Psyc3010 Final Exam

Front 1

Identify the formulae for all degrees of freedom in ANOVA

Back 1

df total = N-1
df factor = # levels of factor - 1

df interaction = profuct of df for factors in the interaction (b-1)x(a-1)

df error= total # observations (N) - # treatments

Front 2

Identify the formulae for all degrees of freedom in 3-way factorial ANOVA

Back 2

Front 3

Identify the formulae for all degrees of freedom in within participants ANOVA

Back 3

df total = nj (#ps x # conditions) - 1 = N (# conditions) - 1

df p = n-1

df tr = j-1

df error = (n-1)(j-1) - Now an interaction : ps x treat

Front 4

Identify the formulae for all degrees of freedom in a mixed ANOVA

Back 4

df total = gbn -1

df between ps = (g)(n) -1

> df group = g-1

> df Ps within G = dfP - dfG

df within Ps = df total - df ps

> df block = b-1

> df BG = (b-1)(g-1)

> df BxP within G = df within - dfB - dfBG

Front 5

What is a one-way design aiming to determine?

Back 5

Are the mean dependent variabl scores of populations for each level of the factor different from the grand mean?

Front 6

What is a factorial design aimed at determining?

Back 6

Is there a main effect of factor A

Is there a main effect of factor B

Is there an A x B interaction

Front 7

What are the advantages of factorial designs

Back 7

- requires fewer participants because we average over the levels of the other factors

- allows examination of the interaction of IVs

-- generalisability of results can be assessed:is the difference described by the main effect the same across the levels of the other factor?

Front 8

In factorial Anova what is on the X axis and what is on the Y?

Back 8

Y = DV

X = IV (with the most levels or most important)

Lines = other factor

Front 9

What do non-parallel lines tell us in factorial ANOVA

Back 9

Interaction!
Ordinal or disordinal (crossed lines)

Front 10

How do we determine if theres a main effect in factorial ANOVA plots

Back 10

Differences in the average height of the levels of the factor

Front 11

What are the source of variance in a one-way ANOVA

Back 11

Between groups - distribution of group means around grand mean

Within groups - distribution of individual DV scores around the group mean

Front 12

if MStreat is a good estimate of error variance, F = ...

Back 12

MStreat/MSerror = 1

Front 13

if MStreat is more than just error variance, F = ...

Back 13

MStreat/MSerror > 1

Front 14

What do larger F values in ANOVA indicate?

Back 14

H0is probably wrong

Front 15

Derivation for one-way ANOVA: expected mean squares

Back 15

- an expected value of a statistic is defined as the ‘long-range average’ of a sampling statistic

- our expected mean squares are:

E(MSerror) --> oe 2 i.e., the long term average of the variances within each sample (S2) would be the population variance oe 2

E(MStreat) --> oe 2 + not 2 where ot 2 is the long term average of the variance between sample means and n is the number of observations in each group i.e., the long term average of the variances within each sample PLUS any variance between each sample

Front 16

How is variance partitioned in a two-way factorial ANOVA

Back 16

Total variation

- Within groups

-Between Groups

-- Variance due to factor A

--Variance due to factor B

--Variance fur to A x B

Front 17

Assumptionsof ANOVA

Back 17

Population

- treatment populations are not normally distributed and have the same variance

Sample

- sample are independent

-independent random sampling

-each sample has 2 pbservations and equal n

Data (DV scores)

- measured using a continuous scale (interval/ratio)

-calculations for means, variance, ect do not make sense for other kinds of scales

Main effects and interactions are omnibus tests

Front 18

What are the problems associated with significance testing as a function of determining the importance of findings

Back 18

-use of arbitrary acceptance criterion (alpha) results in a binary outcome (sig or not sig)

-no info about the practical significant of findings

- a large p-value (ns) will eventually slip under the acceptance criterion as the sample size increases

Front 19

What does effect size allow you to do in terms of assessing results?

Back 19

- the effect size gives you another way of assessing the reliability of the result in terms of variance

- can compare size of effects within a factorial design: how much variance explained by factor 1, factor 2, their interaction, etc.

-differentiating effect sizes (Cohen, 1973):

-- 0.2 = small

-- 0.5 = medium

-- 0.8 = large

Front 20

What are the two main approaches to estimating effect sizes in ANOVA

Back 20

Eta-squared (n2)

Omega-squared (w2)

The difference between them depends on sample size and error variance

Front 21

What does eta-sqaured tell us?

Back 21

-describes the proportion of the variance in the sample's DV scores that is accoundted for by the effect

-considered a biased estimate of the true magnitude of the effect in the population

-most commonly reported effect size because it's easily interpretable (ranges from -1 to +1)

Front 22

What does omega-sqaured tell us?

Back 22

- describes the proportion of variance in the population's DV scores that is accounted for by the effect

-a less biased estimate of the effect size

-more conservative estimate

Front 23

What is partial eta squared?

