Final exam questions Flashcards
(220 cards)
1
Q
In a 2-way within-subjects ANOVA, there are n participants. ______
A
True.
2
Q
In a 2-way mixed-factors ANOVA where A is the within-subjects factor, there are a n participants. ______
A
False
3
Q
For a 2-way within-subjects ANOVA, the main effects of the treatments and the interaction are all tested using different MSError terms. ______
A
True
4
Q
For a 2-way mixed-factors ANOVA, the main effects of the treatments and the interaction are all tested using different MSError terms. ______
A
False
5
Q
The maximum value of eta^2 is ∞. ______
A
False
6
Q
For treatment A in a 2-way design, the value of partial eta^2A is always greater than or equal to the value of eta^2A. ______
A
True
7
Q
For a 1-way design, the value of eta^2 does not depend on whether you perform a within-subjects or between-subjects analysis. ______
A
True
8
Q
A small Cohen’s effect size, f, for an ANOVA means that the null hypothesis will fail to be rejected. ______
A
False
9
Q
9) ANOVA is robust to violations of homogeneity of variance so long as the design is balanced. ______
A
True
10
Q
In a 1-way within-subjects analysis, if n = 8 then dfSubjects = 7. ______
A
True
11
Q
In a 1-way within-subjects analysis, if N = 32 and you find F(3,21) = 3.12 then n = 11. ______
A
False
12
Q
n^2 and r^2 are similar in that they both range between 0 and 1.
A
True
13
Q
for a simple ANOVA, the df between is:
A
k-1
14
Q
for a simple ANOVA, the df within is:
A
N-k
15
Q
MS is…?
A
sums of squares of variance
16
Q
Xji is such that j refers to
A
the order of group overall/level
17
Q
Xji is such that i refers to
A
the order of the individual observation in a group
18
Q
what is the structural model?
A
a method to decipher the individual sample as a part of an ANOVA, as it differs from the local treatment as well as the mean of all observations
19
Q
what is the process by which all treatment means depart from a so-called grand mean?
A
centering
20
Q
what are all treatment means departing from when compared to the mean of all observations?
A
the grand mean
21
Q
once the data are centred, what can the structural model be viewed as accounting of?
A
why any observation deviates from the ground mean
22
Q
what is the structural model for ANOVA composed of?
A
the total deviation of an observation from the grand mean which equals
the component of the deviation that is due to treatment differences, plus
the component of the deviation that cannot be accounted for by treatment differences
23
Q
for the structural model, what does the total deviation from the mean look like between levels?
A
a bell curve on the left has its datapoint reaching as far to the centre mean/grand mean
24
Q
for the structural model, what does the ERROR/within deviation from the mean look like between levels?
A
a bell curve on the left has its datapoint reaching to the centre of the LOCAL mean
25
for the structural model, what does the TREATMENT/between deviation from the mean look like between levels?
a bell curve on the left and the difference between that local mean from the grand mean
26
what are other names for treatment in the structural model?
the explained, or between
27
what are other names for error in the structural model?
the unemplained or within
28
What according to the structural model describes a treatment effect?
the between component (or "group" or "treatment" or "explained" component") expresses the extent to which treatment j shifts the mean of its population from the overall mean
29
What would the structural model characterize as the "sums of squares"?
the sums and then squared of the individual deviations of observations in each sample in the dataset from the overall mean
30
What would the structural model characterize as the F-ratio?
the between variance from the mean over the within variance from the mean
31
What does ANOVA terminology call a variance?
"mean squares"
32
What are the degrees of freedom for dftotal for a 1-way anova?
dftotal = total numbers of observations minus 1, or N - 1
33
What are the degrees of freedom for dftbetween for a 1-way anova?
dfbetween = # of groups/levels/treatments minus 1, or k - 1
34
What are the degrees of freedom for dfwithin for a 1-way anova?
dfwithin = dftotal - dfbetween
35
What is the structural model for a 1-way ANOVA?
