Chapters 11, 12 & 13 Analysis of Variance ANOVA Quiz 9
In a factorial experiment, the sum of squares of A plus the sum of squares of B plus the sum of squares of AB is equal to SSto SScells SSerro none of the other alternatives are correct
SScells
A group of 36 subjects was equally divided into 3 groups. A Tukey HSD produced a value that led to the conclusion that Mean 1 was significantly larger than Mean 2, p < .05. Which of the following situations would lead to such a conclusion? x̄ 1= 9, x̄ 2= 2, MSerror = 50 x̄ 1= 24, x̄ 2= 14, MSerror = 84 both of the descriptive alternatives are correct neither of the descriptive alternatives are correct
x̄ 1= 24, x̄ 2= 14, MSerror = 84
For a one way ANOVA, which of the following is a medium effect size index, d? 0.05 0.50 0.95 1.0 to 2.0
0.50
For a one way ANOVA, an effect size (d) that qualifies as large is: 0.05 0.20 0.80 all of the other alternatives are correct
0.80
In a 3 x 4 factorial design with five participants per cell, the df for the interaction F would be 2, 48 3, 48 5, 48 6, 48
6, 48
The actual amount of difference the independent variable makes is most closely associated with: whether or not to use hypothesis testing assumptions of ANOVA effect size .05 or .01 a level
effect size -The effect size in ANOVA is calculated by using either d or f effect size indexes. The formulae for d and f are on page 255 in your text.
"The means of the populations from which the samples were drawn are identical." This is a statement of the null hypothesis of one of the assumptions required of data analyzed with factorial ANOVA about an interaction of the alternative hypothesis
of the null hypothesis
The ANOVA technique described in the text can be used on paired-samples designs Correct! independent-samples designs both of the descriptive alternatives are correct neither of the descriptive alternatives are correct
independent-samples designs - Analysis of Variance (ANOVA) is an inferential technique used to compare two or more group means using variances rather than means in the calculations.
Drug A increases heart rate by eight beats per minute on the average. Drug B increases heart rate by 16 beats per minute on the average. Suppose both drugs were administered simultaneously. Which of the following changes in heart rate is not an illustration of an interaction? +24 +16 +8 -8
+24
When a seam is backstitched it is stronger (it can stand an additional 10 pounds of pull). If the stitches are closer together (say setting 1 rather than setting 3), the stitch will stand an additional 6 pounds of pull. Suppose a sewer used close stitches and backstitched. Which of the following additional pounds of pull would indicate no interaction between the two techniques? 16 10 6 4
16
A group of 50 participants was divided equally into 5 groups. A Tukey HSD produced a value that led to the conclusion that Mean 1 was significantly larger than Mean 2, p < .05. Which of the following situations would lead to such a conclusion? x̄ 1= 13, x̄ 2= 5, MSerror = 36 x̄ 1= 54, x̄ 2= 36, MSerror = 240 x̄ 1 = 5, x̄ 2= 2, MSerror = 40 none of the other alternatives are correct
1= 13, 2= 5, MSerror = 36
A repeated-measures ANOVA with three subjects who provide data in six conditions would have what critical value of F (a = .05)? 2.81 4.10 3.33 none of the other alternatives are correct
3.33
In a 6 x 7 factorial design with three observations per cell, the df for the interaction F would be 42, 125 42, 60 30, 125 30, 84
30, 84
dftreat = a. Ntot - 1 b. K - l c. K(Ntot - 1) d. Ntot - K
K - l
An F value obtained from the data is 3.65 based on 2 and 18 degrees of freedom. Alpha = .05. With such results it is possible to make a blank error. Type I Type II both of the descriptive alternatives are correct neither of the descriptive alternatives is correct
Type I
If an ANOVA led to the statement, "p < .05" you can be sure that the data produced an F ratio that is greater than: 1.00 the tabled value for F at the .05 level both of the descriptive alternatives are correct neither of the descriptive alternatives is correct
both of the descriptive alternatives are correct
Which of the following expresses a significant interaction? paint alone will seal the wood 10 years; primer by itself seals for 5 years; together they last 15 years paint alone will seal the wood 5 years; primer by itself seals for 5 years; together they last 10 years paint alone will seal the wood 10 years; primer by itself seals 2 years; together they last 15 years all of the other alternatives are correct
