Flashcards in Summa Week 10 Deck (73):

1

## What is factorial ANOVA between-subjects design?

### 2 or more IV each with multiple levels

2

## In Factorial ANOVA, are the levels of IV fixed or continuous?

### fixed

3

## In Factorial ANOVA, are participants randomly or purposely assigned to levels, and if so, how many?

###
randomly assigned

assigned to only ONE combo of the levels

4

## In Factorial ANOVA, are levels of one variable possible for all levels of other variables?

### Yes. This is called being "fully crossed"

5

## In Factorial ANOVA, how are DVs measured?

### continuously

6

## In Factorial ANOVA, what is the SS formula?

### SStotal = SSa + SSb + SSab + SSerror

7

## In Factorial ANOVA, what is SStreatment (change due to the model)?

### SSa (main effect of a) + SSb (main effect of b) + SSab (interaction effect)

8

## In Factorial ANOVA, what is added to SStreatment to equal the SStotal, or total variance in the data?

### SSerror (error in the model)

9

## What is a main effect?

###
the effect of one IV averaged over the other variable or when the other variable is ignored

e.g. Assignment 4, Study 2

main effect of reinforcement scheduling on studying practices

10

## What is an interaction effect?

###
one IV is modified by the levels of another variable

e.g. Assignment 4, Study 2

interaction effect of reinforcement schedule on levels of reinforcer type

11

## What is a simple effect?

###
the effect of one variable at a SPECIFIC level of another IV

e.g. Assignment 4, Study 2

simple effect of random scheduling on studying

12

## What is the ANOVA summary table for 2-way analysis?

###
Source SS df MS F

A SSa a-1 MSa MSa/MSerror = main effect A

B SSb b-1 MSb MSb/MSerror = main effect B

AxB SSab (a-1)(b-1) MSab MSab/MSerror = interactino

Within SSerror ab(n-1) MSerror

Total SStotal N-1

13

## What is the same calculation for two-way ANOVA and one-way?

### Total = SStotal, and df = N-1

14

## When should the main effects be further examined?

### only when there is NOT a significant interaction effect. The presence of a significant interaction LIMITS the sense of the main effects - it is difficult to make a general statement about a variable's effect when the size of the effect depends on the level of a second variable

15

## A significant interaction indicates what?

### that the effect of ONE IV differs depending on the LEVEL of another IV

16

## Why are main effects misleading in the presence of interaction terms?

### taking the crossing line plot for yield by temperature and pressure, although the lines intersect, there is no main effect of pressure because the average score at the two pressures is the same. So note that it doesn't mean that pressure has no effect on the yield but that there is when it interacts with temperature

17

## When two lines in a factorial anova line chart are parallel, this indicates:

### no significant interaction

18

## When two lines in a factorial anova touch or cross, this indicates:

### a significant interaction

19

## What do you do after noting a significant interaction effect?

### test the simple effects!

20

## What does testing the simple effects of an interaction effect require?

### NO follow-up tests; examination of the interaction plot

21

## Why aren't supplemental analyses required if the researcher sees an interaction effect?

### the data also can provide information on how one variable differs depending on the level of another variable, which indicates a simple effect, the goal of further analysis

22

## What is the factorial anova formula for SStotal?

###
SStotal = Sum of (Xijn - X_..)^2

Sums of squares total equals the sum of data points each subtracted by the grand mean, squared

23

## What is the factorial anova formula for SStask?

###
SStask = nc x sum of (data from column/task of inquity - X_..)^2

sums of squares for task equals the number of comparisons x sum of data points for the task each subtracted by the grand mean, squared

24

## What is the factorial anova formula for SScondition?

###
SScondition = na x sum of (data points for the condition - X_..)^2

sums of squares for condition equals the number of conditions for variable A x sum of data points for the condition each subtracted by the grand mean, squared

25

## What is the factorial anova formula for SScell?

###
SScell = n x sum of (data points for the individual cell - X_..)^2

sums of squares for cell equals the number of cells x sum of data points for the cell each subtracted by the grand mean, squared

26

## What is the factorial anova formula for SStc?

### SStc = SScell - SStask - SScondition

27

## What is the factorial anova formula for SSerror?

### SSerror = SStotal - SScell

28

## How can you tell in a table if there are very large differences in means in the different tasks but small differences among conditions?