(Xji-u) = Tj + Eji
36
According to the structural model, what is the ANOVA ratio, or F?
the ratio of MS estimates of the variance in the population
37
What are the degrees of freedom for error in a 1-way ANOVA?
dferror = k(n-1); OR....dftotal - dftreatment
38
Do degrees of freedom depend on experimental results in a 1-way ANOVA?
No
39
What is the formula for MS in the ANOVA table?
Respective SS/respective df = same MS
40
What is a general term for ANOVA designs with more than 1 independent variable?
a multi-way ANOVA
41
Are treatments/factors determined randomly?
Not necessarily. Such can include gender, which is inherent to the participant and not malleable
42
What are the different categories of eacah treatment called?
levels
43
What is a key attribute of a design having multiple independent variables?
multiple treatments are applied simultaneously
44
How does a multiple anova differ in tabling data?
```
1-way = k = # of treatments
2-way = a for 1st level, b for 2nd level, etc. (axb)
```
45
if you have 2 levels of treatment a, and 3 levels of treatment b, what would you label individual datapoints?
xa,b,order in group
e.g. item 4 in level a2 b3 would be X234
46
What is each particular combination of treatment levels within the design for a multiple ANOVA design called?
a cell
47
Why do observations within a cell differ?
Solely due to experimental error
48
What is the cell mean?
The mean of all observations within a particular cell, similar to the treatment means for 1-way ANOVA design
49
What is the formula for number of observations in a multiple ANOVA design?
N = sum (nkj);
| if 2-way, axbxn
50
What are designs where all the cells have observations?
a factorial design; if all the same, a balanced factorial design
51
How would you indicate a test for a ___ effect in a multiple ANOVA?
The simple effect of IV1 on DV, for IV2 level 2 (e.g. the simple effect of intervention on stress for/at females (from gender)
52
What kind of test can follow those for simple effects?
pairwise comparisons (or multiple pairwise comparison t-tests)
53
How would you plot a simple effect of B on A1 or A2?
You would likely plot an interaction plot with the levels of B on the horizontal axis, the interval amount for DV on the horizontal axis, and then 2 lines both indicating points for A1 and another for A2 to signify the simple effect of B on each of them at different levels of B
54
After you plot a simple effect, are you done?
No! a t-test needs to be determined in order to assess whether it is significant; at present it is simply a visual analysis
55
How many possible simple effects can be investigated using an a x b factorial ANOVA?
a + b possible simple effects
56
What do you typically consider main effect?
collapsing across levels of a variable in an effect; the effect of IV1 on DV (with no mention of IVx anywhere)
57
What do you calculate when you collapse across means in the margins of a 2-way table in order to calculate the means necessary for examining the main effect of one fof the IVs?
the marginal means
58
Is it possible to have a main effect for one IV but not the other?
yes
59
What is the best order to assess effects?
interaction, simple and then (if applicable), main
60
What is another way of indicating an interaction?
a modulation of the simple effects of IV2 by the variable IV1
61
What are 2 points about interaction effects?
1 - the lines in an interaction plot DO NOT need to cross for an interaction to be present
2 - the lines in an interaction plot may be nonparalleld due only to sampling variability, i.e., there is no real interaction only an apparent one due to sampling variability
62
Is it possible for an interaction to be present even if neither variable exhibits a main effect?
Yes. It can simply be interactions masking main effects
63
Analyses in which there is only 1 DV are called “” analyses
“univariate”
64
What is the structural model formula for a 2-way ANOVA?
Xkji - u = ak + Bj + aBkj+Ekji , or Xkji - u = Tkj + Ekji; ak = effect of treatment a; Bj = effect of treatment B; aBkj = effect of a x b interaction
65
What do the terms in the structural model form?
the various sum-of-squares used in a 2-way ANOVA; Xkji - u = SStotal; ak = SSa; Bj = SSB; aBkj = SSaxb; Ekji = SSerror
66
For the Eysenck example of age x instruction on time(?), what would be on the ANOVA table?
```
Source would have:
age/a
instruction/b
age x instruction/axb
error/E
total
```
67
What are the degrees of freedom for ak or Bj (main effects) in the ANOVA table?
k - 1
68
What is the df for an interaction in the ANOVA table?
product of all df for main effects: dfa x dfb (NOT ka x kb)
69
What is used to form all F-ratios in a 2-way ANOVA?
the MSerror, which estimates the within estimate of population variance
70
What do each of the F-ratios in a 2-way ANOVA test?
either a main effect or an interaction effect
71
what is the structural model of overall effect?