paint alone will seal the wood 10 years; primer by itself seals 2 years; together they last 15 years
If an ANOVA with four samples produces a significant F, you can find out which samples are significantly different from the others by: -performing several independent-samples t tests -performing HSD tests -finding the effect size index -neither performing several independent-samples t tests nor performing HSD tests is satisfactory
performing HSD tests
When the F value in the F table is smaller than the F value calculated from the data reject the null hypothesis retain the null hypothesis reject or retain the null hypothesis, depending on how far apart the group means are reject or retain the null hypothesis, depending on the number of groups
reject the null hypothesis
An F value of 3.50 with 4 and 10 degrees of freedom is obtained from the data. You should blank the null hypothesis if a = .05, even though you might be making a blank error. reject; Type I reject; Type II retain; Type I retain; Type II
reject; Type I
Consider a factorial ANOVA in which the dependent variable is reaction time scores. Three different drugs are tested on both females and males. The researchers concluded that the effect of a drug did not depend on whether the person taking it was a female or male. The factorial ANOVA would certainly show that there is no main effect for drug there is no main effect for gender there is no interaction all of the other alternatives are correct
there is no interaction
In a 3 x 6 factorial ANOVA with four participants per cell, the df for the interaction F is 1, 71 10, 71 18, 72 none of the other alternatives are correct
none of the other alternatives are correct
Planning a limited number of post-ANOVA tests before the data are gathered goes with blank tests, and choosing any and all differences to test after looking at the data goes with blank tests. F, t t, F post hoc, a priori a priori, post hoc
a priori, post hoc
If a tabled value of F is 10.00 and the F obtained from the data is only 9.00, you should retain the null hypothesis reject the null hypothesis calculate the data again, such numbers are not possible not enough information is given
retain the null hypothesis
For a one-way ANOVA, an effect size index (f) that is considered large is 0.50 1.00 1.50 all of the descriptive alternatives are correct none of the descriptive alternatives are correct
all of the descriptive alternatives are correct
If the F value obtained from the table is larger than the F value obtained from the data, you should: reject the null hypothesis retain the null hypothesis either of the descriptive alternatives, depending on the size of the obtained F either of the descriptive alternatives, depending on the df
retain the null hypothesis
A repeated-measures ANOVA partitions the total variance into blank component(s). 1 2 3 4
1
A 3 x 5 factorial ANOVA has blank independent variables. 1 2 3 5
2 -Factorial design is a design with two or more independent variables. Factor is an independent variable. Cell is a group of scores that receive the same combination of levels of the independent variables. Main effect is the differences that may exist between the levels of one independent variable. Interaction is when the effect of one independent variable depends on the level of another independent variable.
In a 2 x 3 factorial design with five participants per cell, the df for the interaction F would be 1, 28 2, 24 6, 30 4, 20
2, 24
In a 5 x 6 factorial design with four observations per cell, the df for the interaction F would be 30, 119 30, 90 20, 119 20, 90
20, 90
What is the critical value of F (for a = .05) for a repeated-measures ANOVA that has three subjects who provide data in four conditions? 4.76 5.14 3.59 none of the other alternatives are correct
4.76
A repeated-measures ANOVA with four subjects who provide data in three conditions would have what critical value of F (a = .05)? 4.76 5.14 3.98 none of the other alternatives are correct
5.14
Which of the following is an advantage of a repeated-measures ANOVA over a one-way ANOVA? Repeated-measures ANOVA is more efficient Repeated-measures ANOVA eliminates variance due to participants Repeated-measures ANOVA is more powerful All of the other alternatives are correct.
All of the other alternatives are correct.
The null hypothesis for a repeated-measures ANOVA is: H0: μ1 = μ2 = μ3 H0: μ1 ≠ μ2 ≠μ3 H0: μ1 < μ2 < μ3 H0: μ1 > μ2 > μ3
H0: μ1 = μ2 = μ3
Two schedules for giving rest were compared—the massed schedule and the spaced schedule. Twenty observations of the spaced schedule produced a mean of 26 errors. On the massed schedule 14 observations resulted in a mean of 36 errors. An a level of .05 was adopted and an F = 4.21 was obtained. What conclusion is appropriate? The null hypothesis should be retained. Massed practice produces fewer errors than spaced practice. Spaced practice produces fewer errors than massed practice.
Spaced practice produces fewer errors than massed practice.
The techniques of Chapter 11 are not appropriate if the data come from Correct! a paired-samples design populations that do not have the same mean both of the descriptive alternatives are correct neither of the descriptive alternatives is correct
a paired-samples design
For a one way ANOVA, an effect size (d) that is considered small is 0.05 0.10 0.20 all of the other alternatives are correct none of the other alternatives are correct
all of the other alternatives are correct
For a one way ANOVA, an effect size (d) that is considered large is 0.80 1.00 1.50 all of the other alternatives are correct
all of the other alternatives are correct - The effect size in ANOVA is calculated by using either d or f effect size indexes. The formulae for d and f are on page 255 in your text.
The null hypothesis tested by the analysis of variance is that all sample statistics (means) are the same one or more samples come from a different population one or more samples come from a significantly different population all population means are the same
all population means are the same
In testing for a main effect using a factorial ANOVA, the null hypothesis is that the populations from which the samples were drawn. are identical have equal variances are normally distributed all of the other alternatives are correct
are identical
The F ratio in a repeated-measures ANOVA consists of the: -between-subjects variance divided by the between-treatments variance -between-treatments variance divided by the between-subjects variance -between-subjects variance divided by the error variance -between-treatments variance divided by the error variance
between-treatments variance divided by the error variance
"Assumptions of the analysis of variance" deals with: -whether the different levels of the independent variable produce sets of scores that are about equally variable -the form of the distribution of the dependent variable Correct! both of the descriptive alternatives are correct neither of the descriptive alternatives is correct
both of the descriptive alternatives are correct
A group of 52 participants was divided equally into 4 groups. A Tukey HSD produced a value that led to the conclusion that Mean 1 was significantly larger than Mean 2, p < .05. Which of the following situations would lead to such a conclusion? x̄ 1= 10.9, x̄ 2= 6.1, MSerror = 20 x̄ 1= 152, x̄ 2= 140; MSerror = 130 both of the descriptive alternatives are correct neither of the descriptive alternatives is correct
both of the descriptive alternatives are correct
Which of the descriptions that follow might lead you to choose a statistical test other than a repeated-measures ANOVA? -the populations the samples are from are severely skewed -there are carry-over effects from one administration of the independent variable to the next -both of the descriptive alternatives are correct -neither of the descriptive alternatives is correct
both of the descriptive alternatives are correct
Your text said that the advantages of a repeated-measures ANOVA were: accuracy and elegance precision and adaptability efficiency and power all of the other alternatives are correct
efficiency and power -Repeated measures and independent measures differ based on the relationship between the group means. Repeated measures produce group means that are dependent, or systematically related, group means. Independent measures produce group means that are independent, or not systematically related, group means.
The term main effect refers to a comparison of: means interactions both means and interactions neither means nor interactions
means
Suppose the cell means for a factorial ANOVA are presented as a line graph. Which of the following would indicate there was no significant interaction? crossed lines converging lines both crossed lines and converging lines neither crossed lines nor converging lines
neither crossed lines nor converging lines
a priori and post hoc are terms that refer to whether the null hypothesis should be rejected whether the null hypothesis should be retained both of the descriptive alternatives are correct neither of the descriptive alternatives is correct
neither of the descriptive alternatives is correct
Consider a factorial ANOVA that analyzes self-esteem scores. Three different ages participate: 20 year-olds, 40 year-olds, and 60 year-olds. In addition, each age group is divided into those who have above a median income and those who have below a median income. The researchers concluded that the differences in self-esteem scores of the different age groups did not depend on a person's income. The summary table for the factorial ANOVA would certainly show that there was no main effect for age no main effect for income no interaction all of the other alternatives are correct
no interaction
Which of the following F values, if obtained from an experiment, would lead to rejecting the null hypothesis if a = .01? F = 150.00,df = 1,1 F = 4.08, df = 3,8 F = 5.00, df = 3,18 none of the descriptive alternatives are correct
none of the descriptive alternatives are correct
A cell in a factorial ANOVA refers to one level of the independent variable one level of the dependent variable Correct Answer one level of one independent variable and one level of a second independent variable all the participants in the experiment
one level of one independent variable and one level of a second independent variable
Which of the alternatives below describes a situation for which ANOVA would not be appropriate? -the three population means are different -the three population variances are very large -one population variance is large, one small -all of the descriptive alternatives are correct
one population variance is large, one small
The ANOVA techniques described in Chapter 11 cannot be used to analyze an experiment with: -two levels of the independent variable -three levels of the independent variable -paired samples designs -independent samples designs
paired samples designs
When the cell means of a factorial design are presented as a line graph, a nonsignificant interaction is indicated by: parallel lines crossed lines converging lines any of the descriptive alternatives are correct
parallel lines
Data were gathered comparing four recipes for whole wheat bread. (The dependent variable was a scaled judgment by a trained taster.) Ten judgments were made on each recipe. An F = 2.90 was obtained. Which conclusion is proper? reject H0 at the .05 level reject H0 at the .01 level not enough information is given none of the descriptive alternatives are correct
reject H0 at the .05 level
The F value obtained from the data is 3.45 based on 3 and 12 degrees of freedom. You should blank the null hypothesis if a = .05, even though you might be making a blank error. reject; Type I reject; Type II retain; Type I retain; Type II
retain; Type II
The ANOVA technique as described in Chapter 11 cannot be used when - the number of scores in each group is unequal - subjects are randomly assigned to one of the groups before the independent variable is administered - samples are drawn from populations that have equal variances - subjects participate in every level of the independent variable
subjects participate in every level of the independent variable
A disadvantage of a repeated-measures ANOVA described in your text is that you cannot -make pairwise tests after the F test -test the significance of the between-subjects term -test more than three levels of the independent variable -all of the other alternatives are correct
test the significance of the between-subjects term
"All of the samples in the study came from populations with identical means" is a statement of: an assumption about the data that is required if the F distribution is to be accurate the null hypothesis both of the descriptive alternatives are correct neither of the descriptive alternatives are correct
the null hypothesis
When statisticians talk about effect size, they are referring to: the probability of a Type II error whether the significance level was large or small whether the a level was large or small the size of the differences among the means of the populations the samples are from
the size of the differences among the means of the populations the samples are from
Which of the descriptions that follow might lead you to choose a statistical test other than a repeated-measures ANOVA? the population means are quite different there are carry-over effects from one administration of the independent variable to the next both of the descriptive alternatives are correct neither of the descriptive alternatives is correct
there are carry-over effects from one administration of the independent variable to the next
A factorial ANOVA produces blank F tests. one two three none of the other alternatives are correct
three
A group of 72 participants was equally divided into four groups. A Tukey HSD test produced a value that led to the conclusion that Mean 1 was significantly larger than Mean 2, p < .05. Which of the following situations would lead to such a conclusion? x̄ 1 = 7, x̄ 2 = 0, MSerror = 80 x̄ 1 = 24, x̄ 2 = 13, MSerror = 180 both of the descriptive alternatives are correct neither of the descriptive alternatives is correct
x̄ 1 = 7, x̄ 2 = 0, MSerror = 80 - Tukey Honestly Significant Difference (HSD) test is used to identify what the specific significant differences are between pairs of group means. The formulae for Tukey's HSD are on page 251 in your text.
A disadvantage of a repeated-measures ANOVA is that: it isn't as powerful as other ANOVAs you cannot conduct Tukey HSD tests you cannot test the significance of the between-subjects variance all of the other alternatives are correct
you cannot test the significance of the between-subjects variance
For a one way ANOVA, an effect size (d) that qualifies as small is 0.05 0.50 0.80 none of the other alternatives are correct
0.05
For a one-way ANOVA, an effect size index (f) that qualifies as small is 0.05 0.25 both of the descriptive alternatives are correct neither of the descriptive alternatives is correct
0.05
In a 4 x 5 factorial design with nine participants per cell, the df for the interaction F would be 9, 180 12, 180 12, 160 20, 179
12, 160
A repeated-measures ANOVA with six subjects who provide data in four conditions would have what critical value of F (a = .05)? 3.03 3.29 2.90 none of the other alternatives are correct
3.29
Parents learn tricks that are helpful in raising children and in preserving the sanity of all concerned. When a baby is crying, just changing diapers will stop crying 25 percent of the time. Picking the baby up and walking stops crying 40 percent of the time. Suppose a (desperate?) parent did both. Which outcome (percent) would indicate that the effect of the two tricks is independent, that they do not interact? 25 40 65 75
65
When the null hypothesis is true, which of the following is a good estimate of the population variance? MStreat MSerror Correct Answer both of the descriptive alternatives are correct neither of the descriptive alternatives is correct
MStreat MSerror both of the descriptive alternatives are correct - One-way, between subjects ANOVA is used to compare two or more, independent groups along a single independent variable. The formulae for one-way, between subjects ANOVA are on pages 242 to 246 in your text.
In the Cub Scouts, the Pinewood Derby is a big event. Little boys, with a bit of help from their daddies, carve a 6-inch race car and attach wheels. Several cars race down an incline and a winner is declared. Sometimes the winner even gets his picture in the paper. Daddies often know of ways to increase the speed of the car. Smoothing the axle with emery cloth (a kind of sandpaper for metal) will reduce the race time one second. Putting graphite (a lubricant) on the axle will reduce the race time three seconds. Suppose some ingenious daddy did both to his son's car. Which change in that car's race time is not indicative of an interaction between emery cloth and graphite? decrease 4 seconds decrease 0 seconds decrease 10 seconds increase 2 seconds
decrease 4 seconds -Main effects are the differences that may exist between the levels of one independent variable. In a factorial design, there will be at least two possible main effects. Interaction is when the effect of one independent variable depends on the level of another independent variable. In a factorial design, there will be at least one possible interaction.
post hoc tests are to a priori tests as Correct! - examining data and deciding on tests is to deciding on tests before the data are examined - checking the data analysis for errors is to doing the initial analysis - obtaining statistical significance is to not obtaining statistical significance - all of the descriptive alternatives are correct
examining data and deciding on tests is to deciding on tests before the data are examined
Which of the following designs have two factors? t tests one way ANOVAs factorial ANOVAs all of the other alternatives are correct
factorial ANOVAs
John runs the same three-mile route every day. If he takes his dog, it adds 25 seconds to his running time. If it is cold, it adds 10 seconds to his running time. Suppose he ran one cold morning with his dog. What change in his time would represent no interaction between the two variables (dog and temperature)? increase 10 seconds increase 25 seconds increase 35 seconds decrease 15 seconds
increase 35 seconds
Which of the following is (are) true? dfA + dfB = dfAB MSA + MSB = MSAB both of the descriptive alternatives neither of the descriptive alternatives
neither of the descriptive alternatives -Two-way, between subjects ANOVA is used to compare two or more, independent groups along two independent variables. The formulae for two-way, between subjects ANOVA are on pages 285 to 290 in your text.
Suppose the cell means for a factorial ANOVA are presented as a line graph. Which of the following would indicate there was no significant interaction? crossed lines lines that look like a greater-than sign an upside down V above a V parallel lines
parallel lines
If the F value obtained from the data is .001 and df = 2,25, you should reject the null hypothesis retain the null hypothesis rework the problem; such a value is impossible reject the alternative hypothesis
retain the null hypothesis