###
Decide using this data for analysis:

Smoking Pattern Recall Driving Total

Condition Task Simulation

Nothing 9.40 28.87 9.93 16.07

delayed 9.60 39.93 6.80 18.78

active 9.93 47.53 2.33 19.93

total 9.64 38.78 6.36 18.26

the differences under each task (pattern, recall, driving) all differ quite a lot, but the totals for conditions do not vary that much

29

##
Using this data for analysis, what can we say about the task and smoking condition?

Smoking Pattern Recall Driving Total

Condition Task Simulation

Nothing 9.40 28.87 9.93 16.07

delayed 9.60 39.93 6.80 18.78

active 9.93 47.53 2.33 19.93

total 9.64 38.78 6.36 18.26

### it looks as if there is a difference due to task and to smoking condition, which are main effects because they are the effect of one variable AVERAGED over the other variables

30

## In factorial ANOVA, how do you read the table for the main effect of a?

### Source A (IV1) = SSa / dfa (a-1)/ MSa / F= MSa/MSerror / Sig.

31

## In factorial ANOVA, how do you read the table for the main effect of b?

### Source B (IV2) = SSb / dfb (b-1)/MSb / F= MSb/MSerror / Sig.

32

## In factorial ANOVA, how do you read the table for the interaction effect?

### SourceAxB (IV1 x IV2) = SSab / dfab (a-1)(b-1) / MSab / F = MSab/MSerror = Sig.

33

## In factorial ANOVA, how do you read the table for the error in the data?

### Sourceerror = SSerror / dferror (ab(n-1)) / MSerror.

34

## In factorial ANOVA, how do you read the table for the total SS and number of participants?

### SStotal = SStotal / dftotal (N-1), same as 1-way ANOVA calculation

35

## In factorial ANOVA, how do you read the table for the proportion of variation in the DV explained by the IVs?

###
adjusted R squared = .xxx

(below the table)

36

## How do you restrict analysis to one level of the other variable in SPSS?

### use Data/Select Cases in SPSS, filtering which data that will be used, or that I will run separate analyses for each level of Task

37

## What can you remember condition and task as?

### Task has different levels, whereas condition is one or the other, or different

38

## What do you need to use to calculate simple effects?

###
MSerror from the overall ANOVA on the individual task analyses

e.g. first do a univariate comparison of means, and then use that MSerror in calculations when creating t-tests for simple task on data

**NOTE: HETEROGENEITY OF VARIANCE IS QUITE POSSIBLE BETWEEN GROUPS, SO USE WITH CAUTION

39

## What is good practice to consider when calculating simple effects in factorial ANOVA when using the overall MSerror?

### Heterogeneity of variance can fuck it up, so make sure Levene's is passed

40

## What does 3-way ANOVA mean?

### there are 3 iVs, and one DV

41

## How many main effects are in 3-way ANOVA?

### 3

42

## How many interactions are in 3-way ANOVA?

###
3 x 2-way interactions

1 x 3-way interaction

= 4

43

## What is more difficult to interpret in a 3-way anova? 2-way or 3-way interactions?

### 3-way!

44

## What is the ANOVA summary table calculations for 3-way ANOVA, particularly IV1?

### IV1 = A = Source A / SSa / dfa (a-1) / MSa / F= MSa/MSerror

45

## What is the ANOVA summary table calculations for 3-way ANOVA, particularly IV2?

### IV2 = B = source B / SSb / dfb (b-1) / MSb / F=MSb/MSerror

46

## What is the ANOVA summary table calculations for 3-way ANOVA, particularly IV3?

### IV3 = C = Source C / SSc / dfc (c-1) / MSc / F = MSc/MSerror

47

## What is the ANOVA summary table calculations for 3-way ANOVA, particularly the interaction of IV1 and IV2?

### IV1 = A, IV2 = B, so AxB = Source AB / SSab / dfab (a-1)(b-1) / MSab / F=MSab/MSerror

48

## What is the ANOVA summary table calculations for 3-way ANOVA, particularly the interaction of IV1 and IV3?

### IV1 = A, IV3 = C, so AxC = Source AC / SSac / dfac (a-1)(c-1) / MSac / F=MSac/MSerror

49

## What is the ANOVA summary table calculations for 3-way ANOVA, particularly the interaction of IV2 and IV3?

### IV2 = B, IV3 = C, so BxC = Source BC / SSbc / dfbc (b-1)(c-1) / MSbc / F=MSbc/MSerror

50

## What is the ANOVA summary table calculations for 3-way ANOVA, particularly the interaction of IVs 1, 2, and 3?

### IV1 = A, IV2 = B, IV3 = C, so AxBxC = Source ABC / SSabc / dfabc (a-1)(b-1)(c-1) / MSabc / F= MSabc/MSerror

51

## What is the ANOVA summary table calculations for 3-way ANOVA, particularly the error in the data?

### error in data for 3-way between-design ANOVA is within subjects (individual differences), therefore Source = Within / SSerror / dfwithin (abc(n-1)) / MSerror.