Xkji - u = Tkj + Ekji; you would calculate the SSexplained by adding all of the SSmain and interaction effects together, , or you can take the SStotal and substract the SSerror to get the explained total. You can also for df take the dftotal and subtract the dferror to get the dfexplained...you are ignoring the a, b, and axb levels in favour of aggregating them...and the MSexplained can be done by SSexplained/dfexplained= MSexplained
72
What is the explained model entry called in SPSS?
the "corrected model" entry
73
what are two measurements of effect size for ANOVA?
Cohen's f, and n^2 (similar to r^2, a popular regression technique)
74
What are the properties for effect sizes in ANOVA?
- hey don't depend on measurement scales
- they don't depend on sample size
- they don't depend on arbitrary choices made to increase statistical power (e.g. creating a larger alpha)
- they are useful in meta-analysis
75
What does n^2 refer to?
magnitude of the effect, or proportion of explained variation in dependent variable values that is associated with differences in the independent variable
76
How is n^2 pronounced?
eta squared
77
What is the 1-way ANOVA magnitude of the effect formula?
n^2 = SStreatment/SStotal
78
What does the value of n^2 always lie between?
0 and 1 (it's a proportion, therefore a fraction of a total, i.e. 1)
79
What is eta squared according to the null hypothesis?
n^2 = 0
80
What also does the magnitude of the effect measure?
the importance of the effect (e.g. an effect may be significant, but is it important?)
81
Again, what is the formula for magnitude of the effect for 1-way ANOVA?
SStreatment (or SS explained) / SStotal
82
what does SPSS call leta squared or n^2?
R squared, since it works like the r^2 in regression problems
83
What is another way of indicating that the ANOVA tests the null hypothesis such that n^2 = 0?
the null hypothesis consists of saying that differences in treatment do not explain any of the variation in the dependent variable
84
Is eta squared a biased or unbiased estimator of the true proportion of variance?
biased
85
Why is eta squared a biased estimator of the true proportion of variance?
it overshoots the mark when attempting to explain how treatments affect a population
86
What is an unbiased estimator for the proportion of explained variation in the population?
quantity, or "adjusted R squared"; the formula for 1-way anova is =
sStreatment = (k1) MSerror/
(SStotal + MSerror)
87
How do you calculate eta squared for 2-way ANOVA?
SEPARATE N^2 FOR EACH FACTOR/VARIABLE (a, b, and axb):
Na^2 = SSa/SStotal
Nb^2 = SSb/SStotal
Naxb^2 = SSaxb/SStotal
88
What is the value for each eta squared calculation for each variable of a two-way anova?
Each one befit a proportion, therefore each one has a value that is between 0 and 1
89
How is n^2 interpreted for a 2-way anova?
a proportion of the overall variation in the DEPENDENT variable that is explained by differences in a FACTOR (or interaction)
90
Where does SPSS indicate the R squared calculation in the 2-way ANOVA table?
the bottom left portion of the screen
| e.g. R Squared = .729 (Adjusted R Squared = .702
91
What is the Adjusted R Squared the same as?
oo^2 symbol, which is the UNBIASED counterpart of the overall eta squared value
92
How is Cohen's f calculated?
it is the standard error of the mean DIVIDED BY pooled standard deviation over all k treatment conditions, OR
f = Sm/Spooled
93
What is a shortcut to determinee Cohen's f for a 2-way ANOVA?
f = square root of(SStreatment/SSerror), with a result that is between 0 and INFINITY
94
What are the equivalent effect sizes for Cohen's f vs Cohen's d (small, medium, large)?
S - Cohen's d 0.2, f 0.1
M - Cohen's d 0.5, f 0.25
L - Cohen's d 0.8, f 0.4
EFFECT SIZES OF D ARE HALVED TO MAKE F!!!
