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Stats > Midterm 2 > Flashcards

Midterm 2 Flashcards

1
Q

What kind of statistical test only has one mean?

A
  • z-test
  • One-sample t-test
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2
Q

What kind of statistical test has 2 means and one factor?

A

Independent samples t-test

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3
Q

What kind of statistical test has more than 2 means and one factor?

A

One-way ANOVA

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4
Q

What kind of statistical test has more than 2 means and 2 factors?

A

Two-way ANOVA

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5
Q

What are the null hypotheses we need to find with a 2-way ANOVA?

A

Main effect of Factor A
Main effect of Factor B
Interaction between Factor A and B

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6
Q

What would a 3x4 set-up mean for a 2-way ANOVA?

A

3 levels in Factor A
4 levels in Factor B

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7
Q

What are factorial designs?

A
  • Factorial designs are those in which factors are completely crossed
  • They contain all possible combinations of the levels of factors
    Ex: when each factor has 3 levels, it is called a 3 × 3 factorial design, resulting in 9 treatment combinations
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8
Q

What does it mean for a design to be fully crossed?

A

Every level of factor A is combined with every level of factor B

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9
Q

What’s a balanced design?

A

When sample sizes are equal in each condition

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10
Q

What do Factors represent?

A

The independent variables

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11
Q

What’s represented in the cells of the 2 × 2 factorial design of a 2-way ANOVA?

A

Means of all subjects within each cell are displayed

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12
Q

How many effects comprise a two-way factorial experiment?

A

2 main effects
An interaction effect

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13
Q

What are main effects?

A
  • The effect of one factor when the other factor is ignored (by averaging the means over all levels of the other factor)
  • Consists of the differences among marginal means for a factor
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14
Q

What’s the interaction effect?

A
  • The extent which the effect of one factor depends on the level of the other factor
  • An interaction is present when the effects of one factor on the DV change at different levels of the other factor
  • The presence of an interaction indicates that the main effects along do not fully describe the outcome of a factorial experiment
  • Sometimes called a crossover effect
  • Considers pattern of results for all cell means
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15
Q

How could you visualize a main effect for Factor A on a plot?

A

There’s a main effect if there is a difference in average of the 2 dots (coming from both levels) closest to each other -> on both sides of slope

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16
Q

How could you visualize a main effect for Factor B on a plot?

A

There’s a main effect if the average of both lines (slopes) are different

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17
Q

How could you visualize an interaction effect
between Factor A and Factor B on a plot?

A

There’s no interaction if lines are parallel
There’s an interaction if they aren’t parallel and indicate that they’ll eventually cross over

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18
Q

The 2-way ANOVA statistically examines the effects of what?

A
  • 2 factors of interest on the DV
    (Main effects)
  • Interaction between the different levels of these 2 factors
    (Interaction effect)
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19
Q

What are assumptions of the 2-way ANOVA?

A
  • The population distribution of the DV is normal within each group
  • The variance of the population distributions are equal for each group (homogeneity of variance assumption)
  • Independence of observations
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20
Q

State the hypotheses for main effects

A
  • Main effect of Factor A
    H0A : μA1 = μA2 = ··· = μAa (equal row marginal means)
    H1A : Not all μAg are the same
  • Main effect of Factor B
    H0B : μB1 = μB2 = · · · = μBb (equal column marginal means)
    H1B : Not all μBj are the same
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21
Q

State the hypotheses for interaction effect

A
  • Hypotheses for interaction effect
    H0: A×B : All μAgBj are the same OR The interaction between Factor A and Factor B is equal to zero
    H1: A×B : Not all μAgBj are the same OR The interaction between Factor A and Factor B is NOT equal to zero
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22
Q

How is total sums of squares (or total variation) partitioned in 2-way ANOVA?

A
  • It’s divided into 2 parts:
    SST = SSM +SSR
    SSM = Model (Between-group) variation
    SSR = Residual (Within-group) variation
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23
Q

How is sums of squares of the model (SSM) partitioned in 2-way ANOVA?

A

SSA: Variation between means for Factor A
SSB: Variation between means for Factor B
SSA×B: Variation between cell means

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24
Q

What’s the formula for the F ratio for Factor A in 2-way ANOVA?

A

FA = MSA / MSR

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25
Q

What’s the formula for the F ratio for Factor B in 2-way ANOVA?

A

FB = MSB / MSR

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26
Q

What’s the formula for the F ratio for the interaction of Factor A and Factor B in 2-way ANOVA?

A

FA×B = MSA×B / MSR

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27
Q

When should you reject the null hypothesis in a 2-way ANOVA?