Back 23

- proportion of residual variance accounted for by the effect

-residual variance = variance left over to be explained (ie. not accounted for by any other IV)

Front 24

What are the limitations of partial n2?

Back 24

- in factorial ANOVA, partial n2 is inflated because error and effect is less than total

- in factorial anova, n2 adds up to a maximum of 100% but partial n2 can add up to >100%

-hard to make a meaningful comparison

-- Instead of dividing by total variability we're dividing by the variability due to our own effect + error (all other effects eg main effect and interaction are excluded) Therefore we get a number larger (for partial eta-squared) - unless the other factors/effects in model don't account for any variance

Front 25

How do we follow up a main effect in ANOVA?

Back 25

- protected t-test: used to conduct pairwise comparisons (ie.2 means at the same time)

- linear contrasts

Front 26

How do we follow up a main effect in ANOVA

Back 26

- if interaction is significant, must be followed up with a simple effects test

-- tests effects of one factor at each level of the other factor

-simple effects re-partition the main effect and interaction variance

--report F and if factor has only 2 levels

Front 27

What do we do if a simple effects test shows a significant interaction what do we do next?

Back 27

-follow up with a simple comparisons (t-tests or linear contrasts)

-same procedure as simple effects but investigates cell means not marginal means

Front 28

What are the issues associates with follow up comparisons in ANOVA and what are their (2) solutions?

Back 28

- redundancy: explaining same mean difference > once

-- solution: orthogonal (independent) linear contrasts

- icnreases family-wise error rate

--solution: bonferroni adjustment for critical and/or conduct contrast a-priori rather than orthogonal set

Front 29

What determines a higher order factorial design

Back 29

More than two IVs

Front 30

What are the different effects of a higher order factorial design

Back 30

- Main effects: possible main effects for each IV

- Two way interactions: one factor changes depending on the level of the other factor averaging over levels of a 3rd factor (differences in simple effects)

- Three way interactions: two way interaction between two factors changes depending on the level of the 3rd factor (does the two way look the same at each level of the third factor?)

Front 31

How is the variance partitioned in a 3 way ANOVA

Back 31

Main effects

-variance: factor A (alpha)

- Variance: factor B (beta)

- Variance: factor C (Y)

2-way interaction

- Variance: A+B (alpha + beta)

- Variance: B+C (beta + Y)

- Variance: A+C (alpha + Y)

3-way interaction

- variance due to aBY

Error/residual

-Variance due to e

Front 32

In factorial designs how do you follow up significant omnibus effects

Back 32

1. Interpret main effect

2. If >2 levels, main effect comparison (t-tests or linear contrasts)

3. Interpret 2-way interaction

4. Simple effects test (F test)

5. Significant simple effects for factor >2 levels, follow up with simple comparisons

Front 33

How do you follow up 3-way interactions

Back 33

Simple interaction effects

-Breaks down into series of 2-way interactions at each level of 3rd factor

- allows to follow up only sig. ones

Simple simple effects

- Follow up used after omnibus 2-way interaction

- Examine effect of factor A qt each level of factor B, qt each level of factor C

-Use MSerror from omnibus anova tables as error term (unlike one-way)

Simple simple comparisons

-Compute contrasts for each level of a third factor

Front 34

What is type I error

Back 34

Finding a significant effect where one doesn't exist in the population

Front 35

What is type II error

Back 35

Finding no significant effect where there is one in the population

- Hypothesis testing pays little attention to type II error

- Concept of power shifts focus to type II error

Front 36

What is the technical and useful definition of power

Back 36

Technical: the probability of correctly rejecting a false Ho

Useful: degree to which we can detect treatments effects (Including main/simple effects and interactions) when they exist in the population

Front 37

Why should we care about power

Back 37

- Power analyses put the emphasis on researchers ability to find effects that exist, rather than the likelihood of incorrectly finding effects don't exist

- Report post hoc power of significant effect

- Calculate predicted power (a priori) when no significant effect is found but mean difference is thought to exist in population

Front 38

What factors effect power?

Back 38

Significance level (alpha)

- a relaxed alpha means more power

Sample size (N)

- More N means more power

Mean differences (Uo-U1)

- Larger differences mean more power

Error variance (or MSerror)

- Less error variance means more power

Power as a function of effect size (d)

- d indicates how many SDs the means are apart and thus the overlap of the two distributions

- Power and d are closely related

Front 39

What percentage is aimed to be achieved with power?

