midterm Flashcards

1
Q

what is the p value

A

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

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2
Q

p <= ⍺ vs p > ⍺

A

p <= ⍺ : reject H0

p > ⍺ : retain H0

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3
Q

what does it mean when H0 is rejected

A

there is a statistically significant effect in the population

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4
Q

what does a confidence interval mean?

A

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

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5
Q

how do we form confidence intervals?

A

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

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6
Q

what happens to CIs as sample size increases

A

our estimates become more precise and CIs become narrower

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7
Q

what happens to CIs as ⍺ decreases?

A

CIs become larger or wider

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8
Q

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

A

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

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9
Q

Type I and Type II errors

A

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

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

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10
Q

what is ⍺ and β in errors in hypothesis testing

A

alpha: probability of committing type I error

beta: probability of committing type II error

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11
Q

what is power?

A

the probability of correctly rejecting a false H0

1 - β

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12
Q

alpha and beta relationship

A

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

buuuut also higher probability of false positive - good and bad

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13
Q

assumptions of a single mean t test

A

variable, X, is normally distrubuted

independence of observations

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

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14
Q

between subjects design

A

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

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15
Q

correlated samples

A

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

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16
Q

independent samples t test assumptions

A
  • dependent variable normally distributed
  • standard deviations of both populations are the same - homogeneity of variance
  • each subject is independent
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17
Q

what is s^2 under homogeneity of variance?

A

a pooled estimate of within group variance

18
Q

Anova: levels

A

treatments - different values or categories of independent variable/factor

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

19
Q

single factor (one way) designs

A

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

20
Q

factorial designs

A

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

21
Q

One way anova assumptions

A

DV distribution in normal within each group

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

independence of observations

22
Q

null and alternative for one way anova

A

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

23
Q

familywise type I error rate

A

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

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

24
Q

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

A

we recommend post hoc tests

25
Q

MSM

A

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

26
Q

MSR

A

variance within groups, or residual variance

within each group, there is some random variation in the scores for subjects

27
Q

F stat

A

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

28
Q

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

A

F=t^2

29
Q

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

A

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

30
Q

n^2 vs w^2

A

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

31
Q

effect sizes for w^2

A

small = 0.01
medium = 0.06
large = 0.14

32
Q

APA format
- decimal places
- 7 things to report

A

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

33
Q

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

A

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.

34
Q

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

A

when they use a different alpha level

35
Q

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

A

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

36
Q

what is the linear model of ANOVA

A

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)

37
Q

what are the 5 assumptions in ANOVA

A
  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
38
Q

what happens when the assumption of independence is violated?

A
  • underestimation of true variability = increased type I error rate
39
Q

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

A
  • 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
40
Q

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

A
  • groups defined by classification factor (athletes vs non athletes) are part of the same sample
  • experimental manipulations
41
Q

what happens when the homogeneity of variance assumption is violated?

A

excessive type I error rates