Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Stats > Midterms material > Flashcards

Midterms material Flashcards

1
Q

What are the null hypothesis and alternative hypothesis for a one-way ANOVA?

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What’s a factor in a one-way ANOVA?

A

the independent variable

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What are the levels in a one-way ANOVA?

A

The different groups/treatment and control conditions

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What are the assumptions of a one-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
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What’s the familywise Type 1 error rate?

A

The probability of making at least one Type 1 error in the family of tests if the null hypotheses are true

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What’s a family of tests?

A

a set of related hypotheses

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

What does the Overall F-test or first test of ANOVA tell us?

A
  • Overall F-test evaluates is H0 false?
  • If the overall F-test is significant then we use post-hoc tests to look at pairs of groups
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What kind of ratio does ANOVA give us?

A
  • F ratio
  • ANOVA gives us a ratio of variance due to group membership over variance that is not explained by group membership (MSm divided by MSr)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What is variance explained by the model (MSm)?

A

Between-group variance that is due to the IV, or different treatments/levels of a factor -> variance accounted for by group membership

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

What is residual variance (MSr)?

A
  • Within-group variance that can’t be accounted for by group membership
  • Within each group, there is some random variation in the scores for the subjects
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

How are the F statistic and degrees of freedom presented?

A

F (dfM, dfR) = x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What kind of distribution is the F distribution?

A

A right-skewed distribution used most commonly in ANOVA

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

When can you reject the null hypothesis in an ANOVA test?

A

If your F value is greater than or equal to the critical value, you may reject the null hypothesis

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

How does the F ratio relate to the t statistic?

A
  • With only two groups, either a t test or an F test can be used for testing for a significant difference between means
  • Both procedures lead to the same conclusion
  • When the number of groups is 2, then F = t^2
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

In ANOVA formula, what does X-bar stand for?

A

The grand mean (across all observations)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

In ANOVA formula, what does i stand for?

A

An observation (coming from N total observations)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

In ANOVA formula, what does g stand for?

A

A group

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

In ANOVA formula, what does k stand for?

A

Total number of groups

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

In ANOVA formula, what does Ng stand for?

A

Size of group g

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

In ANOVA formula, what does Xbar-g stand for?

A

Group mean

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

In ANOVA formula, what does Xig stand for?

A

Xig - observation i in group g

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

What does SSt stand for?

A

The aggregate variation/dispersion of individual observations across groups

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

What are MST , MSM , and MSR often called?

A

the total, model (between-group), and residual (within-group) Mean Squares, respectively

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

Which effect size is more commonly reported in ANOVA?

A

η2 (eta squared)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

What do the effect sizes (pearson R, eta squared and omega squared) all look for?

A

Proportion of variance in the DV that is explained by the IVs

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

What’s the difference between
eta squared and omega squared?

A
  • η2 is positively biased (overestimates the amount of variance explained in the DV by the IVs)
  • ω2 is unbiased
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

What are the cut-offs for the effect size of
omega squared?

A
  • Small ≈ .01
  • Medium ≈ .06
  • Large ≈ .14
  • Report ω2, even if it’s negative
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

What does fully-crossed mean in a factorial design?

A

That the factor levels are multiplied by each other (ex: factor 1 has 3 levels and factor 2 has 3 levels then it’s a 3x3 factorial design with 9 treatment conditions)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

What elements should be included in the APA style analysis conclusion (in order)?

A
  1. 1-2 sentence overview of analyses that includes the independent and dependent variable, stated conceptually.
  2. Description of overall results of F -test, in a particular format, including effect size measure
  3. Description of the pattern of mean differences among groups, including whether significant differences were found (M for mean and SD for standard dev) -> when working with 3 groups ANOVA test, we’ll have to conduct post-hoc tests to evaluate which pairs of groups have significant mean differences
  4. A conceptual conclusion
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

Provide an example of what elements should be included in the APA style analysis conclusion (in order)?