A

If each observed F value is greater than or equal to its critical value

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28
Q

What does “a” stand for in 2-way ANOVA?

A

Number of levels for Factor A

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29
Q

What does “b” stand for in 2-way ANOVA?

A

Number of levels for Factor B

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30
Q

What are treatment sums in 3-way ANOVA?

A

Sum of raw scores in each treatment group

31
Q

What’s the grand sum (T) in 3-way ANOVA?

A

The sum of all the scores in the experiment

32
Q

How many total effects do we have to compute/find with a 3-way ANOVA?

A
  • 7 effects
  • 3 main effects (A, B, C)
  • 3 simple (two-way) interactions (AxB, AxC, BxC)
  • 1 three-way interaction (AxBxC)
33
Q

Describe the within-subjects/repeated- measures design

A
  • An experimental design in which the DV is measured several times within the same subject
  • Subjects are crossed with at least one experimental factor
  • The simplest design of this kind may be a before and after-treatment design (2 conditions)
34
Q

What is a one-way repeated-measures design comprised of?

A
  • Levels of Factor A (only has 1 factor)
  • Subjects (participants)
35
Q

Describe the one-way repeated measures design

A

n subjects are measured on the DV under k conditions (or levels) of a single IV or factor

36
Q

What are possible research questions with the one-way repeated measures design?

A
  • Are there differences in the mean scores of the DV across groups/conditions?
  • Within-subject effect of the independent variable (each subject is measured at each time point) -> Variation due to the model
  • Are there differences across subjects?
  • The variability of subjects (between-subject effect)
  • Treat each participant as a different level in an experimental design
37
Q

What’s the null hypothesis for the between-subject effect in the one-way repeated measures design?

A

H0: Vs = 0
- this effect represents the variance between subjects

38
Q

What’s the null hypothesis for the within-subject effect of treatment (IV) in the one-way repeated measures design?

A

H0: μ1 = μ2 · · · = μk

39
Q

What are we interested in in a One-way repeated measures ANOVA?

A
  • Usually we are NOT interested in the effect of ‘subjects’ or subject-level variability
  • If this effect is significant, it would simply tell us that subjects differ on the dependant variable which has nothing to do with our treatment (IV) so it’s irrelevant
  • What we are really interested in is whether the IV has an effect on the subjects, regardless of whether differences existed naturally among the subjects
40
Q

What’s referred to as SS error in one-way repeated measures ANOVA?

A

SSaxb

41
Q

SS within is composed of what 2 types of SS in one-way ANOVA?

A

SS(S) and SS(AxS)

42
Q

What are the assumptions in one-way repeated measures ANOVA?

A
  • Normality
  • Homogeneity of variance
  • Homogeneity of covariance
43
Q

Describe the normality assumption in one-way repeated measures ANOVA

A

The distribution of observations on the dependent variable is normal within each level of the factor

44
Q

Describe the homogeneity of variance assumption in one-way repeated measures ANOVA

A

The population variance observations is equal at each level of the factor

45
Q

Describe the homogeneity of covariance assumption in one-way repeated measures ANOVA

A

The population covariance between any pair of repeated measurements is equal (homogenous covariance)

46
Q

What 2 assumptions in the one-way repeated measures ANOVA are considered compound symmetry?

A
  • Homogeneity of variance
  • Homogeneity of covariance
47
Q

Describe the assumption of compound symmetry in one-way repeated measures ANOVA

A

We assume that the variations within experimental conditions is fairly similar and that no 2 conditions are any more dependent than any other two

48
Q

Describe the assumption of sphericity in one-way repeated measures ANOVA

A
  • Given that hypotheses about treatment effects are tested on differences between scores, the assumption of compound symmetry can be replaced by the assumption of sphericity (or circularity)
  • Sphericity means that the variance of differences of a pair of observations is the same across all pairs
  • In the assumption of sphericity, we assume that the relationship between pairs of experimental conditions is similar
  • This assumption is tested in practice, and it is a necessary condition for validity of the F test in repeated measures ANOVA
49
Q

What happens when there’s a violation of sphericity in one-way repeated-measures ANOVA and how do we deal with it?

A
  • Use of tests for violations of sphericity, such as Mauchly’s W (1940) - Mauchly’s test
  • When Compound Symmetry is violated, the omnibus Ftests in one-way repeated measures ANOVA tend to be inflated, leading to more false rejections of H0
  • Violations of CS require adjustments to the F test
  • We can use a conservative critical value based on the possible violation of sphericity (conservative Ftest)
  • The inflation of the F statistic that occurs when sphericity is violated can be adjusted by evaluating the observed F value against a greater critical value, obtained by reducing the degrees of freedom
  • Some of the most popular approaches involve:
    1. measuring the degree of violation of sphericity
    2. using the critical value equal to the value of the F distribution that corresponds to εdf (the adjustment is made for both df numerator and df denominator)
50
Q

What’s the formula for finding the conservative critical value?