52

## What is the ANOVA summary table calculations for 3-way ANOVA, particularly the total SS in the data?

### Total is Source total / SStotal / dftotal (N-1)

53

## When analysing the results of a 3-way ANOVA, what is the first step?

### 1. determine whether 3-way interaction is significant. If so, ignore others; if not, go to next step

54

## When analysing the results of a 3-way ANOVA, what is the second step?

### 2. determine whether 2-way interaction is significant. If so, ignore main effects; if not, go to next step

55

## When analysing the results of a 3-way ANOVA, what is the third step?

### 3. determine the main effects

56

## What is a way to write out 3-way interpretation of a plot?

### the results of the three-way ANOVA between-subjects design indicate a considerable interaction effect between the sinker weight and line weight (see Figure 1): for 1 kg lines, the distance line casts being made with 12 oz sinker was longer than that with 8 oz sinker; whereas, for 2 kg lines, the difference in the distance line casts being made with two types sinker was relatively slight (see tAble 1).

57

## How do you start a factorial ANOVA between-subjects design in ANOVA?

### Analyze - General Linear Model - Univariate - Model - Specify "Full Factorial" model - Posthoc - LSD, Bonferroni, Tukey's, Scheffe

58

## What do you have to report before the ANOVA for factorial between-subjects ANOVA?

### Levene's test (F(dfbetween,dfwithin) = x.xx, p = .xxx). If significant, use modified ANOVA results, if not, don't make special corrections for the design

59

## Once you confirm a significant interaction, what do you report?

### pairwise comparisons

60

## Example reporting main effects for factorial between-subjects design ANOVA...

### The main effect of message discrepancy yielded an F ratio of F(1,24) - 44.40, p < .001, omega-squared = ..., indicating that the mean change score was significantly greater for larger-discrepancy messages (M = 4.78, SD = 1.99) than for small-discrepancy messages (M = 2.17, SD = 1.25). the main effect of source expertise yielded an F ratio of F(1,24) = 25.4, p < .01, omega-squared =..., indicating that the mean change score was significantly higher in the high-expertise message source (M = 5.49, SD = 2.25) than in the low-expertise message source (M = 0.88, SD = 1.21). The interaction effect was non-significant, F(1, 24) = 1.22, p > .05, omega-squared = ...

61

## When a violation of homogeneity assumption is found in factorial between-subjects design ANOVA, what are the options?

###
switch to nonparametric techniques

follow a special procedure

calculate unweight means and calculate F ratio based on those means

62

## How do you calculate weighted marginal means for in factorial between-subjects design ANOVA

### (weighted cell mean for A x N(A) + weighted cell mean for B x N(B))/ (Na+NB)

63

## If A has a weighted cell mean/WCM of -1.2089 and Na = 14, and B has a weighted cell mean of 0.0750 and Nb = 12, what is the weighted MARGINAL mean?

###
WMM= (WCMa x Na + WCMb x Nb)/(Na+Nb)

=(-1.2089 x 14 + 0.0750 x 12)/(14+12)

= -0.6163

= -0.62

64

## How do you calculate unweighted marginal means in factorial between-subjects design ANOVA?

### WCMa + WCMb/k

65

## If WCMa is -1.2089 and WCMb is 0.0750, what is the UNWEIGHTED marginal mean (UMM)?

###
UMM=(WCMa + WCMb)/k

=(-1.2089 + 0.0750)/2

= -0.5670

= -0.57

66

## How do you calculate the F-ratio for means when a violation of homogeneity assumption is found in factorial between-subjects design ANOVA?

###
nh = k/(1/n11 + 1/n12 + 1/n21 + 1/n22)

e.g.

= 4/(1/14 + 1/12 + 1/10 + 1/4)

= 7.925

= 7.93

67

## What do you use to calculate the F-ratio in factorial between-subjects design ANOVA when a violation of homogeneity assumption is found?

### unweighted means, harmonic mean of the nij

68

## What CAN'T you use when a violation of homogeneity assumption is found in factorial between-subjects design ANOVA?

###
unweighted means

SSerror = SStotal - SScell (and therefore SStotal can't be calculated)

69

## Why can't we use SSerror when calculating the F-value in factorial between-subjects design ANOVA when violation of HOV is found?

### Because who the hell really knows what the error is since HOV is violated? It is likely a helluva lot larger

70

## What does SPSS the option to run ANOVA in factorial between-subjects design ANOVA with an unequal sample size?

### using Type III Sum of Squares

71

## What DOESN'T SPSS give the option to run in factorial between-subjects design ANOVA with an unequal sample size?

### unweighted marginal means

72

## If you have IV1 known as D and IV2 known as A in factorial between-subjects design ANOVA, what would SPSS show, and what data to use to report results?

###
Tests of BETWEEN-SUBJECTS EFFECTS

DEPENDENT VARIABLE DV

Source: Type III SS df MS F Sig.

IV1 = D SSd dfD MSd x.xx x.xx = main effect of D on dv

IV2 = A SSa dfa MSa x.xx x.xx = main effect A on dv

IV1x2 = D*A SSab dfab MSab x.xx x.xx = interaction of dxa on dv

within = error SSerror dferror MSerror

73