A
  1. To investigate whether level of fitness (low versus high) had an effect on ego strength (with higher scores indicating more ego strength), we conducted a one-way between-subjects ANOVA
  2. This analysis revealed a significant effect of fitness on ego strength,
    F (1, 8) = 5.32, p < .05, ω2 = .61
  3. 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)
  4. We conclude that having high as opposed to low fitness may increase ego strength
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

How to report numbers in APA format?

A
  • 2 decimal places
  • 3 decimal places for p-values
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
32
Q

True or False: with two groups the results of an independent samples t-test and a between-subjects ANOVA on the same data set will always agree

A

FALSE: they could disagree they use a different value of α

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
33
Q

What are assumptions of a single mean z-test?

A
  • The variable, X, in the population is normally distributed
  • The sample must be a simple random sample of the population (independence of observations)
  • The population standard deviation, σ, must be known
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
34
Q

What are the effect size cut-offs for r?

A

0.10 -> small effect
0.30 -> medium effect
0.50 -> large effect

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
35
Q

What does a 95% Confidence interval mean?

A

If we repeated our experiment many times, 95% of the time a 95% CI will contain the true effect

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
36
Q

What does the p-value represent?

A

The p-value represents the proportion of data sets that would yield a result as extreme or more extreme than the observed result if H0 is true

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
37
Q

What are the effect size cut-offs for r squared?

A

0.01 -> small
0.09 -> medium
0.25 -> large

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
38
Q

What are the effect size cut-offs for cohen’s d?

A

0.2 -> small
0.5 -> medium
0.8 -> large

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
39
Q

What are the assumptions in between subjects ANOVA?

A
  1. Independence of observations
  2. Identical distribution (within group)
  3. Identical distribution (between groups)
  4. Homogeneity of variance
  5. Normal Distribution
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
40
Q

Describe the formula Yij =μ+αj +Eij

A
  • Formula describing the linear model underlying everything we do in ANOVA
  • Yij = person i’s score on the outcome Y and this person i belongs in group j -> Y is the dependant variable
  • Eij -> experimental error - something that allows individual scores of people in that population to vary from this group mean (assumed to be normal)
  • Eij is random, but mu + alpha-j is fixed for every member of that population
  • In this equation, mu + alpha-j is constant for every person in the population (one population = one mean)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
41
Q

The assumptions about normality and equal variances are assumptions about what?

A
  • The population
  • Usually we can examine the sample for evidence about whether these assumptions hold
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
42
Q

What are some methods for Assessing Normality?

A

Descriptive and Inferential Statistics:
- Looking at the mean, median, mode
- Tests for skewness (testing whether skewness is significant -> normal distribution has skew of 0, any type of skewness means that the distribution isn’t perfectly normal)
- Kolmogorov-Smirnov and Shapiro-Wilk tests

Visual methods:
- Histograms
- Normal Quantile (Q-Q) Plot

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
43
Q

Describe tests for skewness when assessing normality

A
  • Skewness represents symmetry and whether the distribution has a long tail in one direction
  • Left (negative) skew = Mean < Median
  • Symmetric (normal) = Mean = Median
  • Right (positive) skew = Median < Mean
  • Skewness should be ~0
    > 0 - positive/right skew (longer right-hand tail)
    < 0 - negative/left skew (longer left-hand tail)
  • Also look at standard errors (SE skewness)
  • Conducting a significance test for whether skewness is significantly different from 0
  • To compute this, we will get an estimate of skewness of our variable, divided by the standard error, and then compare this against a value of 3.2 in absolute value
  • Reject the null hypothesis that skew is 0 in the population if the ratio tskewness is greater than 3.2 in absolute value
  • Here we don’t want to reject the null hypothesis because rejecting it would mean we have found evidence that our scores aren’t normally distributed
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
44
Q

What’s the more unbiased estimate of central tendency?

A

Median, rather than the mean

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
45
Q

What are the statistical tests of normality?

A
  • The Kolmogorov-Smirnov (K-S) test
  • The Shapiro-Wilk (S-W) test
  • If a test is significant, reject the null hypothesis that the distribution of the variable is normal
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
46
Q

What’s the Kolmogorov-Smirnov (K-S) test?

