Statistics Exam 3 (ch 7, 8, 9)

In an analysis of variance, you reject the null hypothesis when the F ratio is a. smaller than 1. b. negative. c. much larger than 1. d. equal to the t score.

c. much larger than 1.

What is the purpose of a post hoc test? a. to determine whether or not a Type I error was made in the ANOVA b. to determine how much mean difference there is between groups c. to determine which groups are significantly different from each other d. to determine whether or not a Type II error was made in the ANOVA

c. to determine which groups are significantly different from each other

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 a. (5 - 4.4) / .85 = 0.71 b. .85 / 5 = 0.17 c. .85 / (5 - 4.4) = 1.42 d. 5 / .85 = 5.88

a. (5 - 4.4) / .85 = 0.71

Suppose you test the effects of a drug on rats' learning by giving them 0, 10, 20, or 30 milligrams of the drug. This experiment has ______ independent variable(s) and ______ values. a. 1;4 b. 4;2 c. 2;4 d. 4;1

a. 1;4

The comparison distribution for a t test for independent means is a a. distribution of differences between means. b. poisson distribution. c. distribution of proportional variance scores. d. Z distribution (that is, a normal curve).

a. distribution of differences between means.

In the formula, Σ(M-GM)2/dfBetween, "GM" is the a. grand mean b. group mean c. group median d. general multiple

a. grand mean

The best way to reduce the variances in the distributions of means when conducting a t test for independent means is to a. increase the size of the samples. b. treat the two samples as one sample. c. raise the study's level of significance. d. use the true population variance.

a. increase the size of the samples

A characteristic of an F ratio is that a. it can never be less than 0. b. the cutoff F equals the calculated F divided by 2 c. the t distribution for ∞ df is the comparison distribution. d. it is negatively skewed.

a. it can never be less than 0

The comparison distribution in a t test for dependent means is a distribution of a. means of difference scores b. difference between means c. means d. dependent means

a. means of difference scores

Analysis of variance should be conducted only when a. population variances can be assumed to be equal. b. sample sizes are greater than 30 per group. c. sample sizes are smaller than 30 per group. d. population sizes are approximately equal.

a. population variances can be assumed to be equal.

To use a one-way, between-subjects ANOVA, the dependent variable must be: a. scale data b. the dependent variable can be nominal, ordinal, or scale data c. ordinal data d. nominal data

a. scale data

The main difference between a Z score and a t score is that a. t scores are used when the population variance is unknown. b. t scores are used when a study is analyzed with a one-tailed test. c. t scores are used only when inferences are made about other samples. d. t scores are used only when the sample size is greater than

a. t scores are used when the population variance is unknown.

A t test for a single sample would be used to compare a. the hours that "C" average students spend on Facebook each week compared with students in general. b. the level of honesty in politicians with the level of honesty in students c. the level of reading comprehension of students at the beginning and at the end of a speed-reading class. d. the hours spent studying each week by freshmen and seniors.

a. 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 a. the level of reading comprehension of students at the beginning and at the end of a speed-reading class. b. the hours spent studying each week by freshmen and seniors. c. the level of honesty in politicians with the level of honesty in students. d. the scores on a tolerance-of-diversity measure between two sororities.

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

The comparison distribution for a t test for independent means is a t distribution instead of a normal curve because a. the population variance is estimated. b. there are more degrees of freedom for two samples than for one. c. tables are not available for the normal curve. d. Z distributions were not used at the time the t test for independent means was invented.

a. the population variance is estimated

Even a very small mean difference can be statistically significant if: a. the sample size is big and the error variance is small b. the sample size and the error variance are both big c. the sample size is small and the error variance is big d. the sample size and the error variance are both small

a. the sample size is big and the error variance is small

One of the assumptions for the t test for independent means is that a. the variance of each of the parent populations is the same. b. sample means are not significantly different. c. the mean of the distribution of differences between means is 1. d. the mean of each of the parent populations vary by no more than 1 standard deviation.

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

Use this ANOVA summary table to answer the questions that follow it: Source of variability SS df MS F Between-groups 21 6 3.50 4.38 Within-groups 229 288 0.80 Total 250 294 What is the sample size for this analysis? a. 288 b. 295 c. 250 d. 294

b. 295

If a research article presented the results of an analysis of variance as, "F (2, 38) = 3.60, p < .05," then how many groups were there in the study? a. 2 b. 3 c. 40 d. 41

b. 3

Joe conducts an analysis of variance. If he rejected the null hypothesis, the most likely F value is a. -5.12 b. 3.57 c. 1.01 d. 0.64

b. 3.57

In an analysis of variance with a between-groups population variance estimate of 30 and a within-groups estimate of 25, the F ratio is a. (30-25)/30=0.17 b. 30/25=1.20 c. 25/30=0.83 d. 25/(30-25)=5.00

b. 30/25=1.20

The results of an analysis of variance would be reported in a research article as a. F (44) = 3.40, significant b. F (2, 44) = 3.40, p < .05 c. F = 3.40, p < .05 d. F (2, 44) < .05

b. F (2, 44) = 3.40, p < .05

Which statement is only true for the t test for dependent means rather than t tests in general? a. The sample scores (in some form) are compared to a t distribution. b. Pretest-posttest experimental designs are common. c. The population means are unknown. d. Population variances are estimated from the information in the sample of scores actually studied.

b. Pretest-posttest experimental designs are common.