95
What formula using Cohen's f makes eta squared?
n^2 = f^2/(1+f^2)
96
What formula using eta squared makes Cohen's f?
f = square root of(eta squared/(1-eta squared))
97
What are the equivalent effect sizes for Cohen's d, f, and eta squared?
S - Cohen's d 0.2, f 0.1, eta squared .01
M - Cohen's d 0.5, f 0.25, eta squared .06
L - Cohen's d 0.8, f 0.4 ], eta squared .14
EFFECT SIZES OF D ARE HALVED TO MAKE F!!!
It's not as simple for eta-squared; memorize! (TREAT THESE SIZES AS PERCENTAGES %%%%%%%%%%%%%)
98
How many Cohen's effect sizes are there for a 2-way ANOVA?
1 for each factor/interaction, therefore 3 (Fa, Fb, and Faxb)
99
What is the formula for calculating Cohen's f for the effect size of variable a?
Fa = square root of (SSa/SSerror)
100
What is the formula for calculating Cohen's f for the effect size of variable b?
Fb = square root of (SSb/SSerror)
101
What is the formula for calculating Cohen's f for the effect size of the interaction in a 2-way ANOVA?
Faxb = square root of (SSaxb/SSerror)
102
Why do we calculate partial eta squared calculations for Cohen's f?
Because there is not a direct relationship between Fa and n^2a, so we say it is n^2a partial to then calculate Cohen's f for individual factors in 2-way ANOVA
103
what names can we use for the cousin of eta squared as related to Cohen's f?
partial eta squared, or eta squared partial
104
How do we calculate treatment A in a 2-way design for eta-squared a partial?
N^2a,partial = (SSa/SSa+SSerror)
105
What elements do we eliminate when calculating n^2a,partial in the formula?
SSb, and SSaxb, because we assume they have no effect (H0 = 0), therefore we can take them out of the equation
106
How can you interpret partial eta squared for level a for a 2-way ANOVA?
the proportion of variation in the dependent variable that would be explained by differences in factor A, IF treatment B has been held steady at a single value (remained consistent) through the entire experiment
107
How else would you call in a 2-way ANOVA calculating the proportion of variation that would be explained by one treatment A when Treatment B is held steady?
partialling out the effect of B!!!!!!!!!!!!!!!!!
108
Is there a distinction between eta squared partial and eta squared in a 1-way ANOVA?
No
109
Are there partial eta squared values for all factors and interactions in a 2-way design?
yes
110
What values ar directly related to Cohen's f in a 2-way ANOVA?
PARTIAL ETA SQUARED VALUES (REGULAR ONES ARE ONLY DIRECTLY RELATED TO COHEN'S F IN A 1-WAY ANOVA)
111
What type of estimates of effect size does SPSS calculate in a 2-way ANOVA?
IT PROVIDES PARTIAL ETA SQUARED VALUES FOR INDIVIDUAL FACTORS, NOT REGULAR ETA SQUARED VALUES
112
Does SPSS calculate the eta squared values for a, b, and axb in a 2-way ANOVA table?
No. It only calculates partial eta squared values for individual factors, and they can be placed on the right column of the table
113
What does SPSS characterize SStotal as in a 2-way output table?
SSCORRECTED TOTAL
114
For a 2-way ANOVA test, what does a higher non-centrality parameter measurement equal?
higher power!
115
If you have a big sample and power, is the non-centrality parameter likely high or low?
High
116
What helps ensure a high non-centrality parameter for a two-way ANOVA design?
a bigger sample, and high power, and a smaller SSerror
117
how do you calculate power?
by calculating the noncentrality parameter
118
What is the formula for a 1-way ANOVA for the noncentrality parameter?
h = f^2N
119
What is another method to calculate h or noncentrality parameter for a 1-way ANOVA?
h = SStreatment/SSerror * N, therefore sample size affects the size of the noncentrality parameter
120
What is the noncentrality parameter?