Back 39

.8 is the minimum / optimum. 80% chance a significant effect found

Front 40

What are the 3 issues with power

Back 40

Effect must exist for you to find it

- Increasing power can help detect very small effects

- but if your theory and predictions (re: mean differences) do not reflect the population, Ho will be right and H1 wrong

Large samples can be bewitching

- Large samples can detect very small effects that may be unstable or unimportant

- Exclusive focus on significance test may lead to overestimation of importance of small effect

Error variance is also important

- Higher error variance means that w large effect may still turn out to be ns. Don't just focus on the sample size

Front 41

How do you maximise power (4)

Back 41

Increase Sample size

Increase Alpha level (increases type I)

Study Larger effects

Decrease Error variance

-Aim to reduce variation in Dv scores from sources other than your iv

1) improve operqlisation of variables: increases validity

2) improve measurement of variables: increases (internal) reliability

3) improve design of your study: account for variance from other sources (eg. Blocking designs)

4) improve methods of analysis: control for variance from other sources (eg. ANCOVA)

Front 42

In blocking: how does adding a second factor increase power by reducing error variance?

Back 42

-Error/residual variance represents all variance left over after accounting for systematic variance accounts for by the IV

- Error variance could reflect chnage or systematic unmeasured influences from the other factors

- Adding 2nd factor (THAT IS CORRELATED WITH DV) may account for some of the left over variance

- Reducing error variance this way will increase power

Front 43

Why would we use a blocking design?

Back 43

- Always want to explain variance in the Dv with a novel IV

- Often variance in the Dv can also be explained by additional factors which are less novel, known as control or concomitant variables

- Blocking introduces control variables into your design: reflect additional sources of variation or pre- existing differences on the DV scores

Front 44

What are the two steps in setting up blocking designs?

Back 44

1) homogeneous blocks created with levels of blocking factor: Ps are matched with the levels of the blocking factor

2) participants within each block then randomly assigned to the levels of the IV (stratified random assignment)

Front 45

Are blocking designs randomised?

Back 45

No, Ps categorised into levels of the blocking factor

Front 46

What happens if a blocking variable does not reduce error term?

Back 46

It either is not associated with DV or it explains the same variance as focal IV

Front 47

What role does blocking play in controls and confounds?

Back 47

A main effect of blocking = a sign of good control variable

- shows systematic variability due to blocking factor, which has been removed from error variance

-increases power of test for focal IV (as long as it doesn't explain the same variance as the IV)

Blocking favtor x IV interaction = sign of condound

- increase spower to detect focal IC main effects because systematic variance due to interaction is removed from error

-but that positive outcome is outweighed by negative outcome: interaction means that effect of focal IV changes dependeing on blocking factor

-significant block x interaction shows failure of treatment IV effect to generalise across levels of blocking variable

Front 48

Error term for within participants ANOVA

Back 48

Conceptually: inconsistencies in the effect being tested across participants

Front 49

Mixed anova error term for main effects

Back 49

Front 50

Mixed anova error term for interactions and follow up tests

Back 50

Front 51

What are the error terms for between participants design?

Back 51

Front 52

What are the advantages of blocking ()

Back 52

-may equate treatment groups better than a completely randomised design (assuming there is an equal N for levels of blocking)

- increased power due to lower error term

-can check interactions of treatments and blocks

Front 53

Disadvantages of blocking

Back 53

-practical costs of introducing blocking factor

-loss of power if blocking variable is poorly correlated with DV because of lower DF error

-blocking factor treated as having discrete levels

-artificial grouping may be necessary- could lose some info

Front 54

For anova what represents the DV?

Back 54

X

Front 55

For Regression what represents the DV

Back 55

Y

Front 56

What is covariance?

Back 56

average cross=product of deviation scores

- scale dependent therefore don't often use

Front 57

What is standardised covariance?

Back 57

Pearson's r

- expresses relationship between two variables in terms of SDs

Front 58

What does r2 allow us to do?

Back 58

Generalise effect size

- proportion of variance in one variabe that is explained by the variance if the other

-whatever isn't explained by the IV is residual

-it is a sample statistic and is biased to the #n in the sample ( increased stat = decreased n)

-- r as a population estimate = radj : caluclate rho (p) the population correlation coefficient. Difference between e and radj lower when n is higher

Front 59

What are correlation and covariance measures of?

Back 59

association

Front 60

What does bivariate regression do?

Back 60

estimates score on one variable (Y, criterion) on the basis of scores on another variable (X, predictor)

-regresssion of X on Y

- objective: find best fitting line on scatter

Front 61

What can't you do in regression

Back 61

infer causality

-no random assignment

-can infer based on theory but wont know what causes what or if a 3rd variable causes both

Front 62

What is the unstandardised regression equation?

Back 62

Yhat = bx + a

Yhat = predicted value of Y(DV)

b = slope of regression line (change in Y associated with one unit change in X)

x= value predictor (IV)

a= intercept (value of Y when X=0

Front 63

What is the standardised regression equation?

Back 63

Zhaty= beta Zx = rxyZx

how many SD changes in Y would you expect from 1 SD change in X

Front 64

In regression, what is the best predictor of Y when X is unknown?

Back 64

Best predictor of Y is Ybar

-error calculated around the mean

Front 65

In regression, what is the best predictor of Y when X is known?

