Chapter 7 and 8 Quiz

The main difference between a Z score and a t score is that

t scores are used when the population variance is unknown.

A medium effect size (d) for a t test for dependent means is

.50

Which of the following statements about degrees of freedom is TRUE?

It is the number of scores in a sample that are free to vary.

Difference scores are computed for

a t test for dependent means.

The best way to reduce the variances in the distributions of means when conducting a t test for independent means is to

increase the size of the samples.

When conducting a t test for independent means, once the variances are known for each of the distributions of means, the variances can be added together to give the

variance of the distribution of differences between means.

The results of a t test for independent means can be misleading when the sample variances are

very different (e.g., a 4 : 1 ratio).

If an experimenter conducts a t test for dependent means with 10 participants and the estimated population variance of difference scores is 20, the variance of the comparison distribution is

20 / 10 = 2.0

In an experiment with 50 participants, which division of participants into groups would have the most power?

25 experimental, 25 control

Which of the following tactics will reduce the power of a planned study using a t test for independent means?

using unequal sample sizes instead of equal ones (for the same number of participants)

Advanced topic: If a study has 18 participants in the experimental group and 7 in the control group, what is the harmonic mean?

(2)(18)(7) / (18+7) = 10.08

The mean of a distribution of differences between means is equal to

0

If a sample includes three individuals with scores of 2, 3, and 4, the estimated population variance is

1

Advanced topic: The value of the harmonic mean

is disproportionately influenced by smaller numbers (meaning, smaller sample sizes).

In the formula for estimating the population variance from the sample, the sum of squared deviations is divided by

the number of participants in the sample minus one.

The t test for dependent means is LEAST robust when

the population is highly skewed.

The comparison distribution for a t test for independent means is a t distribution instead of a normal curve because

the population variance is estimated

If a t test for dependent means is reported in a research article as "t (16) = 2.67, p .05, then

the t score was 2.67.

A t test for independent means is reported as "t (28) = 4.21, p. 01. This means

the t score was 4.21

If a sample includes 27 people, the degrees of freedom used in the formula to estimate the population variance would be

26

The item below is based on the following table from a research article. Mean Score on Four Questionnaire Scales Before and AfterExperimental Manipulation Questionnaire ----------------------------- Qnaire Before. After. Change Cformity 18.97. 17.20. -1.77 N-turance 16.11 13.89. -2.22 ------------------------------------ Which of the following differences were significant at the .05 level?

Conformity and Nurturance

Which statement is only true for the t test for dependent means rather than t tests in general?

Pretest-posttest experimental designs are common.

If 15 participants take a pretest and a posttest and have a mean difference score of 1.5, and if the standard deviation of the comparison distribution is 0.5, the t score is

1.5 / 0.5 = 3

You plan to conduct a study where your directional hypothesis will be assessed with a t test for independent means at the .05 significance level. If you are predicting a medium effect size, how many participants would you need in total (assuming equal Ns per group) to obtain 80% power?

100

The item below is based on the following scenario. A counseling psychologist developing a technique to reduce procrastination has students time their procrastination for a week and uses this as a pretest measure of procrastination. Students then attend a workshop in which they are instructed to do a specific warm-up exercise for studying by focusing on a pleasant activity. Students again time their procrastination for a week, and the time from this second week is the posttest measure. If the psychologist finds that the sum of squared deviations from the mean of the difference scores of the sample is 135, the estimated population variance would be

135 / 9 = 15.0

The item below is based on the following scenario. A professor believes the students in a statistics class this term are more creative than most other students attending the university. A previous study found that students at the university had a mean score of 35 on a standard creativity test, and the current class has an average score of 40 on this scale with an estimated population standard deviation of 7. The standard deviation of the distribution of means is 1.63. The effect size is

(40 - 35) / 7 = 0.71

The most likely way for a t test to be presented in a research article for a study with 25 participants is

t (24) = 2.94, p .01

When figuring the pooled population variance estimate in a t test for independent means,

the estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants.

A t test for a single sample would be used to compare

the hours that "C" average students spend on Facebook each week compared with students in general.

A t test for dependent means would be used to compare

the level of reading comprehension of students at the beginning and at the end of a speed-reading class.

When carrying out a t test for independent means

the null hypothesis is rejected if the computed t score is more extreme than the cutoff t score.

The difference between a t test for a single sample and a Ztest for a single sample is the way

the variance of the known population is determined.