The noncentrality parameter is just a one-number summary that serves as a single overall measure of difference. It gives us a simple way to form a test for any differences between any of the group means
121
How is the noncentrality parameter for 2-way ANOVA calculated
Actually, there is a noncentrality parameter for each factor/interaction of a 2-way anova, so there are THREE calculations:
ha = Fa^2N = SSa/SSerror * N
hb - Fa^2N = SSb/SSerror * N
h
122
What is another name for the SSerror for a 2-way analysis?
residual error
123
Why is it more advantageous to use a 2-way analysis instead of a 1-way?
it tends to create a smaller residual error because more of the unexplained variation is thereby explained in the new variable that is introduced, as well as a potential interaction between the new and old variable in the 1-way ANOVA design
124
What has more power, a 2-way anova or a 1-way anova?
2-way, because it explains more of the variation than the 1-way, UNLESS the second variable does not appear to make a difference, or its interaction, which would make it even weaker than the 1-way variable (the larger the SSerror, the greater the likelihood of more power, a higher noncentrality parameter, and perhaps even a greater likelihood of significance and even importance; also, an ineffective nuisance variable creates a lower degrees of freedom which raises the amount of MSE to then calculate the F-statistic)
125
What kind of variable is often used to simply get rid of some extra residual error in a multiple anova design?
a nuisance variable
126
what do we consider a dependent-groups ANOVA?
when observations in different treatment groups are correlated, such as when we have the same participants appear in the different treatment groups (it is then a dependent-measures design in general, and for this specific method it is a repeated measures design)
127
How do you calculate N for a balanced 2-way factorial design?
N = a x b x n
128
How do you calculate N for a balanced 1-way design?
N = k x n
129
what is the formula for a paired-samples t-test?
t = Md / (Sd x square root of (1/n))
130
As the correlation between samples grows larger (whether due to being from the same participants, or a personality trait having similar components), what happens to the noncentrality parameter?
it gets larger (closer to 1, from 0)
131
How does a dependent-groups design affect the F-statistic?
it typically creates a smaller "within variance" from which to calculate the F-statistic
132
How do you assess how a repeated-measures ANOVA works to remove the effects of individual differences?
1 analyze the data as thought we did not realize it was a repeated measure (i.e. looking at SStotal = SStreatment + SSerror ONLY)
2 reanalyze the data using repeated-measures techniques
133
Do we encode individual differences if they are stable or unstable?
Stable. If they are consistent regardless of the treatment, then are inherent to the individual, and we can theoretically "throw them out" in order to concentrate on the effect of the treatment/s. Otherwise, by focusing on the individual differences, we have included a new independent variable: THE SUBJECT HER/HIMSELF
134
In order to "weed out" individual differences, what would the new structural model look like?
Xji - u = Ti + (pi)i + Eji
OR...
SStotal = SStreatments + SSsubjects + SSerror
135
What does a repeated measures ANOVA table look like?
Source has under it: Treatment, Subject, Error, and Total.
136
What changes when you change a design from 1-way to a repeated measures ANOvA?
the treatment values for SS remains the same, but that for subject, and error (MSE) differs, totalling the SAME as the 1-way
...
SIMPLY CALCULATE THE INCLUSION OF SUBJECT AND CHANGE THE AMOUNT OF ERROR THAT RESULTS, HOWEVER EVERYTHING ELSE SHOULD BE THE SAME, APART FROM THE RESULTING F-STATISTIC
137
What does SSerror split off into from a 2-way anova to a repeated measures ANOVA?
SSerror (Under source, called Error) becomes SS subjects (or Subjects) and SS error (*New Error)
138
How do you calculate the (pi)i (individual difference) measure?
estimated by measuring the deviation of subject mean from the grand meant
...
(pi)i = Msubject,i = M...
...
Taking the subject means and subtracting the grand mean from it...or the marginal means for the individual subject, minus the grand mean for all of the subject/marginal means calculated
139
What do you calculate to get SSsubjects in a repeated-measures ANOVA?
each (pi)i term squared, and then added together
(sums of squares for the subjects in order to "get rid of them" to see what JUST THE TREATMENT shows an effect, not the individuals themselves, creating a very sophisticated design)
140
Again, what is the results table for a 2-way repeated-measures design?