Back 65

- Yhat is the best predictor of Y

-Error caluclated around regression line

-Sy.x = standard error of the estimate

Front 66

What is the standard error of the estimate?

Back 66

- Sy.x reflects the amount of variability around the regression slope (Yhat= conditional value), and is an important statistic in correlation and regression

-regression line is fitted according to the least squares criterion so that error of prediction are a minimum

Front 67

What factors influence the standard error of the estimate?

Back 67

-increased correlated between IV and DV (rxy) decreases standard error of the estimate

-small sample size lead to underestimation of standard error

Front 68

How blocking can help

Back 68

- add 2nd IV that is known to explain your additional vairance therefore now 2-way factorial

-increases chance that focal IV has significant effect

- covariate in blocking: control variable

Front 69

What is the difference between variance and covariance?

Back 69

Variance: tendency for scores to vary around the group mean

Covariance: tendency for scores to vary together

Front 70

What does ANCOVA analyse

Back 70

Covariance

Front 71

How is ANCOVA similar and different to blocking?

Back 71

-same goal as blocking but it adjusts the error term

-covariate like control variable in blocking but continuous and in ANOVA its used to remove error from error term and treatment effect

-treatment means are adjusted to account for differences ont he covariate

-random assignment usually prevents differences in variate means, but int his case covariate does differ accross groups

-ANCOVA partials out the effects of covariance from the focal IV as well as the error term

Front 72

In ANCOVA, how does the covariate reduce error term?

Back 72

If it is related to DV, if not you lose DF (power) without any lowered error

Front 73

ANCOVA model

Back 73

Xij = mu+ aj + BZij + Eij

X= DV

i= Ps

j= group

mu= grand mean

a= 1st IV

BZij= 2nd IV: score on variable Z multiplied by a fixed (B) weight

Eij = error

Front 74

What are some assumptions and commonalities in ANCOVA

Back 74

- score on DV goes up or down depending on score on Z

- NO interaction beween categorical IV and covariate

- in this case B = coefficient (strength/relationship) for control variable and DV

Front 75

How does ANCOVA reduce error variance?

Back 75

If covariate is associated with DV

- this relationship accounts for systematic variance unexplained by focal IV therefore lower variance

-a smaller error term because we've partitioned out cariance die to covariate therefore increase statisfical power in testing the effect of the focal IV

Front 76

Why does ANCOVA adjust treatment means

Back 76

- if focal IV affects DV there is a significant difference between the levels of the IV

- if covariate also differs between levels of the focal IV, which variable explains difference in DV treatment means? therefore confound

- WE CARE ABOUT EFFECTS OF THE FOCAL IV NOT THE EFFECT OF THE COVARIATE

Front 77

How does ANCOVA adjust treatment means on DV? (5)

Back 77

1. Calculate overall covariate sample mean

2.Assume this si the population mean

3.Then assume that in an uncondounded population all groups of the focal IV are assumed to have this covariate mean

4.Therefore for your sample, if a groups mean is different on the covariate than the overall covariate mean, that is confounded

5.Can adjust the groups expected mean on the DV to be what it would be if the groups covariate mean were the overall covariate mean by using the regression line

Front 78

Formal assumptions of ANCOVA

Back 78

-Homogenous variance

-normally distributed

-independence of error

-relationship between covarite and DV is linear (if not then it degrades power)

-relationship between covariate and DV is linear within each group

- relationship between DV and covariate is equal scross treatment groups (homogencity of regression slopes)

Front 79

When is ANCOVA best to use?

Back 79

When you perceive that theres no reason to expect associations between the focal IV and the covariate and that its okay to remove variability if you find differences

Front 80

What makes multiple regression different to bivariate regression?

Back 80

-multiple predictors

- multiple correlation (R)

-- relation between criterion Y and set of predictors

-multiple regression

-- scores on criterion Y are predicted use >1 predictor

Front 81

What are the two tests in multiple regression?

Back 81

1) Strength of overall relationship between criterion and set of predictors: R2 * F test

2) Importance of individual predictors: b, B, sr *t test

-predictors usually correlated so their contribution overlaps; this has implications for both tests

Front 82

WWhat does MR assume about interactions?

Back 82

There are none

Front 83

What coefficients exist for MR with uncorrelated predictors?

Back 83

two coefficients of determination, one for each variable

Front 84

MR with correlated predictors

Back 84

- predictors share overlapping variance with eachother as well as DV

-we can't add up the coefficients of determination as we will double up therefore must adjust estimate

-conceptual distinction betwee the overall model R2 and the individual variability, don't inflate model variable

-R2 measures the non-redundant variance in DV accounted for from the combination of variables

-Need to think about correlation between each IV and the DV adjusted to control for the effects of the other IVs. 2 options: partial correlation or semi-partial correlation

Front 85

What is the partial correlation?

