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Psych 110 (Stats) > ANOVA - Analysis of Variance > Flashcards

ANOVA - Analysis of Variance Flashcards

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1
Q

Very flexible and general technique, and the principles can be applied to a wide range of statistical tests.

  • Has a wide range of applications.
  • Many of applications make some tricky assumptions about the data.
A

ANOVA

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2
Q

In ANOVA we measure an _____ (also called a dependent variable).

A

outcome variable

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3
Q

This outcome must be measured on a ______

A

continuous scale.

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4
Q
  • It is called _____because it depends on one or more predictor variables.
A

dependent

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5
Q

_______ can be Manipulated (Treatment) or variables we simply measure (Sex).

A

Predictor variable

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6
Q

In ANOVA, predictor variables are mostly _____, although continuous variables can also be used in the same framework.

A

categorical

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7
Q

When predictor variables are categorical, they are also called_____ or _____

A

FACTORS or INDEPENDENT VARIABLES

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8
Q

measurement of differences.

A

ANOVA

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9
Q

Differences happen for two reasons: (a) because of the effect of ______ (b) because of ____

A

a. predictor variables
b. other reasons

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10
Q

In ANOVA, we want to know two things:

A
    1. How much of the variance (difference) between the two groups is due to the predictor variable
    1. Whether this proportion of variance is statistically significant, that is, it is larger than we would expect by chance if the null hypothesis were true?
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11
Q

We can divide (statisticians sometimes say partition) variance into three different types:

A

The Total Variance

Variance due to treatment, (Differences between Group)

Variance due to Error (Differences within Group)

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12
Q

In ANOVA, the ______ is conceptualized as sums of squared deviations from the ____

A
  1. variance
  2. mean
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13
Q

It is usually shortened to sum of squares and denoted by _____

A

SS or Sum of Squares

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14
Q

The 3 Sum of Squares

A
  1. Between-groups Sum of Squares
  2. Error Sum of Squares
  3. Total Sum of Squares
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15
Q

Total Sum of Squares, called

A

SStotal

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16
Q

We are asking whether the _____ (or the effect of the predictor) is big enough that we could say it is not due to chance.

A

difference between the groups

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17
Q

________

this is the variance that represents the difference between the groups, and this is called ____
. Sometimes it refers to the
between-groups sum of squares for one predictor, in which case it is called SS predictor. Sometimes it is called

A
  1. Between-groups Sum of Squares
  2. SSbetween
  3. SStreatment
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18
Q

The between-groups variance is the_____ that we are actually interested in

A

variance

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19
Q

also called within-groups sum of squares.

A

Error sum of squares

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20
Q

It’s within the groups, because different people, who have had the same treatment, have ____

A

different scores.

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21
Q

They have different scores because of error. So this is called either ___ or ___

A

SSwithin or SSerror

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22
Q

We need to calculate the three kinds of Sum of Squares,____ and _____

A
  1. TOTAL
  2. WITHIN GROUPS
  3. BETWEEN GROUPS.
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23
Q

sum of squared differences between the mean and each score

A

SStotal

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24
Q
  • Step 1: Find the Mean of the scores.
  • Step 2: Calculate the difference between each score and the mean score.
  • Step 3: Calculate the Squared deviations
  • Step 4: Find the Sum of the Squared Deviations
A

Calculating the SS total

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25
Q
  • Procedure is very similar.
  • This time we are looking for the sum of squares within each group.
  • Rather than using the total mean, we use the mean for each group.
A

Calculating the SSwithin

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26
Q

Easy way and hard way.

  • SStotal = SSwithin + SSbetween
  • Thus: SS Between = SS Total – SS Within
A

Calculating SSbetween

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27
Q

To know how large the effect of the treatment has been.

A

Effect size

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28
Q

The same as asking what proportion of the Total Variance (or Total Sum of Squares) the treatment effect has been responsible for

A

effect size

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29
Q

calculating the effect size

A

This is just: SS Between / SS Total.

30
Q

Effect Size goes under two different names: these are

A

R -Squared or eta-Squared.

31
Q

1st: Calculate the Mean Squares. Often written as MS. * These are MSbetween, MSwithin, MStotal

A

Calculating Statistical Significance

32
Q

this gives us the statistic for ANOVA, which is called___, or sometimes the ____

A

F or F-ratio.

33
Q

____ and___ are exactly the same test

A

ANOVA and t-test

34
Q

To find the probability value associated with F we need to have two sets of ____, the between and within.

