Exam 3 homework questions
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?
(12.8 + 16.3 + 15.1 + 19.9) / 4 = 16.03.
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
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.
1; 4
In the phrase "one-way, between-subjects ANOVA," what does "between-subjects" mean?
Each participant experiences only one of the levels of the independent variable.
The results of an analysis of variance would be reported in a research article as
F (2, 44) = 3.40, p < .05
An analysis of variance (ANOVA) differs from a t test for independent means in that an ANOVA
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.
When estimating the variance of a population from the sample, the sample variance cannot be used directly because______________?
it tends to be slightly too small—it underestimates the population variance.
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 how?
t (18) = 4.36, p < .01
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
A t test for dependent means would be used to compare what?
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 ________.
the population variance is estimated
What is the purpose of a post hoc test?
to determine which groups are significantly different from each other
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?
(15 - 1) + (23 - 1) = 36
If a sample includes three individuals with scores of 2, 3, and 4, what is the estimated population variance?
1
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
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
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
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?
3
Joe conducts an analysis of variance. If he rejected the null hypothesis, the most likely F value is
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
30 / 25 = 1.20
Which of the following research situations is most likely to use a between-subjects design?
Evaluation of the difference in verbal skills between 2-year-old, 4-year-old, and 6-year-old boys.
Which statement is only true for the t test for dependent means rather than t tests in general?
Pretest-posttest experimental designs are common.
In the phrase "one-way, between-subjects ANOVA," what does "one-way" mean?
There is one independent variable.
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
In an analysis of variance, if the within-groups variance estimate is about the same as the between-groups variance estimate, then
any difference between sample means is probably due to random sampling error.
The comparison distribution for a t test for independent means is a ____________?
distribution of differences between means.
In the formula, Σ(M-GM)2/dfBetween, "GM" is the _______.
grand mean
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.
A characteristic of an F ratio is that
it can never be less than 0.
The comparison distribution in a t test for dependent means is a distribution of what?
means of different scores
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
multiplying the estimated variance of the distribution of means by the number of scores in each sample.
Analysis of variance should be conducted only when Analysis of variance should be conducted only when
population variances can be assumed to be equal.
To use a one-way, between-subjects ANOVA, the dependent variable must be:
scale data (interval or ratio)
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 what?
t = (18.8 - 21.3) / 0.9 = -2.78
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)
What is the main difference between a Z score and a t score?
t scores are used when the population variance is unknown.
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.
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 what?
the hours that "C" average students spend on Facebook each week compared with students in general.
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.
If an experimenter conducts a t test for independent means and rejects the null hypothesis, the correct interpretation is that
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.
If a t test for dependent means is reported in a research article as "t (38) = 3.11, p < .01," then
the result is significant
Even a very small mean difference can be statistically significant if:
the sample size is big and the error variance is small
The most serious violation of an assumption for an analysis of variance occurs when
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_________________.
the standard deviation of difference scores is usually low.
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 what?
the t score was 4.21.
