Deck 12: Analysis of Variance

Question 1

If one had to calculate 15 successive t tests, it would mean

A) testing Ho 5 times
B) testing Ho once
C) testing Ho 15 times
D) none of these, since t never tests Ho

Answer 1

C

Question 2

The F ratio was developed by

A) William Sealy Gossett
B) Sir Ronald Fisher
C) Karl Pearson
D) Sir Bryant McKenna

Answer 2

B

Question 3

The concept of "total variability" is based on

A) how far the scores in all groups deviate from the total mean
B) how far the sample means deviate from each other
C) how far the scores in a single group deviate for their own group mean
D) how far each sample mean deviates from the total mean

Answer 3

how far the scores in all groups deviate from the total mean

Question 4

When the distribution of scores within a sample forms a platykurtic shape, then

A) the variance within the sample is small
B) the variance within the sample is large
C) the variance within the sample is negative
D) the variance within the sample equals the standard deviation

Question 5

Analysis of experimental data by the F ratio means that the independent variable could have been manipulated

A) at only two levels
B) at two or more levels
C) at only three levels
D) none of these, since F cannot handle experimental data

Question 6

When the SS, sum of squares, is large, so too is the

A) standard deviation
B) variance
C) both of these
D) neither of these

Question 7

The SS, sum of squares, is equal to

A) the sum of the squared scores
B) the sum of the scores, squared
C) the sum of the squared deviations of all the scores from the mean
D) the sum of the squared deviations of all the scores from the mean, divided

Question 8

The only time the variance becomes equal to the standard deviation is when

A) the variance is small
B) the variance is large
C) the variance is eliminated
D) the variance is equal to 1.00 or zero

Question 9

With the F ratio, the overall hypothesis among 4 group means may be tested by making

A) 4 statistical decisions
B) 3 statistical decisions
C) 2 statistical decisions
D) 1 statistical decision

Question 10

The F ratio may be used to assess differences between (among)

A) two sample means
B) three sample means
C) four sample means
D) all of these

Question 11

The concept of "within variability" is based on

A) how far the scores in all groups deviate form the total mean
B) how far the scores deviate from their own sample means
C) how far each sample mean deviates from the total mean
D) none of these

Question 12

Comparing all means from a four-group design would require the calculation of

A) four t tests
B) six t tests
C) one t test
D) fifteen t tests

Question 13

The smallest possible value for the SS, sum of squares, is

A) -5.00
B) 0
C) .01
D) 1.00

Question 14

For the F ratio, if alpha is set at .05, it remains at .05 if comparisons are made between (among)

A) 2 group means
B) 10 group means
C) 45 group means
D) all of these

Question 15

With the t test, as the number of decisions to reject Ho increases, so too

A) does the number of degrees of freedom
B) does the sampling error
C) does alpha
D) all of these

Question 16

The concept of "between variability" is based on

A) how far the scores in all groups deviate from the total mean
B) how far the scores in a single group deviate from their own group mean
C) how far each sample mean deviates from the total mean
D) all of these, depending on the between degrees of freedom

Question 17

The alternative hypothesis for the F ratio is that the sample means

A) represent a single population
B) represent completely different populations
C) do not all represent a single population
D) none of these

Question 18

With a two-group experimental design, the independent variable has been manipulated at

A) one level
B) two levels
C) three levels
D) four levels

Question 19

Doing successive t tests within the context of a single experiment

A) is theoretically the same as doing an F ratio
B) is theoretically the same as doing a Pearson r
C) is theoretically the same as doing a Spearman r
D) may inflate the alpha error

Question 20

When the distribution of raw scores within a sample forms a leptokurtic shape, then

A) the variance within the sample is small
B) the variance within the sample is large
C) the variance within the sample is negative
D) the variance within the sample equals the standard deviation

Question 21

The larger the F ratio

A) the more likely the samples represent a common population
B) the less likely the samples represent a common population
C) the more likely that the between sum of squares is small
D) the more likely that the within sum of squares is large

Question 22

The mean square (MS) is always equal to (when based on SS/df)

A) the square of the total mean
B) the sum of the squares of the separate group means
C) the variance squared
D) the variance

Question 23

The sums of squares components relates such that SS between is equal to

A) SS within
B) SS total - SS within
C) SS total + SS within
D) none of these

Question 24

The greater the value of the F ratio,

A) the more the sample distributions overlap
B) the less the sample distributions overlap
C) the larger the sum of squares within groups
D) none of these