Back 85

- examines relationship between predictor 1 and criterion, with the variance shared with predictor 2 partialled out of DV and IV

-Effect size measure: pr2= the proportion of residual variance in the criterion uniquely accounted for by the predictor 1

Front 86

What is the semi-partial correlation?

Back 86

- examines the relationship between predictor 1 and the variance shared between predictor 1 and 2

-very useful in regression because it provides the best effect size measure:

spr2= the proportion of total variance in the criterion UNIQUELY accounted for by predictor 1

Front 87

Difference between structure of ANOVA and MR

Back 87

ANOVA

- no test of the overall model

-tests main effects of each IV: other IVs assumed to be uncorrelated

-Report Fs, effect size for each IV and interaction +follow up

-autocmatically tests all interactions

MR

-automatically tests overall model

-tests unique effect of each IV: IV correlation partialled out

-report model R2 with F + each B for IVs + follow up

-must ask for interactions

Front 88

What is the linear model?

Back 88

Criterion scores are predicted using the best linear combination of the predictors

-similar to 'line of best fit', now plane of best fit

-the equation is derived according to the elast-squares criterion: so that deviations from dots on the plane are lowered (E(Y-Yhat)2)

-b1: slope of plane relative to the X1 axis

-b2: slope relative to the X2 axis

-a: point where the plane intersects the Y axis (when X1 + X2 are = to 0)

Front 89

What is the principle of parsimony?

Back 89

We want the simplest explanation of the data

-High parsimony is good because it highlights that predictors are:

> highly correlated with criterion

> lowly correlated with one another

Low parsimony is bad because it indicates that predictors are:

-highly correlated with each other and therefore redundant because they don't explain unique variance

Front 90

What is the regression solution?

Back 90

Distill all IVs down to Yhat predicted score and then take correlation between predicted score and DV = multiple correlation coefficient (R)

-Y is modelled with linear composite formed by multiplying each predictor by its regression weight/slope/coefficient(unstandardised)(just like a linear contrast) and adding the constant

-theres always one parameter for each IV and there is a constant attempt to predict DV

-need to understand scales to interpret the Yhat

Front 91

What is the multiple correlation coefficient ? (R)

Back 91

a bivariate correlation between the criterion and the best linear combination of the predictors (Yhat)

Front 92

What happens to the multiple correlation coefficient (R) at low sample sizes?

Back 92

it will be inflated (like r) and therefore will need to be adjusted to Radj

Front 93

What formula is used to test overall model R2 for significance?

Back 93

F = (R2/p) / ((i-R2)/(N-p-1))

Variance accounted for/df

/ variance not accounted for (error)/df

Front 94

How do we assess the importance of predictor in regression

Back 94

-can't rely on rs (zero order) because the predictors are interellated

-- a predictor with a sig r may contrinbute nothing once other predictors are included

- partial regression coefficients (bs) are adjusted for correlation of the predictor with the other predictors BUT can't use relative magnitudes of bs because they are scale bound

Front 95

What is the standard regression coefficient (Bs)

Back 95

- estimate of relative contribution of predictors because they use the same metric

-can compare Bs within a regression equation

CANNOT COMPARE ACROSS GROUPS AND SETTINGS BECAUSE SDs OF VARIABLES MAY CHANGE ACROSS STUDIES

Front 96

What what happens to the standard regression coefficient (Bs) when IVs are not correlated with eachother?

Back 96

B=r

Front 97

What what happens to the standard regression coefficient (Bs) when IVs are correlated with eachother?

Back 97

B can go up or down depending on the pattern of the correlation among predictors

Front 98

What is hierachical regression?

Back 98

Predictors are entered sequentially in a pre-specified order based on logic and or theory

-each predictor is evaluated in terms of what it adds to prediction at its point of entry (ie. independently of all other predictors in the model)

-Order of prediction based on logic or theory

Front 99

In HMR, what does b based on?

Back 99

- b @ each block is based on unique contribution, controlling for other IVs in current and earlier steps bit not later ones

Front 100

What is the order of entering predictors in HMR?

Back 100

1. Partial out effect of control variable: like ANCOVA predictors at step 1 lie covariance

2. Build a sequential model according to theory

- order is crucial for outcome and interpretation

-broad measures in step 1 and more specific in step 2

Front 101

What is r

Back 101

Pearson/zero-order correlation

-standardised (scale free) covariance between two variables

-ignores correlations between IVs

Front 102

What is r2

Back 102

Coefficient of determination

- proportion of variability in one variable accounted for by another variable

Front 103

What is b

Back 103

Unstandardised slope/regression coefficient

-scale dependent slope of the regression line

- change in units of Y expected with 1 unit increase in X

Front 104

What is B

Back 104

Stardardised slope/regression coefficient

-scale free slope of the regression line if all variable were standardised

-change in SD in Y expected with 1 SD increase in X, controlling for all other varibles

- B= r in bivariate regression

Front 105

What is spr2/sr2

Back 105

Semi-partial correlation squared

-scale free measure of association between two variables controlling for other IVs by removing shared variance between IVs

-proportion of total variance in DV uniquely accounted for by IV

-similar to eta squared

Front 106

What is pr2

Back 106

Partial correlation squared

-scale free measure of association between two variables, controlling for other IVs by removing all shared variance

-proportion of residual variance in DV (after other IVs are controlled for) uniquely accounted for by IV

Front 107

What are the two slope estimates?