```
Source has:
Subjects
Variable A -- F-statistic is noted here because this is the variable that we want to study, NOT THE SUBJECTS
Error
Total
```
141
A treatment effect that is measured WITHIN individuals is called a
within-subjects effect (we are dealing with individual subjects, NOT GROUPS)
142
A treatment effect that is measured BETWEEN individuals is called a
between-subjects effect (we are dealing with individual subjects, NOT GROUPS)
143
Since we are dealing with differences between and within subjects, what is another way of writing the results for a 2-way repeated-measures ANOVA?
```
Source:
Between subjects
Error ---
Within Subjects
Weeks---
Error---
Total
```
144
Again, to delete out individual differences, what are they required to be ?
Stable, otherwise we cannot determine if it is in fact due to individual differences
145
How else can we characterize residual error in a repeated-measures design?
the residual errors can be seen as the TreatmentXsubjects interaction (subjects being a nuisance-like variable)
146
How else can within subjects error be labelled as in a repeated-measures design?
```
treatmentXsubjects interaction...
...
Source
Between
subjects
Within
Treatment
Treatment x subjects (ERROR)
Total
```
147
What is the df for within error?
df treatment x df subjects (k-1) x (n-1)
148
What is a mixed design?
a 2-way design wih 1 within-subjects variable and 1 between-subjects variable, just to confuse the F out of me
149
How would you plot out a mixed design that is 2 x 3 with fact A between, and factor B within?
B
A G1 G1 G1
G2 G2 G2
150
How many participants are in a mixed design that is 2 x 3 with fact A between, and factor B within?
between variable/a x n participants (there are 2 groups for a, whereas it's the same group for b levels)
151
How would you write out the structural model for a mixed design ANOVA, with 1 within-subjects variable and 1 between-subjects variable?
Xkji - u = ak + Bj + aBkj + ((pi)ki + Ekji)
...
it is the same as a 2-way between-subjects (independent) structural model with a new term, (pi)ki added.
...
this shows an interaction between the within-subjects variable B and subjects?????
...
Most importantly, it ciphons off the between-subjects error and the within-subjects (residual) error = total error in parentheses... so what you're really looking at is
Subject datapoint = main effectA + main effect B + interaction effect AxB + total error (between-subjects and within-subjects)
152
How many sums-of-squares calculations are expected in a mixed design ANOVA with 1 within and 1 between?
```
5, PLUS SS total = 6
Source
Between subjects ------------------------------------------------------
A
Subjects (error)
Within subjects ----------------------------------------------------------
B
B x A (interaction)
B x subjects (error)
Total
```
153
What levels do we indicate a F-statistic for in a mixed design ANOVA with 1 W and 1 B?
Between Variable A (main effect)
Within Variable B (main effect)
Within Variable B x A (interaction)
154
How do you calculate the df for a mixed design ANOVA table with 1 B and 1 W?
```
Source
Between
A = kA -1
Subjects = total participants -1) -dfa
Within
B = kB - 1
B x A = (dfB) x (dfA)
B x subjects = (dfB) x (dfBetweensubjects--listed above)
Total = add everything together, or N-1
```
155
What does an ANOVA results table look like for a 2 within-subjects ANOVA design?
```
Source
Between
Error
Within
A (stays the same between designs)
ErrorA
B *stays the same between designs
ErrorB
AxB (stays the same between designs)
ErrorAxB
...
Each effect (2 main, 1 interaction) has their OWN ERROR term, which is used to calculate their SEPARATE MSerror for the F-stat, instead of the "within error" source in a mixed or a standard repeated-measures design
```
156
What is the rule for calculating the between-subjects vs. within-subjects?
For between subjects, all effects tested use the SAME MSE (in order to create some structure amongst different variables)
...
For within subjects, all effects tested use their OWN MSE (in order to create some variability amongst the same participant group)
157
What is a rule for the analysis of multiple within-subjects variables?
for any WITHIN subjects effect, the appropriate SSerror is SSeffectxsubjects (for instance, to test for the main effect of A, use SSaxsubjects
158
What is another way of plotting a 2-within subjects ANOVA table?