A

DF(B) = epsilon x (k-1)
DF(BS) = epsilon x (k-1)(n-1)

51
Q

What’s the function of epsilon?

A

It measures the extent to which sphericity was violated

52
Q

What’s the criteria for determining a violation of sphericity in one-way repeated-measures ANOVA?

A
  • When sphericity holds, epsilon = 1 (i.e., no correction is needed).
  • When sphericity is violated, 0 < epsilon < 1
  • This reduces both DF(B) and DF(BS), and gives a larger critical value for F
  • The further the epsilon value is from 1, the worse the violation
53
Q

How do we decide the value of epsilon?

A
  • Epsilon ≥ 1/(k-1)
  • JASP provides two estimates of epsilon: Greenhouse- Geisser & Huynh-Feldt estimates
54
Q

What’s the difference between the Greenhouse-Geisser & Huynh-Feldt estimates?

A

Greenhouse-Geisser is smaller (more conservative)

55
Q

What’s the effect size for one-way repeated-measures ANOVA?

A

Partial Omega squared (ω2) that excludes the variability due to differences between subjects (MSS)

56
Q

What’s the formula for within-participant variation in one-way repeated-measures ANOVA?

A

SSW =SSA+SSAxS

57
Q

What’s the F-ratio for one-way between subjects repeated measures ANOVA?

A

F = MSA / MSsxa

58
Q

When should you reject the null hypothesis from an F value?

A

If the observed F value is greater than or equal to its critical value, reject the corresponding null hypothesis

59
Q

If there’s a significant result p is < or > than .05?

A

p < .05

60
Q

If there isn’t a significant result p is < or > than .05?

A

p > .05

61
Q

Describe sphericity in one-way repeated-measures ANOVA

A

Variance of difference scores is equal for all pair-wise comparisons

62
Q

What do the null and alternative hypotheses indicate in Mauchly’s test

A
  • The null hypothesis in Mauchly’s test is that the assumption of sphericity is met
  • Rejecting the null hypothesis indicates that the assumption of sphericity is violated
63
Q

When sphericity is violated, using the F ratio with unadjusted degrees of freedom leads to what?

A
  • An increase in Type I error rates (false positives)
  • When sphericity is violated, the type 1 error rate is no longer .05 but it is greater
64
Q

What are the 3 possible ways to calculate epsilon?

A
  • Greenhouse-Geisser approach
  • Huynh-Feldt approach
  • Minimum possible value epsilon can attain which is ε = 1/(a − 1)
65
Q

What’s the preferred and most generally used adjustment for violation of sphericity

A
  • Huynh-feldt
  • Because it tends to have the highest power
  • The adjustment we usually use when reporting the results in APA format
66
Q

What values change when we use the adjustments for violation of sphericity?

A
  • df values
  • MS values (since they’re calculated with df)
67
Q

What values don’t change when we use the adjustments for violation of sphericity?

A
  • SS values
  • Observed F ratios -> because if you multiply both sets of degrees of freedom by epsilon, those 2 adjustments cancel each other out so you end up with the same observed F ratio
68
Q

What test results should always be reported first in an APA summary for a one-way repeated-measures ANOVA?

A
  • (when applicable) Mauchly’s test should always be reported first in APA summary
69
Q

Why is epsilon denoted as 0 < epsilon < 1?

A

Epsilon can’t be zero because the formula always includes a minimum of a=2 (2 levels since repeated measures needs a minimum of 2 levels) so the epsilon formula can’t give 0

70
Q

What measure of effect size do we use for 2-way ANOVA?

A

Omega-squared (ω2)

71
Q

In One-way ANOVA, SSR stands for what?

A

It’s the sum of the squared difference between a group mean and group observations, across all k groups

72
Q

In Two-way ANOVA, SSR stands for what?

A

It’s the sum of squared differences between
a cell mean and cell observations, across all (a × b) cells

73
Q

Describe Mauchly’s Test of Sphericity

A
  • H0 in this test is “variances of differences between conditions are equal”
  • If p < .05, the assumption of sphericity (and CS) is violated
  • Available in JASP
74
Q

How are the Greenhouse-Geisser and Huynh-Feldt values obtained?

A
  • Greenhouse-Geisser was obtained with (a-1) x epsilon
  • Huynh-Feldt was obtained with 2 x epsilon

Stats (4 decks)

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