PSYC 301- final exam

Question 1

data fishiness- definition

Answer 1

properties of data or statistical tests that suggest potential problems (Abelson calls it this)

Question 2

two approaches to evaluating the assumptions of normality

Answer 2

NHST and descriptive approaches

Question 3

repeated measures (within subjects) one way ANOVA tests

Answer 3

mean differences in repeated measure studies with 3+ levels of a single factor

Question 4

what does

T
K
G
n
N
P

mean in within subjects anove

Answer 4

T- sum of scores within a condition
K- # of levels of the IV
G- sum of all scores
n- sample size
N- total # of scores for the sample (kxn=N)
P- sum total of scores for given person in sample

Question 5

variability in the means of scores across conditions exists for two reasons in within subjects ANOVA

(variance between treatments)

Answer 5

treatment effect- the manipulation distinguishing between conditions

experimental error- random chance errors that occur when measuring the construct of interest

*note no individual differences bc this is a constant across conditions; individual is baseline to themselves

Question 6

variability in the means of scores within conditions could be a result of 2 sources

(variance within treatments)

Answer 6

individual differences- differences in backgrounds, abilities, circumstances etc of individual ppl (this can be calculated out though)

experimental error- chance errors that occur when measuring the construct of interest

Question 7

SSerror =
(4.22)

Answer 7

SSerror = SSwithin treatments - SS between subjects (individual diffs)

Question 8

conceptually the F test for repeated measures becomes (4.16)

Answer 8

treatment effect + experimental error/ experimental error

Question 9

4.17 ** repeated measures in a nutshell

Answer 9

F = MSbetween treatments/MSerror

Question 10

computing within treatment variability (4.19)

Answer 10

SSwithin treatments = ∑SSwithin each treatment

Question 11

SStotal =

Answer 11

SStotal = SSwithin + SSbetween

Question 12

total df for repeated measures ANOVA (4.23)

Answer 12

dftotal = N-1

Question 13

df between treatments
(4.24)

Answer 13

df between treatments = k -1

Question 14

df within treatments
(4.25)

Answer 14

df within treatments = N-k

Question 15

formulas for specific MS values in ANOVA
4.28
4.29

Answer 15

MSbetween treatments = SS between treatments/df between treatments

MSerror = SSerror/dferror

Question 16

assumptions of the repeated measures ANOVA

Answer 16

• independence of sets of observations
• distribution of the outcome variable should be normally distributed in each level of the IV
• sphercity (type of homogeneity of variance; equality of variances in different scores across all levels of the IV)
• homogeneity of covariance

Question 17

what is sphercity

Answer 17

Are the differences in performance between Program A and Program B, Program B and Program C, and Program A and Program C equally variable?

equality of variances in different scores across all levels of the IV

Question 18

data fishiness assumptions

Answer 18

assumption of normality
assumption of homogeneity of variance
independence of observations

Question 19

assumption of normality

Answer 19

scores the DV within each group are assumed to be sampled from a normal distribution

Question 20

evaluating the assumption of normality

Answer 20

NHST approach
- tests if sample dist is sig. different from normal dist
- skew- captures symmetry
- kurtosis- captures extreme scores in tails ( 0= normal)

Descriptive approach
- look at descriptive/ graphical displays to quantify the magnitude and nature of non- normality
- skew and kurtosis threshold values ( skew greater than 2, and kurtosis greater than 7), positive kurtosis tends to be worse
- graphical displays (normal qq plots) plot your dist against normal dist with same sample size, if data is normal it looks like straight line, tails, thin or fat

Question 21

pros and cons of NHST and descriptive approachin evaluating normality

Answer 21

NHST bad bc of the role of sample size
- insensitive to non-normality in small samples and too sensitive to non-normality in large samples
- doesn’t take into account the type of non normality and how much, the question itself doesn’t make conceptual sense bc we want to know if the size (magnitude) of the non normality will alter our data

Descriptive approach better than NHST bc it allows us to see magnitude and type of non normality, but there is still the element of subjectivity meaning that it’s easy to see results when clearly good or bad, but its difficult to judge if deviations are consequential in ambiguous cases

Question 22

assumptions of homogeneity of variance

Answer 22

assumption that variances around the means are generally the same

variances in scores on the DV within each group are the same across groups

Question 23

evaluating the assumption of homogeneity of variance

Answer 23

NHST approach
- tests if variances in groups are sig diff from each other; levens test, hartleys variance ratio and f-max test

descriptive approach
- looks at descriptobe stats/ graphical displays to quantify the magnitude of differential variances
- threshold ratio of largest to smallest variances (recommended threshold 3:1)
- graphical displays (qq plots) take data from 2 conditions and plot (lowest and lowest together etc), if condiions satisfied it’ll be a straight line with slope of 1 and intercept equal to the difference between the means

Question 24

assumption of independence of observations

Answer 24

each observation (between subjects) or each set of observations (within subjects) comprising the data set is independent of all other observations or sets of observations in the data set
basically, no inherent structure in the nature of our data; no cluster

excluding couples data or roomates data

positive associations inflate alpha
negative associations inflate beta

Question 25

evaluating the assumption of independence of observations

Answer 25

examine structural properties of data to see if a basis exists for questioning the validity of the assumption if no basis is evident, generally fine to conclude the assumption holds if a basis exists, independence can be assessed by computing the intraclass correlation for the structural property in the data presumed to produce the violation of independence if intraclass correlation is very small (less than .10), prob fine to use t tests or ANOVA clear thresholds for intraclass correlations remain debated so the conceptual basis for expecting violations is important in evaluating this index if violation occurs, best to use alt analysis that accounts for lack of independence

Question 26

addressing violations of assumptions

Answer 26

normality - use alr procedures - transform data to normalize dist - identify and remove outliers (80%of time this is problem) - eval level of measurement assumptions homogeneity of variance - use alt procedures - identify and remove outliers - eval level of measurement assumptions indep of obvs - alt stat procedures like MLM and HLM

Question 27

outliers

Answer 27

extreme values in a data set that differ substantially from other observations in the data set suggesting they might be drawn from a different population often responsible for violations of normality and homogeneity of variance have a disproportionate influence on stat results

Question 28

examples of common outliers

Answer 28

data entry/coding errors responses in latency data open ended estimate data (no upper boundary)

Question 29

identifying outliers

Answer 29

impossible values in freq tables or histograms seen in normal qq plots as steep tails standardized residuals (general thresholds of 4 or 5 are sufficiently weird), includes target observation in mean which can drag it studentized deleted residuals: index of deviation from the mean NOT including the target observation in the calc of the mean - sample of 100, 3.6 - sample of 1000, 4.07

Question 30

thin tails

Answer 30

fewer extreme observations than the normal dist

Question 31

fat tails

Answer 31

more extreme observations than the normal dist

Question 32

responses to outliers

Answer 32

impossible values should be corrected if possible or treated as missing data if not possible to correct trimming or capping to most extreme acceptable value in data set/specified value - conceptual basis not ideal bc no reason to assume value

Question 33

philosophocal issues in outliers

Answer 33

minimalist- data should be minimally altered - dists should have some extreme values maximalist- routine altering or delation of values - outliers create violations intermediate- won't throw out unless really problematic

Question 34

levels of measurement

Answer 34

Nominal - categorical distinctions, no mag Ordinal - rank ordering, no mag Interval - rank ordering and mag Ratio - rank ordering, mag, and ratio of difference for rating scales 7 points is sufficient, 5 is ambiguous, and less than 5 is problematic

Question 35

argument for levels

Answer 35

has been argued that t tests and ANOVA are only meaningful to conduct if DV has at least interval properties very problematic distributional properties of data can sometimes indicate level of measurement is not appropriate

Question 36

factorial ANOVA and its advantages

Answer 36

general term for an ANOVA with more than 1 IV modest gain in efficiency ability to test joint effects - additive- no interaction - nonadditive- interaction

Question 37

in a 2 way anova we test how many effects

Answer 37

3 effects main effect of IV1 main effect of IV2 interaction effect of IV1 with IV2 number of levels doesn't change number of effects!

Question 38

interactions sometimes referred to as

Answer 38

moderator effects - a moderator regulates the effect of another IV if 1st IVs effects change based on the 2nd IV, 2nd IV is the moderator

Question 39

F test associated with null hypotheses for 2 way ANOVA and the hypothesis (4.1)

Answer 39

F = variance between treatments/variance within treatments difference is that between treatment variance will now be further divided into 3 components: Factor A between treatment variance (MSa) Factor B between treatment variance (MSb) Factor AxB between treatment variance (MSaxb) F val of 1 indicates no treatment effect (0) F value greater than 1 indicates given treatment effect exists

Question 40

2 way between subjects ANOVA G N p q n

Answer 40

G- grand total of all scores in entire experiment N- total number of scores in entire experiment p- # of levels in factor A q- # of levels in factor B n- # of scores in each treatment condition (each cell of the AxB matric)

Question 41

computer A x B between treatment variability (6.6)

Answer 41

SSaxb = SS between - SSa - SSb

Question 42

general formula for mean square (4.10)

Answer 42

MS = SS/df

Question 43

articulation (abelson)

Answer 43

extent to which results are presented in a clear and useful manner; as results get more complex, there will be more ways they can be articulated

Question 44

as in 1 way anova, 2 general approaches to follow up tests exist for two way anova

Answer 44

a posteriori tests (post hoc) a priori tests (planned)

Question 45

analysis of simple effects

Answer 45

effect of 1 IV at a specific level of the other IV once we get to 3 levels, simple effect test becomes omnibus itself, need contrasts

Question 46

setting alpha in 2 way between sibjects anova

Answer 46

alpha almost never adjusted for these multiple tests in ANOVA, thus emphasis tends to be on confirmatory analyses replication seen as more essential

Question 47

principle for setting beta in the context of multiple test

Answer 47

minimum acceptable power on the basis of the weakest anticipated effect minimum acceptable power on the basis of the most important effect/ sets of effects