```
Source
Between
Subjects
Within
A SSa dfa MSa MSa/MSaxs
AxS SSaxs dfaxs MSaxs ------
B
BxS
AxB
AxBxS
```
159
What is a formula for looking at the SStotal error for a 2 within-subjects variables design?
SS total error = SSsubjects + SSaxs + SSbxs + SSaxbxs
...
we want to delete all of this error in order to concentrate on simply the effect of the treatments, which we create F-statistics for. The data (except for the F stats) should not change for that of the treatment variables or the Source total; only the errors would be modified
160
What is a rule for analysis of multiple WITHIN-subjects variables?
for any within-subjects effect, the appropriate SSerror is SSeffect x subjects (for instance, to test for the main effect of A use SSaxsubjects)
161
What are the assumptions for ANOVA?
That the population is normal, the distributions of errors for each treatment are indicative of that from the same population, and that each participant is independent/individual of each other within a treatment
162
If violated, what could be a result of an assumption of ANOVA not fulfilled?
the result is losing control over the rate of Type I errors; it may be much larger than we think it is
163
When is ANOVA robust from Type I errors?
- violations of normality (only slightly affected if n < 30)
- if the design is BALANCED
- errors WITHIN a treatment group are INDEPENDENT of each other
164
When is ANOVA NOT robust from Type I errors?
- if the populations from which the samples are drawn are ALL significantly skewed in the SAME direction
- if the design is UNBALANCED
- errors WITHIN a treatment group are DEPENDENT on one another
165
What should be done if samples are skewed in the same direction?
consider a transformation, using SPSS
166
What is actually tested using ANOVA re HoV?
if the treatment populations all have the same variance, and if they are all normally distributed as we also assume, then the ONLY way left for them to differ is in the values of their treatment means
167
How do you test ANOVA for homogeneity of variance?
Using Levene's test! If the result is not significant, then use data as originally intended. If not, use the modified Welch's test ("equal variance is NOT assumed" row of SPSS)
168
What kind of plot do you refer to when a treatment group in an ANOVA design is dependent of another?
a lag plot, in which the observations Xi in a group are plotted against their neighbours Xi+1.
169
What does a lag plot usually look like?
a structureless cloud
170
When are violations of assumption for ANOVA serious?
when using an unbalanced design, and when the observations are NOT independent (this does not refer to repeated participants...this means that another factor ties them together in which would not easily be noticeable in an ANOVA design)
171
When referring to repeated measures design, what is another assumption of ANOVA?
that not only is HoV maintained, but that covariances (similar to correlations) of DEPENDENT-variable values are the SAME between every pair of cells
172
What does it mean when covariances of dependent-variable values are the same between every pair of cells in a repeated-measures ANOVA?
compound symmetry, or sphericity
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What is compound symmetry?
when the covariances (similar to the correlations) of dependent-variable values are the same between every pair of cells (a.k.a. sphericity) in a repeated measures design
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What is sphericity?
when the covariances (similar to the correlations) of dependent-variable values are the same between every pair of cells (a.k.a. compound symmetry) in a repeated measures design
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What do we use to calculate HoV in a 1-way repeated measures design?
a variance-covariance matrix
...
the diagonals give the variances at each treatment level and the off-diagonals give the covariances between treatment levels (covij = covji so the upper part of the matrix is not written down)
var11
cov21 var22
cov31 cov32 var33
cov41 cov42 cov43 var44
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How do you determine sphericity?
if the order of subjects along different treatment levels is consistent throughout the experiment
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What does the assumption of sphericity mean?
that the deviations of subject means from the grand mean represent the variation due to individual differences
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What test do you use to test for sphericity AND homogeneity of variance?
Mauchley's test
179
What conditions can you only use Mauchley's test for?
WITHIN-subjects variables that have 3 or more levels
180
Can you use Mauchley's test for a between-subjects design?
No
181
Can you use Mauchleys' test for a mixed design with 2 levels of within-subjects?
no, use Levene's since determining between two levels doesn't make a big difference
182
Are violations of sphericity common?
Yes, it's sometimes hard to detect changes between subjects.
