Brainscape's Knowledge GenomeTM

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


See full index

STAT PSY3062 > Analysis of Variance (ANOVA) > Flashcards

Analysis of Variance (ANOVA) Flashcards

1
Q

Define

Independent ANOVA

A

used to compare two or more means of several independent (different) groups. It can only tell whether there are differences between the means of the different groups, but not where and in what direction

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

Define

Repeated-measures ANOVA

A

the equivalent of the one-way ANOVA, but for related, not independent groups, and is the extension of the dependent t-test

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

Define

T-test

A

a type of inferential statistic used to determine if there is a significant difference between the means

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

Define

Family-wise alpha level (αFW)

A

Probability of making at least one Type I error amongst a series of comparisons

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

Define

Decision-wise alpha level (αDW)

A

Alpha level for each comparison

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

Define

Type I error

A

occurs when a researcher incorrectly rejects a true null hypothesis

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

Define

Total sum of squares (SSt)

A

Total variability between scores

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Define

Model sum of squares (SSm)

A

Variability between group means (i.e. our model)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Define

Residul sum of squares (SSr)

A

Residual variability that in unexplained and due to chance

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

Define

Critical value

A

a line on a graph that splits the graph into sections. One or two of the sections is the “rejection region“; if your test value falls into that region, then you reject the null hypothesis. A one tailed test with the rejection rejection in one tail

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Define

A priori

A

relating to or denoting reasoning or knowledge which proceeds from theoretical deduction rather than from observation or experience

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

Define

Bonferroni method

A

a simple method that allows many comparison statements to be made (or confidence intervals to be constructed) while still assuring an overall confidence coefficient is maintained

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

Define

Eta-squared

A

a measure of effect size for analysis of variance (ANOVA) models. It is a standardized estimate of an effect size, meaning that it is comparable across outcome variables measured using different units

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

Define

Omega squared

A

a measure of effect size, or the degree of association for a population. It is an estimate of how much variance in the response variables are accounted for by the explanatory variables

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Define

Cohen’s d

A

an effect size used to indicate the standardised difference between two means. It can be used, for example, to accompany reporting of t-test and ANOVA results

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

Define

F-ratio

A

The overall significance of the regression equation; a significant value indicates that the equation predicts a significant proportion of the variability in the Y scores (i.e., more than would be expected by chance alone)

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

Define

Post hoc

A

statistical analyses that were specified after the data were seen

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

Define

Variance

A

tells us how much scores deviate from the mean

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

Define

Homogeneity of variance

A

the assumption that all groups have the same or similar variance

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

Definition

used to compare two or more means of several independent (different) groups. It can only tell whether there are differences between the means of the different groups, but not where and in what direction

A

Independent ANOVA

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

Definition

the equivalent of the one-way ANOVA, but for related, not independent groups, and is the extension of the dependent t-test

A

Repeated-measures ANOVA

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

Definition

a type of inferential statistic used to determine if there is a significant difference between the means

A

T-test

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

Definition

Probability of making at least one Type I error amongst a series of comparisons

A

Family-wise alpha level (αFW)

24
Q

Definition

Alpha level for each comparison

A

Decision-wise alpha level (αDW)

25
Q

Definition

occurs when a researcher incorrectly rejects a true null hypothesis

A

Type I error

26
Q

Definition

Total variability between scores

A

Total sum of squares (SSt)

27
Q

Definition

Variability between group means (i.e. our model)

A

Model sum of squares (SSm)

28
Q

Definition

Residual variability that in unexplained and due to chance

A

Residul sum of squares (SSr)

29
Q

Definition

a line on a graph that splits the graph into sections. One or two of the sections is the “rejection region“; if your test value falls into that region, then you reject the null hypothesis. A one tailed test with the rejection rejection in one tail

A

Critical value

30
Q

Definition

relating to or denoting reasoning or knowledge which proceeds from theoretical deduction rather than from observation or experience

A

A priori

31
Q

Definition

a simple method that allows many comparison statements to be made (or confidence intervals to be constructed) while still assuring an overall confidence coefficient is maintained

A

Bonferroni method

32
Q

Definition

a measure of effect size for analysis of variance (ANOVA) models. It is a standardized estimate of an effect size, meaning that it is comparable across outcome variables measured using different units

A

Eta-squared

33
Q

Definition

a measure of effect size, or the degree of association for a population. It is an estimate of how much variance in the response variables are accounted for by the explanatory variables

A

Omega squared

34
Q

Definition

an effect size used to indicate the standardised difference between two means. It can be used, for example, to accompany reporting of t-test and ANOVA results

A

Cohen’s d

35
Q

Definition

The overall significance of the regression equation; a significant value indicates that the equation predicts a significant proportion of the variability in the Y scores (i.e., more than would be expected by chance alone)

A

F-ratio

36
Q

Definition

statistical analyses that were specified after the data were seen

A

Post hoc

37
Q

Definition

tells us how much scores deviate from the mean

A

Variance

38
Q

Definition

the assumption that all groups have the same or similar variance

A

Homogeneity of variance

39
Q

What type of research questions are appropriate for an ANOVA?

