Deck 11: Analysis of Variance

Question 1

the problem with conducting multiple t-tests instead of using a post-hoc test is that you increase the risk of type-I errors.

Answer 1

True

Question 2

Tukey HSD can only be used if each condition or level has equal number of participants (i.e., equal n's).

Answer 2

False

Question 3

Whether or not a statistical procedure turns out to be significant has nothing to do with the size of the sample.

Answer 3

False

Question 4

A significant effect is not always a meaningful effect.

Question 5

ANOVAs can be done for mean comparisons between two groups

Question 6

In an ANOVA with one factor that has three different conditions, there are a total of 4 levels.

Question 7

Unlike a t-test, a one-way ANOVA is used when there is more than one dependent variable

Question 8

In a 2 x 2 ANOVA, there are two factors, but a total of four conditions

Question 9

Post-hoc tests such as the Tukey should be done regardless of statistical significance when conducting an one-way ANOVA with more than two levels

Question 10

In a one-way ANOVA with 30 participants, and the factor has 4 levels, the between subjects degree of freedom is 25.

Question 11

In a 3 x 5 ANOVA with 60 participants, the total degrees of freedom is 59

Question 12

ANOVA was designed to analyze mean differences when there are two or more groups

Question 13

MS_w is the quotient or ratio of SS_w and df_w

Question 14

The F-statistic is calculated by taking the difference between MS_b and MS_w

Question 15

A factorial model ANOVA has more than 1 factor

Question 16

In a two-way ANOVA, you can test two main effects

Question 17

To obtain the degrees of freedom for the interaction in a two-way ANOVA, you multiply the number of levels in each factor

Question 18

Statistical significance is in part due to the size of the sample

Question 19

The Tukey HSD allows you to determine which means differ in a one-way ANOVA with more than 2 levels

Question 20

An ANOVA assumes independence of observations

Question 21

A 3 x 2 ANOVA is a ___-way ANOVA, with ___ conditions?

A) One; 6
B) Two; 5
C) Three; 6
D) Two; 6

Question 22

A one-way ANOVA makes several assumptions. Which of the following is not an assumption?

A) Independent observations
B) Normal distribution in the data
C) The null hypothesis is the true state of the world
D) Each condition has the same number of observations

Question 23

In general, ANOVA tests for…

A) differences between means.
B) differences between dependent variables.
C) differences between means in only 3 or more groups.
D) Differences between medians between 2 or more groups.

Question 24

If there are two factors, one with 3 levels and the other with 2,, which is the most appropriate test to analyze data obtained from this design (assuming interval or ratio scale)?

A) 3 x 2 ANOVA
B) 2 x 2 ANOVA
C) One-way ANOVA
D) dependent samples t-tests

Question 25

Which of the following is always true of a two-way ANOVA?

A) There are four levels in total.
B) There are two interaction effects.
C) There are two outcome variables
D) There are two factors.

Question 26

When conducting a one-way ANOVA with 30 participants and the factor has 4 levels, the degrees of freedom between is ____.

A) 3
B) 25
C) 26
D) 4

Question 27

$\begin{array}{lcc}\hline \text { Source } & S S & d f& MS &F \\\hline \text { Between } & 4 & 2240.2 & 560.05 & 1.22 \\\text { Within } & 40 & 18434.5 & \\\text { Total } & 45 & &\\\hline\end{array}$ Based on this data, it can be assumed that this was a …

A) one-way ANOVA.
B) 2 x 2 ANOVA.
C) 1 x 2 ANOVA.
D) Independent samples t-test.

Question 28

$\begin{array}{lcc}\hline \text { Source } & S S & d f& MS &F \\\hline \text { Between } & 4 & 2240.2 & 560.05 & 1.22 \\\text { Within } & 40 & 18434.5 & \\\text { Total } & 45 & &\\\hline\end{array}$ How many levels are there for the independent variable?