Back 107

b and B

Front 108

There are two other estimates of association

Back 108

Covariance and corelation (r)

Front 109

The slope estimate b tells you what?

Back 109

The predicted unit change in Y for every unit increase in X.

Front 110

B tells you what?

Back 110

The expected SD change in Y for every SD increase in X (IV)

Front 111

You decide to change from 1-7 scales to 0-10 to measure the same variables. If you are using covariance as your estimate of the association of the variables and b as your estimate of the slope the estimates with Change/not change?

Back 111

Change

Front 112

Again you change you scales and you are using correlation as your estimate of the association and B as your slope estimate, these estimates will not or will change?

Back 112

Will not change

Front 113

What are the three uses of HMR

Back 113

-To account for control variables

-To test mediation: INDIRECT EFFECTS

-To test moderation: INTERACTIONS

Front 114

What are the assumptions of HMR?

Back 114

Distribution of residuals

-conditional Y values are normally distributed around the regression line

-homoscedasicity: variance of Y values are constant across different values of Yhat

-no linear relationship between Yhat and errors of prediction

-independence of error

Scales (predictors and criterion scores

-normally distributed

- linear relationship between predictors and creiterion

-predictors highly correlation

-continuous scale

Front 115

What is multicollineariy and singularity?

Back 115

Assumption of HMR

-Multicollinearity: IVs correlated

-Singlularity: measuring same thing

-measured using tolerance = 1-R2x

-R2x is the overlap between a particular predictor and all other predictors

-low tolerance = multicollinearity --> singlularity

-high tolerance = relatively independent predictors

- MULTICOLLINEARITY LEADS TO UNSTABLE CALCULATION OF REGRESSION COEFFICIENTS (b) EVEN IN R2 IS SIGNIFICANT

Front 116

What are interactions in Moderation

Back 116

-relationship between a criterion and predictor varies as a function of a 2nd predictor

-2nd predictor known as moderator

-moderator enhances or attenuates the relationship between criterion and predictor

Front 117

What does the Moderation model test

Back 117

tests the direct effect of Z, plus the direct effect of X and the ZX interaction

-interactions are not about the shared variance between moderator and predictor

Front 118

What degree of collinearity do we want in SMR? how does that contrast to interactions in regression?

Back 118

Want low collinearity in a SMR but irrelevant in tests of interactions

Front 119

Steps in calculation of Moderation (4)

Back 119

1) Calculate interaction term - based on mean-centered predictors will not as correlated with those predictors (low multicollinearity)

2) test of the interaction term

-1st block: enter centered IVs as predictors

-2nd block: enter interaction term to see if it accounts for additional variance (look for a sig R2 change)

3) test simple slopes - we examine the relationship between X and Y @ high and low values of Z (using +/- SDs)

4)Plot simple slopes on graph

- effect size : sr2

-report B

-Simple slopes report coefficient for IV with high and low moderator and interaction also included

Front 120

In MMR, what would a B closer to zero indicate?

Back 120

A lessened effect

Front 121

In MMR, what is the DV regressed on

Back 121

the key predictor

Front 122

In MMR, what happens to main effects when we find an interaction?

Back 122

they're trumped basically

-no longer a useful or insightful way of interpreting the data

Front 123

What is mediated multiple regression?

Back 123

The mediator EXPLAINS the relationship between the IV and DV

Key word often : because

Front 124

What are the relationships between Iv, DV and mediator in mediated multiple regression

Back 124

The IV is related to (causes) mediator, and related to DV

Mediator related to DV when effect of IV is controlled for (C.B)

IV no longer related to DVwhen effect of mediator is controlled for (B.C)

Front 125

Analysis steps in mediated multiple regression (4)

Back 125

1) SMR: regression mediator on IV. Report: R2 & B

2) HMR: Blcok 1 - predict DV from IV

3) HMR:Block 2- predict DV from IV + mediatior

-if coefficient for mediator is significant, then the conditions 3 is met

-coefficient for IV also matters because if no longer singificant =full mediation but if it is still significant = partial mediation

4) Test signfiicant of significant change: SOBEL / BOOSTRAPPING

-if significant, there isan indirect effect of IV via mediator on DV

Front 126

What does Z do to the relationship between X and Y in Moderation?

Back 126

Z just adjusts it

Front 127

What is expected of collinearities in Moderation?

