Statistics week 5 - 11

Question 1

what are the 3 stage to interpreting SPSS data from two way factorial ANOVA

Answer 1

1. ANOVA itself - test of between subjects
2. if main effects are significant AND have more than 2 levels then check Post Hoc results
3. If interaction result is significant, THEN follow up with Profile plots, interpreting main effect of IV levels and their interaction (parallel lines indicates no interaction)

Question 2

Assumptions of two-way independant ANOVAs

Answer 2

• normality
• Homogeneity of variance (variance in DV should be equivalent across conditions) (tested with Levenes, no correction).
• Independence of observations

Question 3

non parametric equivalent for factorial ANOVAs

Answer 3

there isn’t one.

BUT they are really robust and only serious violations would be a problem

Question 4

diff between partial eta squred and eta squared .
and why is it used in factorial two way ANOVA

Answer 4

eta squared is SSM/SST where in one way anovas, is the same as SSM/SSM+SSR

But in two way anovas this is not true because SST (total of summed squareds) involves all IV levels. BUT partial eta squared only involves one IV level.

i.e. because there are multiple IV levels in Factorial, a measure for each individual IV level is necessary

Question 5

post hoc tests are relevent when

Answer 5

main effect of IV is significant and IV has more than 2 levels.

Question 6

difference in assumptions for repeated measures compared to independant. (ANOVA)
How is this assessed

Answer 6

spherecity of covariance
assessed via Mauchlys and corrected via greenhouse geisser

only when IV has more than 2 levels

Question 7

The range within which 95% of scores in a
normally distributed population fall

formula

Answer 7

95% 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑣𝑎𝑙𝑢𝑒𝑠 𝑓𝑎𝑙𝑙:
𝜇 ± 1.96*SD

Question 8

t formula

Answer 8

. 𝑡 =

𝑥̅𝐷/
𝐸𝑆𝐸

Question 9

df for paired t-test

Answer 9

𝑑𝑓 = (𝑛 − 1)

Question 10

To calculate degrees of freedom for an
independent t-test

Answer 10

𝑑𝑓 = 𝑛𝑡𝑜𝑡𝑎𝑙 − 2

Question 11

theory behind how F is calculated

e.g. written out variance formula

Answer 11

𝐹 =
𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝐼𝑉 𝑙𝑒𝑣𝑒𝑙𝑠/

(𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑤𝑖𝑡ℎ𝑖𝑛 𝐼𝑉 𝑙𝑒𝑣𝑒𝑙𝑠−𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑑𝑢𝑒 𝑡𝑜 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 𝑑𝑖𝑓𝑓𝑠)

Question 12

Components of the F calculation for
ANOVAs, as provided in SPSS output

Answer 12

𝑆𝑆𝑀 + 𝑆𝑆𝑅 = 𝑆𝑆𝑇

𝑆𝑆𝑀/
𝑑𝑓𝑀
= 𝑀𝑆𝑀 (mean square of model)

𝑆𝑆𝑅/
𝑑𝑓𝑅
= 𝑀𝑆𝑅 (mean square residual)

𝐹 =
𝑀𝑆𝑀/
𝑀𝑆R

Question 13

To calculate degrees of freedom for a
bivariate correlation

Answer 13

𝑑𝑓 = 𝑁 − 2

Question 14

R^2 Formula
(measure of effect size): the variance in
the outcome variable that is explained by the
regression model, expressed as a proportion
of total variance

Answer 14

𝑅^2 =
𝑆𝑆𝑀/
𝑆𝑆T

Question 15

SSR =

Answer 15

sum of squares residual.

take diff between inidiv pp scores for group and that group mean. square and add them. (within groups diff)

Question 16

SSM =

Answer 16

take diff between indiv group mean and the grand mean. square and add. (between group model)

Question 17

MSm =

Answer 17

mean square model.

= SSm / dfm

Question 18

MSr

Answer 18

means sum residual

= SSr / dfr

Question 19

diff between repeated measures and independent groups factorial ANOVA

Answer 19

no variance due to individual differences (within group variance is smaller)

Question 20

Marginal means =

Answer 20

mean score for single IV level

Question 21

what does a significant interaction suggest

Answer 21

effect of IVA on DV is dependant on IVB

Question 22

strength of bivariate linear correlations

Answer 22

.1-.3 = weak
.4 - .6 = moderate
.7 . 9 = strong

Question 23

what do inferential statistics measure

Answer 23

infer probability that we have observed a relationship of this magnitude when in fact the H0 is true.