Which of the following is the MOST serious violation of an assumption for the t test for independent means? a. The populations are both dramatically negatively skewed. b. The populations are dramatically skewed in opposite directions. c. The populations are both dramatically positively skewed. d. The sample size is smaller than 15.

b. The populations are dramatically skewed in opposite directions.

In the phrase "one-way, between-subjects ANOVA," what does "one-way" mean? a. There are two or more independent variables. b. There is one independent variable. c. There is one dependent variable. d. There are two or more dependent variables.

b. There is one independent variable.

In which of the following situations would a t test for independent means be conducted? a. a comparison of participants' logical reasoning skills with the general population b. 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 c. a comparison of the SAT scores of a group of 10 students who completed a special SAT preparation course compared to the scores of students in general on the SAT d. a comparison of participants' scores on a skills test before and after attending a training session intended to improve the skill

b. 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

When estimating the variance of a population from the sample, the sample variance cannot be used directly because a. it tends to be slightly too large—it overestimates the population variance. b. it tends to be slightly too small—it underestimates the population variance. c. it is based on using squared deviations. d. it is based on using absolute deviations.

b. it tends to be slightly too small—it underestimates the population variance.

The most common way for a t test for independent means to be reported in a research article is a. independent t (15): 30, p: significant b. t (45) = 3.5, p < .05 c. t (i:29) < .05 d. t (independent) = 2.9, significant

b. t (45) = 3.5, p < .05

Based on the following results, which would be the correct use of the formula, t = (M1 - M2) / S(difference)? Sample 1: Mean = 60; Variance of the distribution of means = 2 Sample 2: Mean = 50; Variance of the distribution of means = 7 a. t = (60 - 50) / √(4+49)/2 b. t = (60 - 50) / √(2+7) c. t = (7 - 2) / √(50+60) d. t = (60 - 50) / (2+7)

b. t = (60 - 50) / √(2+7)

A "distribution of differences between means" can be thought of as a distribution of a. the differences between a single sample from Population 1 and all possible samples from Population 2. b. the differences obtained when a sample mean from one population is repeatedly subtracted from a sample mean from another population. c. difference scores, which are found by subtracting sample means from the population mean. d. the differences obtained when several methods of estimating the population mean are used in sequence.

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

When conducting a t test for independent means, a typical research hypothesis might be a. the mean of Sample 1 is greater than the mean of Sample 2. b. the mean of Population 1 is greater than the mean of Population 2. c. the mean of Population 1 is the same as the mean of Population 2. d. the mean of Sample 1 is the same as the mean of Sample 2.

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

The most serious violation of an assumption for an analysis of variance occurs when a. the number of scores in each group is less than 10. b. the scores between and within groups are dependent. c. the variance estimate of the group with the largest estimate is twice that of the smallest. d. the populations are strongly skewed in the positive direction.

b. the scores between and within groups are dependent.

Studies using difference scores tend to have larger effect sizes than studies using other research designs because a. of the long-standing procedural bias in psychology to set up studies involving dependent means in such a way as to artificially favor large effect sizes. b. the standard deviation of difference scores is usually low. c. participants provide their own baseline, which increases the variance. d. studies with dependent means usually use a larger number of participants, so larger effect sizes are easily detected.

b. the standard deviation of difference scores is usually low.

Ann conducts a study, and finds that the estimated population variances for the groups are 12.8, 16.3, 15.1, and 19.9. What is the within-groups estimate of the population variance? a. (12.8 + 16.3 + 15.1 + 19.9) / (4 - 1) = 21.37. b. (12.8sq + 16.3sq + 15.1sq + 19.9sq) / (4 - 1) = 351.18. c. (12.8 + 16.3 + 15.1 + 19.9) / 4 = 16.03. d. (12.8sq + 16.3sq + 15.1sq + 19.9sq) / 4 = 263.39.

c. (12.8 + 16.3 + 15.1 + 19.9) / 4 = 16.03.

If a sample includes three individuals with scores of 2, 3, and 4, the estimated population variance is a. 1.33 b. 3.67 c. 1 d. 2

c. 1

In the phrase "one-way, between-subjects ANOVA," what does "between-subjects" mean? a. The independent variable has only two levels. b. Each participant experiences all levels of the independent variable. c. Each participant experiences only one of the levels of the independent variable. d. The independent variable has at least three levels.

c. Each participant experiences only one of the levels of the independent variable.

Which of the following research situations is most likely to use a between-subjects design? a. Evaluation of the development of verbal skills between age 2 and age 6 for a sample of girls. b. Evaluation of the effectiveness of a blood pressure medication by comparing blood pressure before the medication, 3 months after, and again 6 months after the medication. c. Evaluation of the difference in verbal skills between 2-year-old, 4-year-old, and 6-year-old boys. d. Evaluation of the effectiveness of an exercise program by measuring how much weight is lost during 6 months of strength training.

c. Evaluation of the difference in verbal skills between 2-year-old, 4-year-old, and 6-year-old boys.

