midterm

Question 1

what is the p value

Answer 1

the significance level
- represents the portion of data sets that would yield a result as extreme or more extreme than the observed result if the null hypothesis is true

Question 2

p <= ⍺ vs p > ⍺

Answer 2

p <= ⍺ : reject H0

p > ⍺ : retain H0

Question 3

what does it mean when H0 is rejected

Answer 3

there is a statistically significant effect in the population

Question 4

what does a confidence interval mean?

Answer 4

if we repeat our experiment a bunch of times, our results will fall in that interval a certain percentage of the time

ex. 95% confidence interval meals 95% of the time, our results will fall in the 95% interval

Question 5

how do we form confidence intervals?

Answer 5

{(1-⍺)x 100}%
ex. if alpha=.05 = 95%Ci, .01=99%CI

Question 6

what happens to CIs as sample size increases

Answer 6

our estimates become more precise and CIs become narrower

Question 7

what happens to CIs as ⍺ decreases?

Answer 7

CIs become larger or wider

Question 8

effect sizes for pearson, correlation ratio squared, cohens d:

Answer 8

small:
pearson (r): 0.10
correlation ratio squared R^2: 0.01
cohens d: 0.2

medium:
pearson (r): .30
R^2: 0.09
d: 0.5

large:
r: .50
R^2:0.25
d:0.8

Question 9

Type I and Type II errors

Answer 9

Type I: reject H0 when it is true - false positive

Type II: retain H0 when it is false - false negative

Question 10

what is ⍺ and β in errors in hypothesis testing

Answer 10

alpha: probability of committing type I error

beta: probability of committing type II error

Question 11

what is power?

Answer 11

the probability of correctly rejecting a false H0

1 - β

Question 12

alpha and beta relationship

Answer 12

higher alpha means lower beta - less conservative test power to reject null is higher

buuuut also higher probability of false positive - good and bad

Question 13

assumptions of a single mean t test

Answer 13

variable, X, is normally distrubuted

independence of observations

t stats follow t distribution - approaches normal distrubtions as sample size (df) get bigger

Question 14

between subjects design

Answer 14

independent samples - each participant only goes through one of two conditions in an experiment

Question 15

correlated samples

Answer 15

dependent subjects, paired samples, repeated measures - participants go through both conditions

Question 16

independent samples t test assumptions

Answer 16

• dependent variable normally distributed
• standard deviations of both populations are the same - homogeneity of variance
• each subject is independent

Question 17

what is s^2 under homogeneity of variance?

Answer 17

a pooled estimate of within group variance

Question 18

Anova: levels

Answer 18

treatments - different values or categories of independent variable/factor

ex. instruction method - 1. in person, 2. online, 3 hybrid, etc

Question 19

single factor (one way) designs

Answer 19

a single IV with two or more levels
- can be repeated measures or independent groups design

Question 20

factorial designs

Answer 20

more than one independent variable with two or more levels
- multiply the number of levels in each factor with each other

ex. two factors: 1st has two levels, second has 3= 2x3

Question 21

One way anova assumptions

Answer 21

DV distribution in normal within each group

variance of population distributions are equal for each group - homogeneity of variance

independence of observations

Question 22

null and alternative for one way anova

Answer 22

H0= µ1=µ2=µ3
H1: not all µ’s are the same

Question 23

familywise type I error rate

Answer 23

probability of making at least one Type I error in the family of tests is the null hypotheses are true

= 1-((1-alpha)^c)

Question 24

what do we do if the overall F test is significant in one way Anova

Answer 24

we recommend post hoc tests

Question 25

MSM

Answer 25

one of the two sources of variance in anova - variance explained by the model means variance between groups that is due to the IV or different treatments/levels of a factor

Question 26

MSR

Answer 26

variance within groups, or residual variance within each group, there is some random variation in the scores for subjects

Question 27

F stat

Answer 27

assessing the relative magnitude of variance explained by the model and residual variance large F value means a greater difference between groups - MSM is large compared to MSR F distributions tend to be right skewed

Question 28

F tests and T tests when the number of groups is 2

Answer 28

F=t^2

Question 29

notation: i, g, k, Ng, Xig, Xbarg, Xbar

Answer 29

i= an observation, a score g= a group - group1, group 2, etc k=total groups Ng= size of group g Xig = observation i in group g Xbarg= group mean for group g Xbar=grand mean - across all groups and observations

Question 30

n^2 vs w^2

Answer 30

n^2 is positively biased - overestimates amount of variance in DV that can be explained by IVs - w^2 is unbiased

Question 31

effect sizes for w^2

Answer 31

small = 0.01 medium = 0.06 large = 0.14

Question 32

APA format - decimal places - 7 things to report

Answer 32

2 decimal places, or 3 for p vals should have : F stat with df, statistic, p value and effect size measures means and SDs as well

Question 33

write an APA report for an ANOVa test of fitness vs ego strength with results: group 1 (low fit): M=4.40, SD=0.92 group 2(high fit): M=6.36, SD0.55 F (1,8) = 5.32 W^2= .61

Answer 33

to investigate whether level of fitness had an effect on ego strength, we conducted a one way between subjects ANOVA. This analysis revealed a significant effect of fitness on ego strength, F(1, 8)=5.32, P<.05, w^2=.61. Participants in the low fitness group (M=4.40, SD=0.92) had significantly lower ego strength than those in the high fitness group (M=6.36, SD=0.55). We conclude that having high as opposed to low fitness may increase ego strength.

Question 34

when do the results of an independent samples t test and a between subjects ANOVA for two groups on the same data set disagree?

Answer 34

when they use a different alpha level

Question 35

what needs to be included in an APA summary for an ANOVA test with more than 2 means

Answer 35

a recommendation for post hoc tests "post hoc tests are needed to understand which pairs of means differ significantly"

Question 36

what is the linear model of ANOVA

Answer 36

Yij=µ+⍺j+Eij Yij = dependent variable µ=grand mean of treatment populations ⍺j=treatment effect for group j - not alpha level!! Eij=experimental error - part that allows individual scores to vary (µ+⍺j is constant for every score in a population)

Question 37

what are the 5 assumptions in ANOVA

Answer 37

1. independence one participant has no effect on another participant's performance - this assumption can be violated when participants replicate each other's responses and when several subjects are sampled from the same class 2. identical distribution(within group) -we assume we don't know more about any one participants score than we do about others 3. Identical distribution (between groups) - groups differ only in their means 4. homogeneity of variance - variance of random variable, Eij, is the same for all groups 5. normal distribution - random variable, Eij, has a normal distribution in all groups

Question 38

what happens when the assumption of independence is violated?

Answer 38

- underestimation of true variability = increased type I error rate

Question 39

what happens when the assumption of identical distribution within groups is violated?

Answer 39

- mean may not be an accurate representation of the population of interest - biased results (bc participants in the group may belong to different sub populations) - error term (MSR) is inflated and the power of the test is reduced

Question 40

what could cause the homogeneity of variance assumption to be violated?

Answer 40

- groups defined by classification factor (athletes vs non athletes) are part of the same sample - experimental manipulations

Question 41

what happens when the homogeneity of variance assumption is violated?

Answer 41

excessive type I error rates