A
  • Very general, but usually less power than Shapiro-Wilk (S-W) test
  • Conceptually, compares sample scores to a set of scores generated from e.g., a normal distribution with the sample mean and standard deviation
  • Used to see if the scores on your variable follow any distribution you think they follow
  • Conceptually, this test takes your observed scores on the variable and it compares them to quantiles from this reference distribution you’re trying to assess whether it’s appropriate for your data
  • If there are large departures from the quantiles from the reference distribution and your observed scores -> this would be evidence against your scores following the distribution you think they follow
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
47
Q

What’s the Shapiro-Wilk (S-W) test?

A
  • Usually more powerful, but only for normal distributions
  • Follows a similar logic to the Kolmogorov-Smirnov (K-S) test
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
48
Q

What are limitations of the normality tests and solutions to overcome these?

A
  • It’s easy to find significant results (reject null hypothesis that data is normal) when sample size is large
  • Same with skewness tests -> as the sample size gets larger, SE gets smaller and with smaller SE, you’re more likely to get a t ratio value larger than 3.2, even with small values of skewness
  • Solution: do the tests, but plot data as well and examine the histogram for evidence of multimodality, extreme scores (outliers), and asymmetry
  • More than one mode is evidence of deviation from normality
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
49
Q

Describe the use of histograms to assess normality

A
  • Create separate histograms for each group to assess normality
  • Look for obvious signs of non-normality
  • Doesn’t have to be perfect, just roughly symmetric
  • Multiple modes may suggest that there are different subpopulations in the sample
  • If that’s the case, include a classification variable as an additional factor in the ANOVA
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
50
Q

Describe the use of normal quantile plot (or normal probability plot or Normal Q-Q plot) to assess normality

A
  1. Compute percentile rank for each score
    - Sort observations from smallest to largest
    - What percentage of scores are below score X?
  2. Calculate (theoretical or expected) z-scores from percentile rank
    - If the scores were normal, what would the z-score be?
    3 Calculate actual z-scores
    4 Plot the observed vs. theoretical z-scores
    - We get some percentiles from the z-distribution and we see how much our observed z-scores deviate from the percentiles from the normal distribution
    - If the data are close to normal, then the points will like close to a straight line
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
51
Q

What do violations of the assumption of normality lead to?

A
  • Non-normality tends to produce Type I error rates that are lower than the nominal value
  • Depending on the context of the research study, this may be less concerning than an assumption violation that results in excessive Type I error rates (above the nominal value α)
  • When we select an alpha of say .05, we’re saying that if the null hypothesis is true, 5% of our findings in the long run will be false positives
  • If you don’t meet the assumption of normality and you pick an alpha level of .05 -> less than 5% of your results in the long run will be false positives if the null hypothesis is true
  • This means you have lower power to detect differences if there is an effect in the population
  • A consequence of the violation of the assumption of normality is that you might miss some effects (not inflating type 1 error rate but you are decreasing your power)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
52
Q

Type 1 error rate and what go hand in hand?

A

Type 1 error rate and power go hand in hand (as one increases so does the other)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
53
Q

What’s the assumption of homogeneity of variance?

A

Assuming that all of the group variances are equal

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
54
Q

What does violation of the assumption of homogeneity of variance lead to?

A
  • Serious violation of this assumption tends to inflate the observed value of the F statistic
  • Too many rejections of H0 = high Type I error
  • This is a more problematic assumption because if you violate this assumption, you will inflate your type 1 error rates
  • If you select an alpha of .05, but your assumption of homogeneity of variance is not met, you may end up with more than 5% of false positives if the null hypothesis is true
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
55
Q

What are the different tests that assess homogeneity of variance?

A
  • The Fmax test of Hartley
  • Levene’s test
  • Brown and Forsythe test
56
Q

What’s the Fmax test of Hartley?

A
  • Fmax = ratio of largest group variance to the smallest group variance
  • Calculate the sample variance for each group, and find the largest and smallest variances
  • Compute Fmax:
    Fmax = maxs2g mins2g′
  • The observed Fmax value is compared against a critical value of this statistic
  • If the assumption of homogeneity of variance is satisfied, Fmax ratio would be close to 1
  • If the observed value of Fmax exceeds the critical value, we conclude that we have to reject the null hypothesis and the assumption is not met
  • Easy to compute, but assumes that each group has an equal number of observations
57
Q

What’s Levene’s test?