e.g. accept 5% risk of type 1 error / false positive

Question 24

Parametric assumptions of Bivariate linear relationship

Answer 24

• Both variables must be continuous (if both ordinal (categorical) then use non-parametric) can use for likert scales if have 6 0r 7 points
• Related pairs (each pp have x and y)
• Absence of outliers
• Linearity (scatterplot shows straight and not curved line

Question 25

non parametric equivalent of Bivariate linear correlation

Answer 25

Spearman's Rho

Question 26

what is covariance

Answer 26

variance shared between x and y variable

Question 27

what does pearsons r value represent

Answer 27

ratio of covariance to separate variances

Question 28

when talking about relative strength of a relationship, you must report

Answer 28

R^2

Question 29

if R^2 is .45 , what does this mean (bivariate correlation)

Answer 29

45 % of the variance is shared by x and y variable

Question 30

partial correlation purpose

Answer 30

allows for examination of relationship without the influence of a 3rd variable

Question 31

in partial correlation: look at diff between correlation when not partialed out and when partialed out. if correlation had decreased but remained significant, suggests if correlation had not decreased, would suggest

Answer 31

relationship between x and y was partially explained by z not influenced by z. BUT may be influenced by another variable still.

Question 32

Regression model purpose

Answer 32

rel between x and y, allowing an estimate of how much y will change as a result of a change in x.

Question 33

regression model y = x =

Answer 33

y = outcome variable. or dependent/criterion variable x = predictor variable or independent/explanatory variable

Question 34

why use a regression model

Answer 34

- strength of x and y - can predict value of y if know x

Question 35

Assumption of regression model result

Answer 35

- assume y is dependant on x (does not infer causality)

Question 36

what is the F ratio of the regression model comparing

Answer 36

compares simpest model (average score as a line of best fit (SST)) Vs Best model (the regression line (SSR)) the difference between the two reflects improvement in prediction

Question 37

The larger the SSM, the

Answer 37

the bigger the improvement (in prediction model)

Question 38

assumptions of multiple regression

Answer 38

- Sample size - Linearity - outliers - Multicolinearity (predictors can't be correlated with one another) - normal p.p plot of regression - Scatterplot of regression rectangularly distributed = homoscedasticity

Question 39

what does hierarchical regression ask

Answer 39

Does adding new predictor variables allow you to explain additional variance in the outcome variable? Examines influence of predictor variables on outcome variable after "partialing out" influence of other variables.

Question 40

in a regression model: - beta represents

Answer 40

standardized slope

Question 41

what are the different models in hierarchical regression?

Answer 41

model 1 (predictor to be controlled) model 2 (all predictors)

Question 42

change statistics for model 1 of hierarchical regression

Answer 42

Compares simplest model (b=0) with model 1. (same job as standard regression)

Question 43

change statistics for model 2 of hierarchical regression

Answer 43

compares model 1 to model 2 Tells about explanatory power of x, after effects of z are controlled for. ΔR^2 = how much overall variance in y is explained by x, after effects of z are controlled for. ΔF = provides a measure of how much the model has improved the prediction of y, relative to the level of inaccuracy of the model. Δp if <.05 indicates that x explains significant proportion of y after z is partialed out

Question 44

higher risk of what error in non-parametric statistics

Answer 44

type 2 e.g.(false negative) risk of failing to reject nul when it is false e.g. saying it's not significant when actually it is

Question 45

Independent t-test non-parametric equivalent

Answer 45

Mann-Whitney U test remember, man is independent of whitney

Question 46

paired t-test non-parametric equivalent

Answer 46

Wilcoxon T test

Question 47

1-way indpendent ANOVA non-parametric equivalent

Answer 47

Kruskal Wallace test

Question 48

1 way RM ANOVA non-parametric equivalent

Answer 48

Friedman test remember Layla Friedman is repeated measured

Question 49

Factorial design non-parametric equivalent

Answer 49

non existant

Question 50

how are Repeated measures designs shown to be normally distributed

Answer 50

the DV difference scores should be normally distributed, between each paired level of the IV

Question 51

Normality assumption can be assessed with what test

Answer 51

Shapiro-Wilk test. use to decide parametric or non-parametric

Question 52

Pearson's correlation coefficient non-parametric equivalent

Answer 52

Spearman's Rho: used when N > 20 Kendall's Tau: used when N < 20

Question 53

parametric or non parametric when thinking about scale

Answer 53

if variable measured is ordinal scale, use non-parametric e.g. if intervals between values is not constant

Question 54

partial correlation and regression non-parametric equivalent

Answer 54

non existant

Question 55

what tests analyse categorical data

Answer 55

One variable Chi Square Chi-square Test of Independence ( two variables) no parametric equivalents