Significance level = alpha
5
What are experimentwise errors?
-Probability of making at least 1 Type I Error over the entire experiment (set of comparisons)
6
What are per comparison errors?
-Per Comparison Error: Probability of making a Type I Error for each individual comparison
7
What are the problems with multiple t-tests?
-Not okay for multiple t-tests because these are NOT independent and you’ve got an inflated Type I error rate
-You may find differences that may not even be there
8
What are the null hypotheses (two-way)?
-Ex:
1. H(sub o): There is no statistically significant difference between the population means of the massed practice and distributed practice groups with regard to stats test scores
-H(sub o): u(sub m) = u(sub d)
2. H(sub o): There is no statistically significant difference between the population means of the in-class and online teaching methods with regard to stats test scores.
-H(sub o): u(sub IC) = u(sub ON)
3. H(sub o): There is no teaching method x (by) study habit interaction in the population.
9
What is a main effect?
-The overall difference among the levels of the independent variable tested
-Average of the simple effects
10
How many main effects in a specific design?
-The number of main effects is the number of independent variables that you have
-You have as many main effects as IVs
11
What is a simple effect?
-The effect of an independent variable at a single level of the other independent variable
-Lack of parallelism (do not cross)
-LOOK ON PAGE 11 OF NOTES
12
How many simple effects in a two-way design?
-The additive rather than the multiplicative
-Ex: 2x2 = 4
-Ex: 2x4 = 6
13
What is an interaction?
-The lack of parallelism in the simple effect
OR
-The effect of an independent variable differs depending upon the levels of the other IV
-If asked to define this, we have to define “simple effect” too
14
How do you plot an interaction? Graph form and in words.
1. Choose an IV to place on the x-axis
2. Values of the cell means go on the y-axis
3. Plot a single curve for each level of the other IV
-MAKE HAND-WRITTEN NOTE CARD (Page 11)
15
What are range tests?
-All pairwise comparisons between means
1. Tukey A
2. Student Newman-Kewls
3. Tukey B
16
What is the studentized range distribution?
-A sampling distribution of a t-test run between the largest and smallest means from a set of k means
17
How do you perform the Tukey A test?
1. Order the means from smallest to largest
2. Compute q for each comparison
3. df(sub # of means, df error)
Compare each q with the critical values of q on the number of means and df error
18
How do you perform the SNK test?
1. Order the means from smallest to largest
2. Compute q for each comparison
3. df(sub # of ordered means, df error)
Compare each q with the critical values of q based on the number of ordered means (or number of steps) and df error
*More power
19
How do you perform the Tukey B test?
1. Order the means from smallest to largest
2. Compute q for each comparison
3. Average the critical values of the Tukey A and SNK for each comparison
20
How do you perform the Fisher-Hayter test?
1. Order the means from smallest to largest
2. Compute the q for each comparison
3. df(sub # of means-1, df error)
Use the number of means - 1 and the df error to obtain the critical value of q
21
What was the rationale behind Duncan’s multiple range test and what are its problems?
-Rationale:
-Focused on trying to obtain greatest power possible
1. Experimentwise error rate similar to the orthogonal comparisons 1-(1-alpha)^g-1 -- “protection level”
2. Step-down procedure similar to SNK
3. Derives out his own critical value tables
-Problems:
-Comparisons not independent
-Inflated Type I error rate; kind of like doing t-tests, so error rates go through the roof
22
The relationship between q and t?
-HAND-WRITTEN NOTE CARD (PAGE 13)
-Gosset and help forgot “2” when computing, which is why we have “t” and “q”
q(sub 2, infinity) = 2.77 (.05); 3.64 (.01) t(sub infinity) = 1.96 (.05); 2.576 (.01)
q=t x(times) square root of 2 t=q/2
23
Problem with unequal n with a one-way ANOVA?
-No problems mathematically, but you lose power.
24
What are the characteristics (coefficients) for orthogonal comparisons with unequal n?
- ∑n(sub i)a(sub i) = 0 (valid comparison)
- ∑n(sub i)a(sub i)b(sub i) = 0 (independence)
25
What are the problems with unequal n in a two-way design?
-Destroy factorial nature of the design, and it lacks robustness
26
What is a factorial design?
-Design in which each level of each independent variable occurs equally often with each level of every other independent variable
-Must have equal n
27
How do you get rid of unequal n?
1. Randomly discard data
2. Yates Substitution Formula
3. Least Squares Solution
-Mathematically ideal
-SAS
4. Unweighted Means Solution
-Used on SPSS
1. SSeffect → use cell means
2. SSwithin → use new data
*LOOK ON PAGE 2
28
What is the harmonic mean and why do you use it? Purpose?
-Average the reciprocals and take the reciprocal of that average
-HAND-WRITTEN NOTE CARD HAS FORMULA
-Used when dealing with unequal n
-purpose:
-weighs smaller samples more and larger samples less
29
What is complete confounding?
-A design in which you do not know where the difference lies
30
What are the null hypotheses (three-way)?
Ex:
1. H(sub o): There is no statistically significant difference between the population means of males and females in regard to Machiavellian personality scores.
-H(sub o): u(sub m)=u(sub f)
2. There is no statistically significant difference between the population means of Political Science majors and Psychology majors in regard to Machiavellian personality scores.
-H(sub o): u (sub psy) = u (sub pol)
3. There is no statistically significant difference between the population means of graduates and undergraduates in regard to Machiavellian personality scores.
-H(sub o): u (sub U) = u (sub UG)
4. H(sub o): There is no sex by major interaction in the population.
5. H(sub o): There is no sex by class interaction in the population.
6. H(sub o): There is no major by class interaction in the population.
7. H(sub o): There is no sex by major by class interaction in the population.
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