Back 127

Low collinearities desired and high collinearities suggest indirect effects

Front 128

In moderation what is the expected relationship between the moderator and IV?

Back 128

Moderator often uncorrelated with IV

Front 129

In mediation, what is the relationship between the mediator and IV

Back 129

Associated in one way or another

Front 130

Structural model of one way between ps anova

Back 130

to find effect of being in a particular condition, we subtract the grand mean from condition mean

Front 131

Structural model of one way repeated measures anova

Back 131

score in condition 1 minus personal average for each ps

Front 132

In between ps designs, what is within-cell variability assumed to be

Back 132

residual error

Front 133

Between participants term used for follow ups

Back 133

In between, MS error is the terms used to test any effect, including simple comapirsons

Front 134

levelWithin participants error

Back 134

Within ps, we partition out and ignore the main effect of participants and compute an error term estimating inconsistency as ps change over WS

Front 135

Why are seperate error terms used in following up main effects of treatment in ANOVA

Back 135

- we expect inconsistencies in treatment effect x participant so in simple comparisons use only data for conditions involved in comparison & caluclate SEPERATE ERROR TERMS FOR EACH TIME

Front 136

What are the error terms used for two-way repeated measures

Back 136

Main effect of A : error term is MSAxP

Main effect of B: error term is MSBxP

Interaction AxB: error term is MSABxP

-Each effect tested has a seperate error term

-this error term corresponds to an invertaction between the effect due to ps and the treatment effect

-within treatment not considered at all

Front 137

Following up main effects

Back 137

-A seperate error term must be calculated for each comparison undertaken

-Simple effects

-- the interaction between A treatment and pariticpants at B1

-Simple comparisons

--interaction between A treatement (only data contributing to comparison) and participants at B1

Front 138

What are the two approaches to within-participants designs?

Back 138

Mixed model approach

Front 139

What is the mixed model approach of within-ps ANOVA

Back 139

-treatment is a fixed factor and participants are random factor

--fixed factor: choose levels of IV

--random factor: levels of IV chosen at random from a larger pool of levels of that IV

- this can be powerful but restrictive assumptions come with it

Front 140

What are the assumptions of the mixed model approach?

Back 140

-sample randomly drawn from population

- DV scores normally distributed in population

- compound symmetry

--homogeneity of variance in levels of repeated measures factor

--homogeneity of covariances (rqual correlation/covariance) between pairs of levels

-variance-covariance matrix: compount sym = covariances roughly equal

Front 141

What are the methods of dealing with violations of the mixed model approach

Back 141

- Mauchly's test of spherity

- Epsilon adjustment

--Lower bound

--Greenhouse-Geiser

--Huynh-Field

Front 142

What is Mauchly's test of spherity

Back 142

- it examines overall structure of covariance matrix, determines whether covariances and variances are roughly equal

- Evaluated as X2 and if significant there is a violation

- not robust at all and fails to find significance even when present in the data

Front 143

When does sphericity not matter

Back 143

Repeated measure variance

IV has only 2 levels

Front 144

When does sphericity matter

Back 144

- in within-ps with 3+ levels

-when sphericity assumption is violated, F ratios are positively biased

--critical values of F are too small therefore type 1 error prob increases

Front 145

What is the epsilon edjustment?

Back 145

- value by which degrees of freedom for F-test is multiplied

-equal to 1 when assumption is met and <1 when violated

-lower the value (further from 1) means increased conservativity of test

-Closer to 0 = problem

Front 146

What does the lower-bound Epsilon adjustment do?

Back 146

-act as if we only have 2 treat levels with maximal heterogeneity

-used for conditions of maximal heterogeneity or worst case violation of sphericity

-often too conservative

-type II error, not enough power

Front 147

What does the Greenhouse-Geisser Epsilon adjustment do?

Back 147

-size of epsilon depends on degree to which sphericity is violated - each cal F compared to different crit F to investigate

-it puts forward an epsilon based on data therefore it it the perfect method to use

Front 148

What does the Huynh-Feldt Epsilon adjustment do?

Back 148

-adjustment to GG increased to make more lax

-often results in epsilon exceeding 1

-used when the value of ep. believed to be >or = to .75

Front 149

What is the multivariate approach to within-ps design

Back 149

Multivariate linear composite of variance (MANOVA)

-creates linear composite of multiple DVs

-Manova treats repreated measure variable is treated as multiple DVs and combined/weighted to maximise the difference between levels of other varaibles

--multivariate tests: Pillars TRace, Wilk's Lambda, Hotellings trace and roy's largest root

-does not require restrictive assumptions that mixed within ps does (sphericity)

Front 150

What are the advantages of within design

Back 150

-more efficient: n PS in j treatment generate nj data points

- more sensistive: estimate individual differences (ss participants) and remove from error term

Front 151

What are the disadvantages of within design

Back 151

-restrictive statistical assumptions

- sequencing effects

--learning: improving due to practice

--fatigue: deterioration

--habituation: insensitivity to latermanipulations

--sensitisation: more responsive

--contrast: previous treatment sets standard

--adaptation: adjustment to previous condition

--direct carry-over: learn something and carry it over

-Need to counterbalance

--but can still get treatment x order interactions and this increases error

Front 152

In within ps design what is the error term used for any effect?