A) 2
B) 3
C) 4
D) 5

Question 29

$\begin{array}{lcc}\hline \text { Source } & S S & d f& MS &F \\\hline \text { Between } & 4 & 2240.2 & 560.05 & 1.22 \\\text { Within } & 40 & 18434.5 & \\\text { Total } & 45 & &\\\hline\end{array}$ How many participants were in this ANOVA?

A) 49
B) 55
C) 45
D) 50

Question 30

$\begin{array}{lcc}\hline \text { Source } & S S & d f& MS &F \\\hline \text { Between } & 4 & 2240.2 & 560.05 & 1.22 \\\text { Within } & 40 & 18434.5 & \\\text { Total } & 45 & &\\\hline\end{array}$ What is the F-ratio?

A) .12
B) 1.22
C) 1.36
D) 49.78

Question 31

$\begin{array}{lcc}\hline \text { Source } & S S & d f& MS &F \\\hline \text { Between } & 4 & 2240.2 & 560.05 & 1.22 \\\text { Within } & 40 & 18434.5 & \\\text { Total } & 45 & &\\\hline\end{array}$ What is the critical value, assuming alpha = .05?

A) 2.61
B) 2.56
C) 2.45
D) There is insufficient information based on the source table.

Question 32

$\begin{array}{lcc}\hline \text { Source } & S S & d f& MS &F \\\hline \text { Between } & 4 & 2240.2 & 560.05 & 1.22 \\\text { Within } & 40 & 18434.5 & \\\text { Total } & 45 & &\\\hline\end{array}$ Which of the following is FALSE regarding post-hoc tests?

A) They should not be run if the omnibus ANOVA is not statistically significant
B) Tukey HSD test is a post-hoc test for multiple comparisons.
C) Post-hoc tests are generally done before ANOVAs are done.
D) None of the above are false.

Question 33

$\begin{array}{lcc}\hline \text { Source } & S S & d f& MS &F \\\hline \text { Between } & 4 & 2240.2 & 560.05 & 1.22 \\\text { Within } & 40 & 18434.5 & \\\text { Total } & 45 & &\\\hline\end{array}$ Which of the following is the correct formula to obtain mean squares within?

A) Sums of squares between divided by degrees of freedom between.
B) Sums of squares within divided by degrees of freedom within.
C) Sums of squares within multiply degrees of freedom within.
D) Sums of squares within subtract degrees of freedom within.

Question 34

$\begin{array}{lcc}\hline \text { Source } & S S & d f& MS &F \\\hline \text { Between } & 4 & 2240.2 & 560.05 & 1.22 \\\text { Within } & 40 & 18434.5 & \\\text { Total } & 45 & &\\\hline\end{array}$ How are ANOVA and t-tests similar? How are they different?

A) ANOVA allow for only comparisons between two means, whereas t-tests allow for comparisons for 2 or more means. They are similar in that both types of procedures tell us about differences between means.
B) t-tests allow for only comparisons between two means, whereas ANOVA allow for comparisons between two or more means. They are similar in that both types of procedures tell us about differences between means.
C) t-tests and ANOVAs both test for differences. However, t-tests test for differences between medians, but ANOVAs test for differences between Means
D) t-tests are ANOVAs are exactly the same. The only difference is that ANOVAs are used for samples and t-tests are used for populations.

Question 35

$\begin{array}{lcc}\hline \text { Source } & S S & d f& MS &F \\\hline \text { Between } & 4 & 2240.2 & 560.05 & 1.22 \\\text { Within } & 40 & 18434.5 & \\\text { Total } & 45 & &\\\hline\end{array}$ Which of the following best describes the F-ratio?

A) It is the ratio of MS_b to MS_w, and the smaller the F-value, the greater chance of it being statistically significant.
B) It is the ratio of SS_b to SS_w.
C) It is the ratio of MS_b to MS_w
D) The F-value is a ratio. Smaller F-values are associated with larger sample sizes.

Question 36

In a two-way ANOVA, how many effects are there to test?

A) One main effect and two interactions.
B) Two interactions and two main effects.
C) Two main effects and one interaction.
D) One interaction and one main effect.