Question 25

If the F ratio were performed on a four-group design and F were equal to 4, then t would be equal to

A) 16
B) 4
C) 2
D) none of these, since t is only appropriate on a two-group design

Question 26

When the variance within a sample group is equal to 16, then the standard deviation for that sample is equal to

A) 16
B) 8
C) 1.00
D) none of these

Question 27

The greater the sum of squares within groups

A) the more the sample means deviate from the total mean
B) the more the sample means deviate from each other
C) the more the individual scores deviate from the total mean
D) none of these

Question 28

When the between sum of squares is relatively large, then the shape of the sampling distribution is necessarily

A) leptokurtic
B) platykurtic
C) mesokurtic
D) none of these

Question 29

If a significant F ratio is obtained, then

A) Ho must be accepted
B) Ho must be rejected
C) Ha must be rejected
D) there must be at least four sample means

Question 30

The less overlap there is among the various sample-group distributions

A) the larger the F ratio
B) the smaller the F ratio
C) the greater the degrees of freedom
D) none of these

Question 31

An F ratio of 5, tells us specifically that the variance between groups is

A) 5 times smaller than the variance within
B) 5 times larger than the variance within
C) 5 times smaller than the total variance
D) 5 times larger then the total variance

Question 32

When doing an F ratio on a three-group design, 5 subjects in each group, the within degrees of freedom will equal

A) the MS within
B) 2
C) 5
D) none of these

Question 33

When doing an F ratio, subtracting the number of groups from the total number of subjects yields the

A) alpha error
B) between degrees of freedom
C) within degrees of freedom
D) total degrees of freedom

Question 34

The greater the value of the MS between groups,

A) the more likely Ho will be rejected
B) the less likely Ho will be rejected
C) the more likely the various group means will equal each other
D) none of these

Question 35

When doing an F ratio on a four-group design, 4 subjects in each group, the between degrees of freedom will equal

A) the MS between
B) 4
C) 3
D) 12

Question 36

When four leptokurtic sampling distributions show no overlap whatever, then

A) the MS within is likely to be large
B) the MS between is likely to be small
C) the F ratio is likely to be significant
D) there must be zero degrees of freedom

Question 37

When the within sum of squares is relatively large, then the shape of the sampling distribution is necessarily

A) leptokurtic
B) platykurtic
C) mesokurtic
D) none of these

Question 38

The sums of squares components relate such that SS total is equal to

A) SS between
B) SS between + SS within
C) SS within - SS between
D) none of these

Question 39

The sum of squares components relate such that SS within is equal to

A) SS total
B) SS total + SS between
C) SS total - SS between
D) SS between - SS total

Question 40

If the F ratio were performed on a two-group design and F were equal to 9, then t would be equal to

A) 81
B) 9
C) 3
D) none of these

Question 41

When the calculated F ratio is equal to or greater than the critical, tabled value of F for a given number of degrees of freedom, then

A) alpha is inflated
B) There is a failure to reject Ho
C) Ho is rejected
D) none of these

Question 42

When doing an ANOVA with one degree of freedom between groups, then

A) only one sample group has been selected
B) exactly two sample groups have been selected
C) more than two sample groups have been selected
D) cannot tell without knowing the within degrees of freedom

Question 43

In order to calculate an F ratio, there must be

A) more than one sample group
B) interval data
C) homogeneous variances among the sample groups
D) all of these

Question 44

When analyzing experimental research via the F ratio, the action of the independent variable is most clearly shown in the value of the

A) MS total
B) MS within
C) MS between
D) degrees of freedom

Question 45

When analyzing experimental research via the F ratio, random error and individual differences among the subjects is most clearly shown in the value of the

A) MS total
B) MS within
C) MS between
D) degrees of freedom

Question 46

Once an F ratio has been found not to be significant, we must immediately

A) apply Tukey's HSD
B) increase the alpha level to a point where the F is significant
C) re-allocate the degrees of freedom
D) none of these

Question 47

If the tabled value for F, for a given number of degrees of freedom, were equal to 5.14, and the calculated value of F also was equal to 5.14, then

A) There is a failure to reject Ho
B) Ho is rejected
C) Ho is equal to Ha
D) cannot tell from the above information

Question 48

The F ratio can never be significant unless

A) the MS between is significantly smaller than the MS within
B) the MS between is equal to the MS within
C) the MS between is significantly larger than the MS within
D) none of these