Question 48

calcuating standardized effect sizes in 2 way between subjects anova

Answer 48

np2 = SSeffect/ SSeffect + SS within

Question 49

pearson correlation coefficient

Answer 49

index of association that assesses the magnitude and direction of linear relation between 2 variables r = covariability/ variability separately (7.2)

Question 50

sum of the products of devation (7.3)

Answer 50

SP = ∑(X - X̄)(Y- Ȳ) taking deviation products and summing them index of covariability - lots of above/above and below/below pairs will produce big positive SP values -lots of below/above and above/ below pairs will produce big negative SP values - equal mix of both will produce near 0 SP values

Question 51

r coefficient is an index of covariability of X and Y relative to variability of those separately formula (7.4)

Answer 51

r = SP/ square root of SSxSSy

Question 52

relationship of r to z scores

Answer 52

z scores reflect an individual's scores standing within the distribution for that score tells us where they fall in the distribution of everyone so r can be expressed in terms of z scores

Question 53

r expressed in terms of z scores (7.5)

Answer 53

r = ∑ZxZy/n seen by some as best formula for r

Question 54

coefficient of determination

Answer 54

if pearson correlation coefficient (r) is squared, it reflects the proportion of variance in one variable linearly accounted for by the other variable ex. r=50 indicates that the first variable accounts for .25 (25%) of the variability in the second score - 25% overlap

Question 55

formula for t test of r (7.6)

Answer 55

t = r√n-2/√1-r2 bigger rs make bigger ts bigger correlation gets in denominator, smaller the number gets

Question 56

factors influencing the size of r

Answer 56

distributions of variables - perfect correlations only possible if shape of dists is exactly same reliability of measures - perfect correlations only possible with perfect reliability in both measures restrictions of range - restricting the range on either variables can attenuate correlations

Question 57

regression

Answer 57

formal procedure by which scores on one variable can be used to predict scores on another variable; it's the statistical procedure by which we use a data set to arrive at a formula to produce the best fitting line for that data set ex. GRE on yale undergrad grades the better our predictor, the more tighly data points will cluster around the line

Question 58

when two variables are linearly associated, can be described with basic equation (7.7)

Answer 58

Y = bX + a X- scores on first variable (predictor) Y- scores on second variable (outcome) b- fixed constant reps the slope of the best fitting line a- fixed constant reps the Y intercept (expected value of Y when X is 0

Question 59

the extent to which the line generated by a given regression equation fits a specific data set is defined by the following (7.8) foundational to regression

Answer 59

total squared error (SSerror) Total squared error = ∑ (Y - Yhat)2 y reps an actual data point and y hat reps the predicted value for that data point given its X value small values reflect less error

Question 60

formula for b (7.9)

Answer 60

b = SP/SSx Sp is measure of covariability SSx is measure of total variability of X higher Sp increases b higher SSx decreases b

Question 61

formula for a (7.10)

Answer 61

a = Ybar -bXbar

Question 62

when x and y are z scores, the simple regression equation becomes (7.11)

Answer 62

Zyhat = rZx r becomes our slope and a becomes 0 so it can be dropped

Question 63

explain how b becomes r and a becomes 0

Answer 63

r= SP/square root of SSxSSy and b = SP/SSx so they're the same and then both x and y have means of 0 when they're z scores so a = Yhat - bX a = 0 - b0 a = 0

Question 64

standard error of estimate

Answer 64

a measure of the standard distance between a regression line and actual data points total squared error is in it look at ipad SSerror is related to r, as r approaches 1, SS error becomes smaller and as r approachs 0 SSerror becomes larger

Question 65

SSerror equation (7.13)

Answer 65

SSerror = (1-r2)SSy this leads to an alternative formula for standard error of estimate

Question 66

standard error of estime alt formula (with r)

Answer 66

look at ipad

Question 67

F test for the regression coefficient

Answer 67

F = variance predicted by the regression/ error variance

Question 68

MS values of regression

Answer 68

look at ipad x 2

Question 69

F test (7.20)

Answer 69

F = MS regression/ MSerror

Question 70

regression assumptions

Answer 70

independence of observations linear relationship between X and Y residuals (errors in prediction) normally dsitributed with mean of 0 homoscedasticity of residuals- equal variance around regression line

Question 71

MAGIC

Answer 71

M- magnitude the mag of an effect can play a role in the persuasive strength of a research claim - big effects not always practical - small effects sometimes impressive - conceptual implications sometimes matter more than size of effect A- articulation persuasive strength of a claim will be influenced by how efficiently, accurately and clearly an analytical strategy is used to capture key conclusions from the data G- generality generality across studies and researchers (replication) generality across pops and contexts I- interestingness interesting as function of method interesting as function of theory interesting as function of surprise (novelty/mag) interesting as function of importance (prac, implications) C- credibility conceptual basis for credibility - fits with existing theory - fits with common sense methodological basis for credibility - data fishiness - improper stat procedures - alt explanations beyond IV - IV and DV reflect their constructs?

Question 72

main effect, what is it

Answer 72

effect of 1 ivs overall on the dv

Question 73

interaction

Answer 73

differences of differences; compares the differences in one factor across levels of another to determine whether they are consistent or not