Which of the following is the MOST serious violation of an assumption for the t test for independent means?

The populations are dramatically skewed in opposite directions.

"Student's" t test was invented by

William Gosset.

The item below is based on the following scenario. A social psychologist interested in cultural differences compared women of two ethnic groups on a Role Approval Index on which high scores indicated high degrees of approval of one's own social role. The results were as follows. Ethnic Group A: N = 15 M = 55 S2 = 6.5Ethnic Group B: N = 23 M = 51 S2 = 4.5 What is the pooled estimate of the population variance?

[(14 / 36) (6.5)] + [(22 / 36) (4.5)] = 5.28

In which of the following situations would a t test for independent means be conducted?

a comparison of scores of participants in a memory study where one group is assigned to learn the words in alphabetical order and another group is assigned to learn the words in order of length of the word

The comparison distribution for a t test for independent means is a

distribution of differences between means.

The process of estimating the population variance from the scores in the sample involves

dividing the sum of squared deviations by N - 1 instead of N.

The comparison distribution in a t test for dependent means is a distribution of

means of difference scores.

The most common way for a t test for independent means to be reported in a research article is

t (45) = 3.5, p .05

If a sample includes three individuals with scores of 4, 6, and 8, the estimated population variance is

(4 + 0 + 4) / 2 = 4

The item below is based on the following scenario. A professor believes the students in a statistics class this term are more creative than most other students attending the university. A previous study found that students at the university had a mean score of 35 on a standard creativity test, and the current class has an average score of 40 on this scale with an estimated population standard deviation of 7. The standard deviation of the distribution of means is 1.63. The t score is

(40 - 35) / 1.63 = 3.07

The item below is based on the following scenario. A school psychologist is using a depression inventory—on which a score of 0 indicates no depression and a score of 10 indicates severe depression—to see if the level of depression in fourth graders in a particular class of 20 students differs from that of fourth graders in general at a school. The results of previous testing indicate that fourth graders at the school usually have a score of 5 on the scale, but the variation is unknown. The current sample of 20 fifth graders has a mean depression score of 4.4. If the psychologist figures S = .85, the effect size (d) is

(5 - 4.4) / .85 = 0.71

You plan to conduct a study where your nondirectional hypothesis will be assessed with a t test for independent means at the .05 significance level. If you are predicting a large effect size, how many participants would you need in total (assuming equal Ns per group) to obtain 80% power?

52

"Monte Carlo" methods

are often used to test the effect of violating assumptions of statistical tests.

An experimenter hypothesizes that biology majors score higher than literature majors on an intelligence test. If the mean score for biology majors was 18.8 and the mean score for literature majors was 21.3, and the Sdifference was 0.9, the tscore was

t = (18.8 - 21.3) / 0.9 = -2.78

Professor Q has designed a repeated measures experiment. Which information does he NOT need when looking up the power of his planned study in a power table?

estimated population variance of difference scores

An experimenter hypothesizes that biology majors score higher than literature majors on an intelligence test. If the mean score for biology majors was 18.8 and the mean score for literature majors was 21.3, and the Sdifference was 0.9, the t score was

t = (18.8 - 21.3) / 0.9 = -2.78

When conducting a t test for independent means, a typical research hypothesis might be

the mean of Population 1 is greater than the mean of Population 2.

You conducted a t test for independent means, and found that the t score equaled 0. This means that

the two sample means must be equal.

One of the assumptions for the t test for independent means is that

the variance of each of the parent populations is the same.

In the formula, S^2difference = S^2M1 + S^2M2, the "S^2M1" is

the variance of the distribution of means for Population 1.

In a t test for dependent means, 15 participants are each tested twice. This makes a total of 15 "before" scores and 15 "after" scores. What are the degrees of freedom?

14

The item below is based on the following scenario. A school psychologist is using a depression inventory—on which a score of 0 indicates no depression and a score of 10 indicates severe depression—to see if the level of depression in fourth graders in a particular class of 20 students differs from that of fourth graders in general at a school. The results of previous testing indicate that fourth graders at the school usually have a score of 5 on the scale, but the variation is unknown. The current sample of 20 fifth graders has a mean depression score of 4.4. If the unbiased estimate of the population's variance is 15, the variance of the distribution of means is

15 / 20 = 0.75

The item below is based on the following scenario. A social psychologist interested in cultural differences compared women of two ethnic groups on a Role Approval Index on which high scores indicated high degrees of approval of one's own social role. The results were as follows. Ethnic Group A: N = 15 M = 55 S2 = 6.5Ethnic Group B: N = 23 M = 51 S2 = 4.5 If a t test for independent means is conducted, how many degrees of freedom will be used to locate the cutoff score in the t table?