Back 152

- error term used for any effect is equal to the interaction between that effect and the effect of participants (a random factor)

-this applied to:

--main effects and follow up main comparisons

--interactions: simple effects and follow up simple comparosons

Due to the issue of compound symmetry (sphericity), adjust df where needed

Front 153

What is a mixed anova?

Back 153

-also known as split plot

- has a within ps and between ps factor

Front 154

In mixed ANOVA what happen with Within ps design?

Back 154

- mixed model WP is done the normal way as WP anova: evaluate sphericity and report an adjusted F such as GG

Front 155

Why use a mixed ANOVA?

Back 155

- WP anova is great for power, but some variables can be difficult to manipulate in WP

- can also manipulate a varaible BP to excluse the potential cary-over effects (because BP observations are independent)

Front 156

What are assumptions of Mixed ANOVA

Back 156

-DV is normally distributed

-Between Ps terms:

-- homogeneity of variance

- with ps terms:

--homogeneity of variance: assume WPFxP interactions constant at all levels of between Ps factor

--variance-covariance matrix same @ all levels

--pooled variance-covariance matrix exhibits compount symmetry (c.f sphericitty)

-- usual epsilon adjustments apply when within ps assumptions are violated

Front 157

In a split-plot design, what is the block factor?

Back 157

a within-participant factor

Front 158

In a split-plot design, what is the group factor?

Back 158

a between participants design

Front 159

In a split-plot design, ifone of the IVS is a WP factor what do we include in the partitioning of variance?

Back 159

Random factor participants

Front 160

The participants factor is said to be ? under levels of the ? factor group

Back 160

The participants factor is said to be nested within each level of the BP factor group (each ps is tested in one group only)

Front 161

In a split-plot design, what is variability in within groups considered?

Back 161

Error for BPF effect

Front 162

In a split-plot design, inconsistencies in the block effect cross participants =

Back 162

error for WP effect

Front 163

In a split-plot design, inconsistencies in block effect across ps (interaction) =

Back 163

error for WPFxBPF interaction

Front 164

In a mixed ANOVA, the error for th BP main effect is..

Back 164

participants within groups (deviations of means for each p from group mean)

Front 165

In a mixed ANOVA, the error for th WP main effect & interaction is..

Back 165

WPFxPwithinG (inconsistencies in effect of the WSF across Ps, adjusted for group differences)

Front 166

In a mixed ANOVA, how do you follow up a main effect in BP

Back 166

-same as one way BP

-ue original error term from test of BF main effect

-MSpsWithinG

Front 167

In a mixed ANOVA, how do you follow up a main effect in WP

Back 167

- seperate error term for every follow up test

-MS BcompxPwithinG

Front 168

What to look for in a significant main effect of block (example)

Back 168

- comparisons between different groups doesn't really tell us if any learning has occured, we need to see that ps are improving towards end of study

-could test linear contrasts

-need error for each comparison based on only data involved in that comparison

-could also examine simple effects of group for each of the four blocks

Front 169

What are the two approaches for simple effects in BPF

Back 169

1) use seperate error term for each simple effect (recommended) : run 4 oneway BP anovas to compare groups at each of four blocks. Then use MSpsWithinG @ B1 and again at B2 ect

2) A special pooled error term

Front 170

What does a special pooled error term method involve

Back 170

-MSPswithinCell

-this is an estimate of the average error variance with cells

-using same powerand distributes error

-SSwithinCell = SSPWithinG + SSBxPWithinG

-MSPswithinCell= SS withincell/ (dfPsWithinG+dfBxPsWithinG)

ot may be okay to pool because ps effects are independent

Front 171

Simple effects of BPF: similarities and differences for two methods

Back 171

in both cases the SS for simple effects are derived just as we have seen in BF anova

The seperate error term method is a little quicker byt df is compromised (power)

Front 172

Simple effects in WPF

Back 172

To conduct simple effects of block (for each group), we always run a one-way ANOVA WP on block seperately (each has own error)

Front 173

MEthods of simple comparisons

Back 173

Can do linear contrasts

But whatever test was used for simple effects is to be used here too

Front 174

Error term for WP effects is the effect being exmined in ? with ? PS WG

Back 174

Error term for WP effects is the effect being exmined in interaction with random factor PS WG

Front 175

error term for BP main effects is

Back 175

PS within groups

Front 176

In mixed anova there are two error terms for omnibus tests

Back 176

-BP main effect has own error term: PsWithinG

--deviation of averages of Ps from their group mean are proposed to be error

-WP main effect and interaction: block x PwithinG