A

Which treatment is most effective for decreasing depressive symptoms?

Does loneliness vary by attachment style?

Is number of days of exercise influenced by geographical location?

40
Q

What is the null hypothesis of an ANOVA?

A

ANOVA tests the null hypothesis that the means for all groups are identical

41
Q

What does an ANOVA tell us?

A

A statistically significant ANOVA indicates that not all means are identical

  • at least one group mean differs from the rest
  • Note that more than one group means may be different
42
Q

Why do we use ANOVAs instead of multiple t-tests?

A
  • We cannot look at more than one independent variable at a time
  • Inflates our Type I error rate (i.e., chance of rejecting H0 when we should NOT)
  • When assumptions are met, ANOVA is more powerful than t-tests (for 2+ groups)
43
Q

αFW = 1 – (1 – αDW)C

Let’s say the number of comparisons (C) = 3 αDW = .05

What is the probability of commiting at least one Type I error?

A

αFW = 1 – (1 – .05)3

αFW = 1 – (.95)3

αFW = .14

Our probability of committing AT LEAST ONE Type I error has increasing from 5% to 14%

44
Q

How does Total sum of squares relate to model and residual sum of squares?

A

SST = SSM + SSR

45
Q

Which statistic do we use to explain whether the model explains more variability than the residuals in an ANOVA?

A

F-ratio

46
Q

If the treatment has no effect, what do we expect of the F-ratio?

A

The differences between the model and residual are entirely due to chance. The numerator will be SMALLER than the denominator and we conclude there is no treatment effect (i.e., the F will be smaller than 1 and the test will be non-significant)

47
Q

If the treatment has an effect, what do we expect of the F-ratio?

A

The numerator will be LARGER than the denominator and we will get a significant result (i.e., the F will be greater than 1). A larger F-ratio indicates that the differences between treatments are greater than chance.

48
Q

What does the F-ratio tell us?

A

If F is large, the variability attributable to the model is greater than the variability that occurs simply due to chance (e.g., error)

If the F-ratio is larger than the critical value for our set alpha level (most often .05), it tells us that 1 or more group means are statistically significantly different from each other

49
Q

What causes an F-ratio to be large?

A

MSM is large = large differences in group means

MSR is small = very little variability within groups

50
Q

What does an independent ANOVA assume?

A
  1. Independence of observations
    • The observations within each sample must be independent
  2. Interval / ratio data
  3. Normality
    • The parameter sampling distributions, can also check residual distributions
  4. Homogeneity of variance
    • The variance of each group must be approximately equal (i.e., homogeneous)
    • If they are unequal (i.e., heterogeneous), this assumption is violated
51
Q

What do we do if normality is violated?

A
  • If sample sizes are equal (across groups) and large (e.g., dferror > 100), ANOVA is largely robust to violations of the normality assumption
    • Central limit theorem
  • If sample sizes are not equal or small, ANOVA is more sensitive to violations of normality
    • Depends on the smallest group sample size
    • Consider:
      • Transforming your data to see if the residuals are closer to a normal distribution after the transformation
      • You can use a non-parametric test (the Kruskal-Wallis test)
52
Q

What do we do if the homogeneity of variance is violated?

A

In the case of violations, you can use the Brown-Forsythe or Welch F, df, and p values instead of the regular F

53
Q

What does a repeated measure ANOVA assume?

A
  1. Continuous data for dependent variable, independent variable categorical
  2. Normality
    • Also, outliers
  3. Homogeneity of variance
    • The variance of each group must be approximately equal (i.e., homogeneous)
    • If they are unequal (i.e., heterogeneous), this assumption is violated
54
Q

Why do we use post-hoc tests?

A
  • The F-ratio only tells us whether or not the treatment worked (i.e., group means were different)
    • We don’t know which means differ from one another
    • We need to run a follow-up test to find where the differences lie
55
Q

How do we avoid the increase in false positives that occurs due to running multiple post hoc tests?

A

Calculate a Bonferroni value

56
Q

Which values can we use to calculate the proportion of variance accounted for by a variable?

A
  1. 𝑟 2 (r-squared)
  2. 𝜂 2 (eta-squared)
  3. 𝜔 2 (omega-squared)
57
Q

What is a small, medium and large Cohen’s d?

A

Small effect = 0.20

Medium effect = 0.50

Large effect = 0.80

STAT PSY3062 (9 decks)

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