Question 37

Which of the following pieces of information is necessary to determine critical value of the Tukey HSD in a one-way ANOVA?

A) df_b, the F-value, and the alpha level.
B) F-value, df_w, and the alpha level
C) Number of levels and df_b, and the alpha level
D) Number of levels, df_w, and the alpha level.

Question 38

$\begin{array}{lcc}\hline \text { Source } & S S & d f& MS &F \\\hline \text { Factor 1 } & 577.2 & 1 \\\text { Factor } 2 & 2586.4 & 1 \\\text { Factor }{ }^{*} \text { Factor 2 } &3359.7 & \\\text { Error } & 14235.2 & 26\\\hline\end{array}$ There were ________ participants and the interaction has ____ degree(s) of freedom.

A) 30; 2
B) 30; 1
C) 30; 3
D) 40; 2

Question 39

$\begin{array}{lcc}\hline \text { Source } & S S & d f& MS &F \\\hline \text { Factor 1 } & 577.2 & 1 \\\text { Factor } 2 & 2586.4 & 1 \\\text { Factor }{ }^{*} \text { Factor 2 } &3359.7 & \\\text { Error } & 14235.2 & 26\\\hline\end{array}$ This ANOVA is best characterized as a…

A) 2 x 3 ANOVA
B) One-way ANOVA
C) 2 x 2 ANOVA
D) 2 x 1 ANOVA

Question 40

$\begin{array}{lcc}\hline \text { Source } & S S & d f& MS &F \\\hline \text { Factor 1 } & 577.2 & 1 \\\text { Factor } 2 & 2586.4 & 1 \\\text { Factor }{ }^{*} \text { Factor 2 } &3359.7 & \\\text { Error } & 14235.2 & 26\\\hline\end{array}$ This ANOVA has how many possible main effect and interactions to test for?

A) 2
B) 3
C) 4
D) Insufficient information

Question 41

A Tukey HSD value tells you which of the following?

A) The size of a mean difference necessary to be significant
B) The probability of a mean difference to exist
C) The size of a mean difference necessary to be testable
D) The necessary sample size to detect an honestly significant difference (HSD)

Question 42

A 2 x 3 ANOVA has ____ factors, ___ possible interaction(s), and ___ total conditions

A) 2; 2; 5
B) 2; 1; 6
C) 3; 1; 6
D) 2; 2; 6

Question 43

A researcher is interested whether vitamin supplements help with preventing the cold. The placebo group drank fruit juice that actually had no vitamins at all. The researcher then measured the number of days each participant spent sick in a month.
Conduct a one-way ANOVA and determine if it is significant at the .05 level.

Question 44

A researcher is interested whether vitamin supplements help with preventing the cold. The placebo group drank fruit juice that actually had no vitamins at all. The researcher then measured the number of days each participant spent sick in a month.
Is a post-hoc test necessary? If so, conduct a Tukey HSD at the .05 level. The critical value is 3.514

Question 45

Identify 2 assumptions of the one-way ANOVA and explain what it means.

Question 46

A researcher examining factors that influence sleep quality tested the effects of two variables. Her first factor has 2 levels and the second factor has 3 levels. She recruited 30 participants. Use the following source table to answer the next few questions.
There are how many degrees of freedom for each source of variability?.

Question 47

A researcher examining factors that influence sleep quality tested the effects of two variables. Her first factor has 2 levels and the second factor has 3 levels. She recruited 30 participants. Use the following source table to answer the next few questions.
What is the critical value for each F ratio at the .05 significance level, and what is the observed F? Are any of the effect significant?

Question 48

Use the following source table to answer the questions below.
How many effects can one test?

Question 49

Use the following source table to answer the questions below.
This is a ___ x ___ ANOVA. (fill in the blanks)

Question 50

Use the following source table to answer the questions below.
Determine if the effects are significant at the .05 level.

Question 51

Why are post-hoc tests important with regards to making multiple comparisons?