A
  • Measures how much each score deviates from its group mean
    Zij =|Yij −Ybarj|
  • Instead of using the original scores Yij to run the ANOVA, you use the absolute deviation scores Zij
  • If we retain the null hypothesis, we can conclude that the assumption of homogeneity of variance is met
  • The downside of this test is that it’s easier to obtain a significant F-ratio for this ANOVA when your sample size is large
58
Q

What’s the Brown-Forsythe test?

A
  • It measures how much each score deviates from its group median
  • The median is less weighed by outliers than the mean and isn’t pulled by a skewed variable
  • Zij =|Yij −Mdj|
  • Instead of using the original scores Yij to run the ANOVA, you use the absolute deviation scores Zij
  • For both the Levene and Brown-Forsythe tests a statistically significant finding (e.g., p ≤ .05) leads to the conclusion that the variances are significantly different across groups (i.e., the assumption of homogeneity of variance is not met)
  • The Brown-Forsythe test is slightly more robust than Levene’s test
59
Q

For both the Levene and Brown-Forsythe tests a statistically significant finding (e.g., p ≤ .05) leads to what conclusion?

A

That the variances are significantly different across groups (i.e., the assumption of homogeneity of variance is not met)

60
Q

Which test is recommended more than the other: Brown-Forsythe test or Levene’s test?

A

Brown-Forsythe test is recommended over the Levene’s test

61
Q

What are the 5 assumptions in ANOVA?

A
  • Independence of observations (random sampling)
  • Identical distribution (within groups) (random sampling)
  • Identical distribution (between groups)
  • Homogeneity of variance
  • Normal distribution
62
Q

What kind of statistical test only has one mean?

A
  • z-test
  • One-sample t-test
63
Q

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

A

Independent samples t-test

64
Q

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

A

One-way ANOVA

65
Q

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

A

Two-way ANOVA

66
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

67
Q

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

A

3 levels in Factor A
4 levels in Factor B

68
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
69
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

70
Q

What’s a balanced design?

A

When sample sizes are equal in each condition

71
Q

What do Factors represent?

A

The independent variables

72
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

73
Q

How many effects comprise a two-way factorial experiment?

A

2 main effects
An interaction effect

74
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
75
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
76
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

77
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

78
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

79
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)
80
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
81
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
82
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
83
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
84
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

85
Q

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

A

FA = MSA / MSR

86
Q

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

A

FB = MSB / MSR

87
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

88
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

89
Q

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

A

Number of levels for Factor A

90
Q

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

A

Number of levels for Factor B

91
Q

What are treatment sums in 3-way ANOVA?

A

Sum of raw scores in each treatment group

92
Q

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

A

The sum of all the scores in the experiment

93
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)
94
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)
95
Q

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

A
  • Levels of Factor A (only has 1 factor)
  • Subjects (participants)
96
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

97
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
98
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

99
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

100
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
101
Q

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

A

SSaxb

102
Q

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

A

SS(S) and SS(AxS)

103
Q

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

A
  • Normality
  • Homogeneity of variance
  • Homogeneity of covariance
104
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

105
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

106
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)

107
Q

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

A
  • Homogeneity of variance
  • Homogeneity of covariance
108
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

109
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
110
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)
111
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)

112
Q

What’s the function of epsilon?

A

It measures the extent to which sphericity was violated

113
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
114
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
115
Q

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

A

Greenhouse-Geisser is smaller (more conservative)

116
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)

117
Q

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

A

SSW =SSA+SSAxS

118
Q

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

A

F = MSA / MSsxa

119
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

120
Q

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

A

p < .05

121
Q

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

A

p > .05

122
Q

Describe sphericity in one-way repeated-measures ANOVA

A

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

123
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
124
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
125
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)
126
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
127
Q

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

A
  • df values
  • MS values (since they’re calculated with df)
128
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
129
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
130
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

131
Q

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

A

Omega-squared (ω2)

132
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

133
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

134
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
135
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)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions