Psychology Statistics exam 3, Exam 4 (Ch. 12 & 13), Chapter 11 STATS FINAL

For an ANOVA comparing three treatment conditions, what is stated by the alternative hypothesis (H1)?

At least one of the three population means is different form another mean

When comparing more than two treatment means, why should you use an analysis of variance instead of using several t tests?

Using several t tests increases the risk of a Type I error

In an analysis of variance, differences between participants contribute to which of the following variances?

Both between-treatments variance and within-treatments variance

In an analysis of variance, differences caused by treatment effects contribute to which of the following variance?

Between-Treatments variance but not within treatment-treatments variance

On average, what value is expected for the F-ratio if the null hypothesis is true?

1.00

A research study comparing three treatments with n=5 in each treatment produces T1=5, T2=10, T3=15, with SS1=6, SS2=9, SS3=9, and ∑X2=94. For this study, what is SStotal?

34

A research study comparing three treatments with n=5 in each treatment produces T1=5, T2=10, T3=15, with SS1=6, SS2=9, SS3=9, and ∑X2=94. For this study, what is SSwithin?

24

An ANOVA is used to evaluate the mean difference among three treatment conditions with a sample of n=12 participants in each treatment. For this study, what is df-between treatment?

2

An analysis of variances produces df-bewteen=3 and df-within=24. If each treatment has the same number of participants, then how many participants are in each treatment?

7

The following table shows the results of an analysis of variance comparing four treatment conditions with a sample of n=5 participants in each treatment. Note that several values are missing in the table. What is the missing value for MSwithin?

Source SS df MS

between 30 xx xx F=xx

within xx xx xx

total 62 xx

2

In an independent-measures ANOVA, individual differences contribute to the variance in the numerator and in the denominator of the F-ratio. For a repeated-measures ANOVA, what happens to the individual differences in the numerator of the F-ratio?

they do not exist because the same individuals participate in all of the treatments

In a repeated-measures analysis of variance, how does the magnitude of the mean differences from one treatment to another contribute to the F-ratio?

The mean differences add to the numerator of the F-ratio

A researcher uses a repeated-measures ANOVA to test for the mean differences among three treatment conditions using a sample of n=10 participants. What are the df values for the F-ratio from this analysis?

2,18

a repeated-measures ANOVA with n=5 subjects has a df within-treatment equal to 12. What is the value for df-error for this analysis?

8

a researcher reports an F-ratio with df=2,40 from a repeated-measures ANOVA. How many subjects participated in this experiment?

63

For repeated-measures study comparing three treatment conditions with a sample of n=4 participants, the participant totals (the P values) are 3, 6, 9, and 6. What is the value for SS-between subjects?

6

A repeated-measures ANOVA produced an F-ratio of F=4.00 with df=1,14. If the same data were analyzed with a repeated-measures t-test, what value would be obtained for the t statistic?

2

In a two-factor analysis of variance, a main effect is defined as_____.

the mean difference among the levels of one factor

How many separate groups of participants would be needed for an independent-measures, two-factor study with 3 levels of factor A and 4 levels of factor B?

12

If the mean and variance are computed of each sample in an independent-measures, two-factor experiment, which of the following types of sample data will tend to produce large F-ratios for the two-factors ANOVA?

large differences between sample means and small sample variances

For a research study with 2 levels of factor A, 3 levels of factor B, and n=5 in each treatment condition, what are the df values for the F-ratio evaluating the main affect for factor A?

1,24

In a two-factor ANOVA, which of the following is not computed directly but rather is found by subtraction?

SS-AxB

The results of a two-factor analysis of variance produce df=1,30 for the F-ratio for factor A, and df=2 for the F-ratio for the AxB interaction. Based on this information, how many levels of factor B were compared in the study?

3

What is the relationship among the separate F-ratios in a two-factor ANOVA?

they may have different df values, but they all have the same denominator

If a two-factor analysis of variance produces a statistically significant interaction, what can you conclude about the main effects?

the significance of the main effects is not related to the significance of the interaction

For an ANVOA comparing three treatment conditions, what is stated by the null hypothesis?

There are no differences between any of the population means

In an analysis of variance, differences caused by treatment effects contribute to which of the following variances?

Between-treatments variance but not within-treatments variance

On average, what is the value expected for the F-ratio if the null hypothesis is false?

Much greater than 1.00

In an ANOVA, what is represented by the letter N?

The number of scores in the total research study

A research study comparing three treatments with n = 5 in each treatment produces T1 = 5, T2 = 10, T3 = 15, with SS1 = 6, SS2 = 9, SS3 = 6, and ΣX(squared) = 94. For this study, what is SS(between)?

5

An ANOVA is used to evaluate the mean differences among three different treatment conditions with a sample of n = 12 participants in each treatment. For this study, what is the df(total)?

35

k=3, n=12, N=36

df(total) = N-1

An ANOVA is used to evaluate the mean differences among three different treatment conditions with a sample of n = 12 participants in each treatment. For this study, what is the df(within treatments)?

33

k=3, n=12, N=36

df(within treatments) = N-k

An analysis of variances produces df(total) = 29 and df(within) = 27. For this analysis, what is the df(between)?

2

29-27

An analysis of variances produces SS(total) = 80 and SS(within) = 30. For this analysis, what is the SS(between)?

50

80-30

An analysis of variances produces SS(between) = 40 and MS(between) = 20. In this analysis, how many treatment conditions are being compared?

3

df = 2

Which of the following is expected if the null hypothesis is true for an analysis of variance?

MS9between) should be about the same as MS(within)

A researcher uses analysis of variance to test for mean differences among three different treatments with a sample of n = 12 in each treatment. The F-ratio for this analysis would have what df values?

df = 2, 33

df(w) = N-k

df(b) = k-1

k=3, n=12, N=36

An independent measures research study compares three treatment conditions using a sample if n = 5 in each treatment. For this study, the three samples have SS1 = 10, SS2 = 20, and SS3 = 15. What value would be obtained for MS(within)?

45/12

A researcher reports an F-ratio with df=1, 24 for an independent-measures experiment. If all the treatments had the same number of participants, then how many individuals were in each treatment?

13

For an independent-measures ANOVA comparing three treatments with a sample of n = 5 in each treatment, what is the critical value for the F-ratio using α = .05?

3.88

Which of the following describes a typical distribution of F-ratios?

Positively skewed with all values greater than or equal to zero

Explain the difference between the testwise alpha level and the experimentwise alpha

When a single research study involves several hypothesis test, the testwise alpha level is the value selected for each individual test and the experimentwise alpha is the total risk of a Type 1 error that is accumulated doe all the separate tests

The term "analysis: means separating or breaking a whole into parts. What is the basic analysis that takes place in analysis of variance?

In ANOVA, the total variability for a set of scores is separated into two components: between-treatments variability and within-treatments variability

If there is no systematic treatment effect, then what is the expected, on average, for the F-ratio in an ANOVA?

When the null hypothesis is true, the expected value for the F-ratio is 1.00 because the top and bottom of the ratio are both measuring the same variance

What is the implication when an ANOVA produces a very large value for the F-ratio?

A large F-ratio indicates the existence of a treatment effect because the differences between the treatments (numerator) are much bigger than the differences that would be expected if there were no effect (denominator)

A two-factor study with two levels of factor A and three levels of factor B uses a separate group of n = 5 participants in each treatment condition. How many participants are needed for this entire study?

30

5*6

A two-factor ANOVA produces a F-ratio factor A with df = 1, 36 and an F-ration for factor B with df = 2, 36. Which of the following describes the experiment producing these F-ratios?

2 levels of factor A and 3 levels of factor B

df(rows) = # of rows - 1

df(column) = # od columns - 1

The following data represent the means for each treatment condition in a two-facto experiment. Note that one mean is not given. What value for the missing mean would result in no AxB interaction?

20

In a two-facto experiment with 2 levels of factor A and 2 levels of factor B, three of the treatment means are essentially identical and one is substantially different from the others. What result(s) would be produced by this pattern of treatment means?

The pattern would produce main effects for both A and B, and an interaction

In a two-factor ANOVA, which of the following is not computed directly but rather is found by subtraction?

SS(AxB)

For an experiment involving 3 levels of factor A and 3 levels of factor B, with a sample of n = 8 in each treatment condition, what are the df values of the F-ratio for the AxB interaction?

4, 63

df(A) = 3 - 1 = 2

df(B) = 3 - 1 = 2

df(AxB) = 2 * 2 = 4

df(within) = 9 * 7 = 63

= # of cells * (n-1)

A two-factor research study has 2 levels of factor A and three 3 of factor B with n = 8 participants in each treatment condition. For this study, what is the value for df(between treatments)?

5

For a two-factor experiment with 2 levels of factor A and 3 levels of factor B and n = 10 subjects in each treatment condition, how many participants are in each level of factor A?

30

If a two-factor analysis of variance produces a statistically significant interaction, what can you conclude about the main effects?

The significance of the main effect is not related to the significance of the interaction

The following table shows the results of a two-factor analysis of variance with 2 levels of factor A, 3 levels of factor B, and a separate sample of n = 5 participants in each of the treatment conditions. Note that several values are missing in the table. What is the missing value for the F-ratio for the AxB interaction?

Source SS df MS

Between 80 xx

A 8 xx xx F= xx

B xx xx 20 F= xx

AxB xx xx xx F= xx

Within xx xx xx

Total 176 xx

4

For the following data, what is the value of SS(B)?

B1 B2

A1 n = 5 n= 5

M = 1 M = 2

SS = 10 SS = 20

A2 n = 5 n= 5

M = 1 M = 4

SS = 10 SS = 20

20

For which of the following situations would a repeated-measures research design be appropriate?

comparing pain tolerance with and without acupuncture needles

A researcher plans to conduct a research study comparing two treatment conditions with a total of 20 scores in each treatment. Which of the following designs would require only 20 participants?

a repeated-measures design

The following data were obtained from a repeated-measures research study. What is the value of MD for these data?

3

A repeated measures study using a sample of n = 20 participants would produce a t statistic with df = ____.

19

A repeated-measures experiment and a matched-subjects experiment each produce a t statistic with df = 10. How many individuals participated in each study?

11 for repeated, and 22 for matched

A researcher uses a repeated-measures study to compare two treatment conditions with a set of 20 scores in each treatment. What would be the value of df for the repeated-measures t statistic?

df=18

A repeated-measures study and an independent-measures study both produced a t statistic with df = 16. How many individuals participated in each study?

17 for repeated-measures and 18 for independent-measures

A matched-subjects study and an independent-measures study both produced a t statistic with df = 16. How many individuals participated in each study?

34 for matched-subjects and 18 for independent-measures

For the repeated-measures t statistic, df = _____.

n - 1

Which of the following is the correct null hypothesis for a repeated-measures t test?

µD = 0

If the null hypothesis is true, what value is expected on average for the repeated-measures t statistic?

0

The null hypothesis for a repeated-measures test states:

The entire population will have a mean difference of μD = 0.

What is the value of the estimated standard error for the following set of D scores? Scores: 2, 2, 10, 2

2

14. d. For a repeated-measures study comparing two treatments with a sample of n = 9 participants, the difference scores have a mean of MD = 4.90 with SS = 288. What is the estimated standard error for the sample mean difference?

d. 2

A repeated-measures study comparing two treatments with a sample of n = 4 participants produces a mean of M = 18 with SS = 24 for the scores in the first treatment, a mean of M = 14 with SS = 18 for the scores in the second treatment, and a mean of M = 4 with SS = 12 for the difference scores. What is the estimated standard error for the sample mean difference?

1

For a repeated-measures study comparing two treatment conditions, a researcher obtains a sample of n = 9 difference scores with a mean of MD = 4 and a variance of s2 = 36. What is the value for the repeated-measures t statistic for these data?

4/2

If a repeated-measures study shows a significant difference between two treatments with

α = .01, then you can be sure that _____.

A significant effect does not necessarily mean that the effect size will be large.

A sample of difference scores has a mean of MD = 5 with a variance of s2 = 100. If effect size is measured using Cohen's d, what is the value of d?

d = 5/10

For a repeated-measures study comparing two treatment conditions, a researcher obtains Cohen's d = 0.50 for a sample of n = 4 scores with a variance of s2 = 16. What is the value of the sample mean?

A researcher obtains t(20) = 2.00 and MD = 9 for a repeated-measures study. If the researcher measures effect size using the percentage of variance accounted for, what value will be obtained for r2?

4/24

A researcher conducts a repeated-measures study to evaluate a treatment with a sample of n = 16 participants and obtains a t statistic of t = 1.94. The treatment is expected to increase scores and the sample mean shows an increase. Which of the following is the correct decision for a hypothesis test using α = .05.

Reject the null hypothesis with a one-tailed test but fail to reject with two tails.

A researcher obtains t = 2.35 for a repeated-measures study using a sample of

n = 8 participants. Based on this t value, what is the correct decision for a two-tailed test?

fail to reject the null hypothesis with either α = .05 or α = .01

A research report describing the results from a repeated-measures study states: The data show no significant difference between the two treatments, t(10) = 1.65, p > .05. Based on this report, you can conclude that a total of ____ individuals participated in the research study

11

A research report describing the results from a repeated-measures t test states, "t(22) = 1.71, p > .05." From this report you can conclude that the outcome of the hypothesis test was ______.

to fail to reject the null hypothesis with a sample of n = 23 participants

A researcher reports t(12) = 2.86, p < .05 for a repeated-measures research study. How many individuals participated in the study?

n=13

In general, if the variance of the difference scores increases, then what will happen to the value of the t statistic?

It will decrease (move toward 0 at the center of the distribution).

A researcher uses a repeated-measures design to compare individuals' performance before treatment with their performance after treatment. If all of the participants show improved performance of 8 or 9 points after treatment, then the researcher should find ______.

the variance of the difference scores is near zero

In general, what is the effect of an increase in the variance for the sample of difference scores?

an increase in the standard error and a decrease in the value of t

In general, what characteristics of the difference scores are most likely to produce a significant t statistic for the repeated-measures hypothesis test?

a large number of scores and a small variance

What is indicated by a large variance for a sample of difference scores?

an inconsistent treatment effect and a low likelihood of a significant difference

A researcher is using a repeated-measures study to evaluate the difference between two treatments. If the difference between the treatments is consistent from one participant to another, then the data should produce ______.

a small variance for the difference scores and a small standard error

If other factors are held constant, which of the following sets of data is most likely to produce a significant value for the repeated-measures t statistic?

n = 30 and SS = 10 for the difference scores

Assuming that other factors are held constant, which of the following would tend to increase the likelihood of rejecting the null hypothesis?

increase the sample mean difference

Which of the following possibilities is a serious concern with a repeated-measures study?

The results will be influenced by order effects.

Compared to an independent-measures design, a repeated-measured study is more likely to find a significant effect because it reduces the contribution of variance due to ______.

individual differences

For which of the following situations would a repeated-measures design have the maximum advantage over an independent-measures design?

when very few subjects are available and individual differences are large

In a repeated-measures experiment, each individual participates in one treatment condition and then moves on to a second treatment condition. One of the major concerns in this type of study is that participation in the first treatment may influence the participant's score in the second treatment. This problem is called ______.

order effects

What value is estimated with a confidence interval using the repeated-measures t statistic?

the mean for a population of difference scores

A sample of n = 9 college students is used to evaluate the effectiveness of a new Study Skills Workshop. Each student's grade point average (GPA) is recorded for the semester before the workshop and for the semester after the workshop. The average GPA improved by MD = 0.60 points with s2 = 0.09. The researcher would like to use the sample to estimate how much effect the workshop would have for the entire college population. Which of the following is the 80% confidence interval for these data?

µD = 0.60 + 0.10(1.397)

If the sample size is held constant, which of the following will produce the widest 90% confidence interval for the population mean difference for a repeated-measures study?

MD = 5 with s2 = 5 for the difference scores

Briefly explain the advantages and disadvantages of using a repeated-measures design as opposed to an independent-measures design.

A repeated measures design tends to be more precise or more powerful than an independent measures design because it eliminates variability due to individual differences. Also, a repeated-measure design uses fewer subjects than an independent-measures design. However, the results from a repeated-measures experiment can be confounded by time-related factors and order effects

Describe the circumstances under which you should use ANOVA instead of t tests, and explain why t tests are inappropriate in these circumstances.

ANOVA should be used when there are more than two treatment conditions. In this situation it would require several t tests to compare all the treatments, and the more tests that are done the more risk there is for a Type I error

Describe the circumstances in which post tests are used and explain why these tests are necessary.

Post tests are done after an analysis of variance that rejects the null hypothesis and is comparing three or more treatments. The decision to reject H0 simply indicates that at least one of the treatment means is different from another. The purpose of the post tests is to determine exactly which treatment means are different.

What value is expected, on average, for the F ratio in ANOVA when the null hypothesis is true? Explain why this value is expected.

When the null hypothesis is true, the F ratio is expected to be near 1.00. The structure of the F ratio is balanced so that the numerator and denominator are measuring identical sources of variance if the treatment effect is zero (H0 is true).