Question 49

Dividing the MS between by the MS within, yields the

A) F ratio
B) alpha level
C) variance
D) ANOVA

Question 50

The one-way ANOVA may only be used when

A) the direction of the difference is specified
B) the F ratio is significant
C) there are more than 3 sample groups
D) there is only one independent variable

Question 51

When doing an F ratio, subtracting the constant, 1, from the total number of sample groups yields the

A) alpha error
B) between degrees of freedom
C) within degrees of freedom
D) total degrees of freedom

Question 52

If the MS between equals 10, and the MS within equals 10, the total degrees of freedom are equal to

A) 1
B) 20
C) 0
D) cannot tell from the above information

Question 53

When analyzing a significant ANOVA, in order to establish precisely where the sample differences may have occurred, we may

A) apply the HSD
B) reduce the alpha error
C) calculate the coefficient of determination
D) none of these, since a significant F indicates precisely where the sample

Question 54

Dividing the sum of squares (SS) by the degrees of freedom (df), yields the

A) F ratio
B) alpha error
C) the mean square
D) ANOVA

Question 55

Tukey's HSD is used in order to

A) establish the significance of the overall F ratio
B) allocate the degrees of freedom
C) establish the alpha error
D) none of these

Question 56

An F ratio which equals exactly 1.00, indicates that

A) the total degrees of freedom are equal to 1
B) the between degrees of freedom are equal to 1
C) the within degrees of freedom are equal to 1
D) the MS between has exactly the same value as the MS within

Question 57

Once an F ratio is found to be significant, then

A) each sample mean must represent a different population
B) each sample mean must represent a single population
C) each sample mean deviates by the same amount
D) none of these

Question 58

If the MS between equals 10, and the MS within equals 5, then the F ratio equals

A) 15.00
B) .50
C) 2.00
D) cannot tell from the above information

Question 59

When analyzing experimental research via the F ratio, the number of sample groups, and the number of subjects in each sample group, are most clearly shown in the value of the

A) MS total
B) MS within
C) MS between
D) degrees of freedom

Question 60

The factorial ANOVA is only applied when

A) there is more than one independent variable
B) there is more than one dependent variable
C) there is exactly one independent variable
D) there is 1 degree of freedom between groups

Question 61

The F ratio may compare two or more sample means.

Question 62

When several independent variables are manipulated simultaneously, an appropriate analysis would be the

A) one-way ANOVA
B) factorial ANOVA
C) partial ANOVA
D) none of these

Question 63

Within variability results from the accumulated differences between each individual score and the total mean.

Question 64

A significant F ratio can only occur when the between variability is less than the within variability.

Question 65

When the data form is nominal, the appropriate F ratio is

A) the one-way
B) the two-way
C) the factorial
D) none of these, since F should not be calculated from nominal data

Question 66

A factorial ANOVA may show the significance of

A) treatment A
B) treatment B
C) the interaction between A and B
D) all of these

Question 67

An ANOVA cannot be done unless the sample sizes are unequal.

Question 68

On a factorial ANOVA, a significant interaction indicates

A) the cumulative effect of two or more independent variables
B) the partial effect of several independent variables taken separately
C) the interactive effect of several dependent variables
D) none of these

Question 69

The F ratio may only be calculated when the independent variable has exactly two levels.

Question 70

A factorial ANOVA must have a minimum of

A) two cells
B) four cells
C) eight cells
D) none of these, since the factorial ANOVA may be performed on any number of

Question 71

In order to calculate an F ratio, there must be

A) interval data
B) a normal distribution in the population from which the samples were selected
C) similarity among the within variances for each sample
D) all of these

Question 72

Between variability results from the accumulated differences between each sample mean and the total mean.

Question 73

The between SS plus the within SS equals the total SS.

Question 74

Total variability results from the accumulated differences between each individual score and the total mean.

Question 75

The variance, or mean square, results from dividing the SS by the degrees of freedom.

Question 76

The F ratio, like the t ratio, can be used to predict the direction of the mean difference.

Question 77

The F ratio cannot be used on post-facto data.

Question 78

In a factorial ANOVA, the row variability, column variability and rxc variability, are all components of the

A) MS within
B) MS total
C) MS between
D) interaction effect

Question 79

On a factorial ANOVA, the number of different variations in treatment conditions, determines the number of

A) cells
B) dependent variables
C) subjects within each group
D) all of these

Question 80

When doing a factorial ANOVA, the main effects are found from the

A) rows
B) columns
C) both of these
D) neither of these