183
What does E stand for in the structural model?
epsilon, a measure of how far the data depart from sphericity
184
What does epsilon measure in a repeated measures design?
how far the data depart from sphericity...needs to be in a repeated measures design
185
What should you do if Mauchley's test is significantly smaller than 1?
use an alternative to the usual within-subects ANOVA that has a reduced number of degrees of freedom to preserve the Type I error rate. This is so that you can allot for changes of individual differences throughout the exam
186
What are alternate procedures in SPSS for sphericity?
Greenhouse-Geisser
187
Why is using the Huynh-Feldt procedure more preferred than the Greenhouse-Geisser test, even though the latter is traditionally used most often for tests of sphericity?
it tends to give up less power
188
If Mauchley's test isn't passed, what do you do?
Ues either the G-G or the H-F tests for the appropriate df to get the SAME F and significance level (controls for more error to make sure the info is more accurate)
189
How do you calculate n^2 (proportion of variance explained by the treatment)?
Usually it's SStreatment tested over SStotal
190
What is ANOVA a test of?
The means
191
What do all ANOVA designs presuppose?
a single dependent variable that is at least interval in nature (so that you can calculate the means) and one or more categorical independent variable
192
When would you not use an ANOVA?
you'd use an analog design if the iV is interval or better, or you would if the ANOVA violated tests of HoV, sphericity, balance, etc.
193
What is higher power: ANOVA or analog designs?
ANOVA designs, IF assumptions of HoV and normalcy and independence of participants are met)
194
What test would you use for 1 IV with 2 or more levels?
a one-way ANOVA
195
What test would you use for ordinal or interval IVs for 2 or mroe levels?
Kruskal Wallis
196
What test would you use for categorical IVs for 2 or mroe levels
chi-squared test
197
What are examples of ordinal data?
rank in the army, grades (letter), etc.
198
What are examples of categorical data?
pass or fail an exam, gender, etc.
199
What are examples of interval data?
temperature levels
200
What are examples of ratio data?
weight scales
201
What is the Kruskal-Wallis test?
it's a DV (ordinal) and IV (categorical) design, with RANK scores given for each observation, and teh mean rank score is calculated in teach group
202
What stats are used for the Kruskal-Wallis test?
H or K, giving a x^2 distribution if all the samples come from the same population
203
What are tests that do not require normal distribution
nonparametric or distribution-free
204
What is another name for the Mann-Whitney test?
Wilcoxon test, a nonparametric analog test for the independent-samples t-test
205
What test do you use for a nonparametric, 1-way WITHIN-subjects test with an ordinal DV?
Friedman's test
206
What is a dichotomous variable?
one that we can't calculate means, therefore calculate proportions
207
What analog test do you use to test 1 iv with 2 or more levels that are CATEGORICAL?
x^2/chi squared test of independence (proportionality, like percent extro or introvert and colour test)
208
What is another name for the chi squared test?
the x^2 test of independence
209
Are there nonparametric tests for all ANOVA designs?
yes
210
What are the advantages of nonparametric analog tests?
they do not require assumptions of normality, and do nto have to always test for the mean
211
What is an advantage of using an ANOVA over a nonparametric analog?
more power
212
What kinds of tests are best for interval x interval design tests?
correlation and regression tables
213
Are correlation or regression tables in a different order?
Yes, which is the main advantage over ANOVA design, albeit we would get the same results for both in either design
214
What if in a regression or correlation table there IS an important order required for the data?
then a straight line would go through it to determine the equal intervals in x are associated with equal intervals in yk
215
what do you call the line representing the regression onf Y on x in a regression table?
a PREDICTION
216
What does the regression line always include?
```
the mean (Mx, My) of ALL DATA POINTS
...
Y = a + bX
...
(a = value of Y when X is p)
(b = slope of the line)
```
217
In a regression table, if b is zero, then what can be said about the relationship?
x and y are not connected with each other in any way
218
What dos the regression line in a regression table do?
- it shows the part of the overall variation in Y that is explained by differences in X
- it maximizes explained variation in Y
219
What kind of test is it for b in a regression table?
Y = a + bX
a t-test
220
What to study for ANOVA tables in the exam
1-way within-subjects design, and 2-way within- and 2-way between-subject designs, as well as mixed designs