A

degrees of freedom

35
Q

In fact, if we take the value of t and square it. We get the value of ____

A

F

36
Q

This is a general rule when there are 2 groups

A

F = t-squared

37
Q

restricted to comparing 2 groups.

A

t-test

38
Q

extends in a number of useful directions.

A

ANOVA

39
Q

Can be used to compare 3 groups or more, to calculate the p-value associated with the Regression Line, and in a wide range of other situations.

A

ANOVA and T-test

40
Q

When there are 2 groups, ANOVA____ is equivalent to a t-test, and it therefore makes the same assumptions as the t-test.

and it makes these assumptions regardless of the number of groups that are being compared

A

When there are 2 groups, ANOVA is equivalent to a t-test, and it therefore makes the same assumptions as the t-test.

41
Q

ASSUMPTIONS IN ANOVA

We do not assume that the outcome variable is normally distributed.

What we do assume is that data within each group are normally distributed.

A

Normal distribution within each group

42
Q

ASSUMPTIONS IN ANOVA

  • As with the t-test, we assume that the standard deviation within each group is approximately equal.
  • the variance being the square of the SD.
  • However, as with the t-test, we don’t need to worry about this assumption, if we have approximately equal numbers of people in each group.
  • Formulae are all the same.
A

Homogeneity of Variance

43
Q

most elementary analysis of variance

A

one way ANOVA

44
Q

one way ANOVA also called as
1.
2.
3.
4.

A

simple-randomized groups design, independent groups design, or the single factor experiment, independent groups design.

45
Q

not limited to single factor experiments.

A

ANOVA

46
Q

The effect of many different factors may be investigated at the same time in____

A

one experiment

47
Q

one in which the effects of two or more factors or IVs are assessed in one experiment.

A

Factorial experiment

48
Q

used are combinations of the levels of factors.

A

Conditions or treatments

49
Q

more complicated. However, we get a lot more information

  • It allows in one experiment to evaluate the effect of two IVs and the interaction between them.
A

TWO WAY ANOVA

50
Q

Since this is an independent groups design, subjects would be_____to each of the cells so that a different group of subjects occupies each cell.

A

randomly assigned

51
Q

Two-Way ANOVA

We want to determine whether factor A has a significant effect, disregarding the effect of factor B. This is called the ____

A

main effect of factor A.

51
Q

the levels of each factor were systematically chosen by the experimenter rather than being randomly chosen.

A

Fixed effects design

52
Q

Two-Way ANOVA

We want to determine whether factor B has a significant effect, without considering the effect of factor A. This is called the ___

A

main effect of factor B.

53
Q

Two-Way ANOVA

we want to determine whether there is an interaction between factors A and B.

A

interaction effect of factors A and B.

54
Q

In analyzing data from a two-way ANOVA, we determine four variance estimates:

A
  • MS within cells
  • MS rows
  • MS columns
  • MS interaction
55
Q

The estimate MS within cells is the within cells variance estimate and corresponds to the within groups variance estimate used in the ____

A

one-way ANOVA.

56
Q

The other estimates are sensitive to the effects of the____

A

IVs. or independent variables

57
Q

The estimate MS rows is called the ____.

It is based on the variability of the row means and, hence, is sensitive to the effects of variable A.

A

row variance estimate

58
Q

The estimate MS columns is called the ____

It is based on the variability of the column means and, hence, is sensitive to the effects of variable

A

column variance estimate.

59
Q

If variable A has no effect, MS rows is an independent estimate of the____

A

σ-squared.

60
Q

Finally, if there is no interaction between variables A and B, MS interaction is also an independent estimate of ____

A

σ – squared.

61
Q

Thus, the estimates MS rows, MS columns, and MS interaction are analogous to the between-groups variance estimate of the _____

A

one-way ANOVA design.

62
Q

Each F (or F obtained) value is evaluated against F crit (critical value) as in the____

A

one way analysis.

63
Q

In a_____, we can essentially two one-way experiments, plus we are able to evaluate the interaction between the two independent variables.

A

two-way ANOVA

64
Q

In a ____, we partition the total sum of squares (SS total), into four components:

A

2-way ANOVA

the within-cells sum of squares,

the row sum of squares,

the column sum of squares, and

the interaction sum of squares.

65
Q

When these Sum of Squares (SS) are divided by the appropriate degrees of freedom, they form four variance estimates.

A

(MS within-cells, MS rows, MS columns and MS interaction)

66
Q
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69
Q
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Psych 110 (Stats) (9 decks)

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