Based on the following table from a research article. Mean Score on Four Questionnaire Scales Before and After the Experimental Manipulation Questionnaire Before After Change Dominance 18.42 16.31 -2.11 Independence 17.25 21.38 -4.13** Conformity 18.97 17.20 -1.77* Nurturance 16.11 13.89 -2.22* *p < .05 **p < .01 Which of the following statements is most likely to be true based on the results presented? a. The various scales probably all had just about the same population variances. b. The t scores are all larger than the raw difference scores. c. The hypothesis testing procedure was probably a t test for dependent means. d. The hypothesis testing procedure probably used one-tailed tests.

c. The hypothesis testing procedure was probably a t test for dependent means.

In an analysis of variance, if the within-groups variance estimate is about the same as the between-groups variance estimate, then a. an error has been made in computing the between-groups and the within-groups variance estimates. b. any difference between sample means is probably due to a real difference caused by experimental conditions. c. any difference between sample means is probably due to random sampling error. d. the null hypothesis should be rejected.

c. any difference between sample means is probably due to random sampling error.

When carrying out an analysis of variance with equal sample sizes, the estimated variance of the distribution of means is converted to an estimated variance of the population of individual scores by a. multiplying the estimated variance of the population of individual scores by the number of groups. b. dividing the estimated variance of the distribution of means by the number of scores in each sample. c. multiplying the estimated variance of the distribution of means by the number of scores in each sample. d. dividing the estimated variance between groups by the number of groups.

c. multiplying the estimated variance of the distribution of means by the number of scores in each sample.

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 S(difference) was 0.9, the t score was a. t = (18.8 - 21.3) / [(2) (0.9)] = -1.39 b. t = (18.8 - 21.3) (0.9) = -2.25 c. t = (18.8 - 21.3) / 0.9 = -2.78 d. t = (18.8 - 21.3) / 0.81= -3.09

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

When figuring the pooled population variance estimate in a t test for independent means, a. the scores from both samples are combined to form a single sample, and the estimated variance is figured in the usual way using this combined sample. b. the variance of BOTH of the original populations must be known, as opposed to estimated. c. 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. d. the variance of at least one of the original populations must be known, as opposed to estimated, but the other can be estimated from sample scores.

c. 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.

If an experimenter conducts a t test for independent means and rejects the null hypothesis, the correct interpretation is that a. the variance of one sample is so much larger than the variance of the other sample that the variances of the parent populations must not have been the same after all. b. the samples were from populations that were actually dependent rather than independent. c. the mean of one sample is so far from the mean of the other sample that the samples must come from populations with different means. d. the mean of one sample is statistically the same as the mean of the other sample, so they probably come from populations with equal means.

c. the mean of one sample is so far from the mean of the other sample that the samples must come from populations with different means.

A t test for independent means is reported as "t (28) = 4.21, p < .01." This means a. the power was high. b. there were 28 participants in the study. c. the t score was 4.21. d. the result is not statistically significant.

c. the t score was 4.21.

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 a. t (19) = 4.36, p < .05 b. t (4.36), p (.05) c. t (4.36), p (.01) d. t (18) = 4.36, p < .01

d, t (18) = 4.36, p < .01

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 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? a. 15 + 23 = 38 b. (15 + 23) - 1 = 37 c. (15 + 23) / 2 = 19 d. (15 - 1) + (23 - 1) = 36

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

If a sample includes three individuals with scores of 4, 6, and 8, the estimated population variance is a. (2 + 0 + 2) / 2 = 2 b. (4 + 0 + 4) / 3 = 2.67 c. (2 + 0 + 2) / 3 = 1.33 d. (4 + 0 + 4) / 2 = 4

d. (4+0+4)/2=4

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 a. -2.500 b. -0.113 c. 35.000 d. 1.699

d. 1.699

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 a. 10/135=.074 b. 135/10=13.5 c. 9/135=.067 d. 135/9=15.0

d. 135/9=15.0

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 a. 400/9=44.4 b. 20/9=2.2 c. 400/10=40.0 d. 20/10=2.0

d. 20/10=2.0

An analysis of variance (ANOVA) differs from a t test for independent means in that an ANOVA a. is usually used to compare two groups, while a t test for independent means can be used to compare two or more groups. b. is conducted before the experiment, while a t test for independent means is conducted after the experiment. c. includes computation of group variances as part of the analysis, while a t test does not include these computations. d. can be used to compare three or more groups, while a t test for independent means cannot be used to compare more than two groups.

d. can be used to compare three or more groups, while a t test for independent means cannot be used to compare more than two groups.

If a t test for dependent means is reported in a research article as "t (38) = 3.11, p < .01," then a. the result is not significant. b. there were 39 degrees of freedom. c. you can assume a one-tailed test was used. d. the result is significant.

d. the result is significant.

If a t test for dependent means is reported in a research article as "t (16) = 2.67, p < .05," then a. there were 16 participants. b. the t score was 16. c. the result is not significant. d. the t score was 2.67.

d. the t score was 2.67.