(15 - 1) + (23 - 1) = 36

The item below is based on the following scenario. A social psychologist interested in cultural differences compared women of two ethnic groups on a Role Approval Index on which high scores indicated high degrees of approval of one's own social role. The results were as follows. Ethnic Group A: N = 15 M = 55 S2 = 6.5 Ethnic Group B: N = 23 M = 51 S2 = 4.5 If the standard deviation of the distribution of the difference between means is 0.76, what is the t score?

(55 - 51) / 0.76 = 5.26

The item below is based on the following scenario. A counseling psychologist developing a technique to reduce procrastination has students time their procrastination for a week and uses this as a pretest measure of procrastination. Students then attend a workshop in which they are instructed to do a specific warm-up exercise for studying by focusing on a pleasant activity. Students again time their procrastination for a week, and the time from this second week is the posttest measure. If the psychologist wants to see if there is a change (increase or decrease) in procrastination by 10 of the students who attended his workshop using the .05 significance level, the cutoff t score(s) would be

-2.262, +2.262

You plan to conduct a study where your directional hypothesis will be assessed with a t test for independent means at the .05 significance level. Assuming that you will recruit 50 participants per group and predict a small effect size, how much power will your study have?

.26

The item below is based on the following scenario. A professor believes the students in a statistics class this term are more creative than most other students attending the university. A previous study found that students at the university had a mean score of 35 on a standard creativity test, and the current class has an average score of 40 on this scale with an estimated population standard deviation of 7. The standard deviation of the distribution of means is 1.63. If there were 30 students in the class and the professor wanted to test the null hypothesis described in the scenario using the 5% level of significance, the cutoff t score would be

1.699

Assuming that the difference between two independent sample means is 6.24, and S^2difference = 27, what is the calculated t score?

6.24 / √27 = 6.24 / 5.20 = 1.20

Advanced topic: If a study has 18 participants in the experimental group and 7 in the control group, the harmonic mean will be closest to a value of

7

The item below is based on the following table from a research article. Mean Score on Four Questionnaire Scales Before and AfterExperimental Manipulation Questionnaire Qnaire Before. After. Change Dominance 18.42. 16.31. -2.11 -------------------------------------- "p< .05 "p<.01 Which of the following differences were NOT significant?

Dominance

Which of the following statements is true if a study measures two groups on each of 27 variables, and the experimenter carries out a t test for independent means for each variable (that is, 27 t tests) using the .05 significance level?

The chance of at least one t test being significant is greater than 5%.

Which of the following is an assumption for the t test for dependent means?

The population follows a normal distribution.

The item below is based on the following scenario. A counseling psychologist developing a technique to reduce procrastination has students time their procrastination for a week and uses this as a pretest measure of procrastination. Students then attend a workshop in which they are instructed to do a specific warm-up exercise for studying by focusing on a pleasant activity. Students again time their procrastination for a week, and the time from this second week is the posttest measure. If the psychologist wants to see if there is a change (increase or decrease) in procrastination by students who attended his workshop, the appropriate description of "Population 2" (the comparison population) would be people whose

difference scores will be 0.

Your professor asks you to update a manuscript with the results of a t test for dependent means and provides you with the following information: there were 19 people in the study, the t score was 4.36, and the result was significant at the .01 level. The best way to present this information would be

t (18) = 4.36, p .01

Based on the following results, which would be the correct use of the formula, t = (M1 - M2) / Sdifference? Sample 1: Mean = 60; Variance of the distribution of means = 2 Sample 2: Mean = 50; Variance of the distribution of means = 7

t = (60 - 50) / √(2+7)

A "distribution of differences between means" can be thought of as a distribution of

the differences obtained when a sample mean from one population is repeatedly subtracted from a sample mean from another population.

Studies using difference scores tend to have larger effect sizes than studies using other research designs because

the standard deviation of difference scores is usually low.

When using a t table, the degrees of freedom used for a t test for independent means is

the sum of the degrees of freedom for the two samples.

The variance of a distribution of differences between means is equal to

the sum of the variances of the two distributions of means.