Statistics of Psychology
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 / 3
Which of the following is an example of the most common way for a t test for independent means to be reported in a research article?
t(45) = 3.52, p < .05
When determining 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
The estimated population variance is:
the sum of squared deviation scores divided by N − 1
Suppose you are planning a study involving five groups and you expect a medium effect size (and will use the .05 level).For 80% power, how many participants will you need in each group?
39
In a t test for independent means, the weighted average of the estimates of the population variance from two samples is known as the:
pooled estimate of population variance
All of the following are true for both the t test for independent means AND the t test for dependent means, EXCEPT:
pretest-posttest experimental designs are common
For analysis of variance, an approach to effect size is to calculate the:
proportion of variance accounted for (R2)
Tukey's HSD test is a type of:
protected t test
" S2Within" equals:
the population variance estimate based on the variation within each of the groups
The comparison distribution for a t test for independent means is a t distribution (as opposed to a normal curve) because:
the population variance is estimated
What effect size did Professor Juarez find?
(40 − 35)/7 = .71
If the standard deviation of the distribution of the difference between means is .76, what is the t score?
(55-51)/.76 = 5.26
Cohen's conventions for the t test for independent means are approximately __________ for a small effect size, __________ for a medium effect size, and __________ for a large effect size.
.2, .5, .8
The conventions for R2 are as follows for small, medium, and large effect sizes, respectively:
01, .06, .14
For the following question(s): A sociologist interested in cultural differences compared women of two ethnic groups on a Role Approval Index (high scores mean high degrees of approval of one's social role). The results were as follows: If you conduct a t test for independent means, how many degrees of freedom are in the t distribution?
15-1) + (23-1) = 36
In ANOVA, the ratio of the between-groups population variance estimate to the within-groups population variance estimate is known as the:
F ratio
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.
Difference scores are usually used with:
a t test for dependent means
A research article based on a t test for independent means reports a result as "t(28) = 4.21, p < .01."
all of the above
When using the F table, one must pay attention to:
all of the above
Power for a t test for dependent means can be determined using:
any of the above
In the formula"S2Difference= S2M1 + S2M2" the "S2M1" is:
the variance of the distribution of means for Population 1, based on an estimate of the population variance
n an analysis of variance, if the null hypothesis is rejected then:
the variation between sample means reflects the variation within the populations and the variation between the population means
In an analysis of variance, if the null hypothesis is true, then
there is less variance among the sample means than if the null hypothesis was not true
Suppose the standard deviation she figures (the square root of the unbiased estimate of the population variance) is .85. What is the effect size?
(5 − 4.4)/.85 = .71
What is the approximate level of power for a study using ANOVA at the .05 significance level with four groups of 30 participants each (expected effect size is medium).
.61
Suppose you carry out a study using a t test for independent means. The number of participants in each group is 40 and you conduct a one-tailed test. What would be the approximate level of power if you anticipated a medium effect size? (Consult the power table 9-4.)
.72
A sample has three individuals, with scores of 2, 3, and 4. What is the estimated population variance?
1
There is an entire family of t distributions that vary in shape according to the degrees of freedom used to estimate the population variance. However, for any particular degrees of freedom, there is/are only _____ t distribution (s).
1
If 15 research participants take a pretest and a posttest with a mean change score of 1.5, and if the standard deviation of the comparison distribution is .5, what is the t score?
1.5/.5 = 3.00
In a study with 10 degrees of freedom, what would be your cutoff score for a t distribution using a one-tailed test at the .05 level of significance?
1.813
If three samples have means of 10, 20, and 15, respectively, what is their grand mean?
15
For the following question(s): A school counselor tests the level of depression in fourth graders in a particular class of 20 students. The counselor wants to know whether the kind of students in this class differs from that of fourth graders in general at her school. On the test, a score of 10 indicates severe depression, while a score of 0 indicates no depression. From reports, she is able to find out about past testing. Fourth graders at her school usually score 5 on the scale, but the variation is not known. Her sample of 20 fifth graders has a mean depression score of 4.4. Use the .01 level of significance. The counselor calculates the unbiased estimate of the population's variance to be 15. What is the variance of the distribution of means?
15/20 = 0.75
Suppose you were conducting an ANOVA with four groups of five participants each. What are your within-groups and between-groups degrees of freedom, respectively?
16;3
In a study with 15 degrees of freedom, what would be your cutoff score for a t distribution using a two-tailed test at the .01 level of significance?
2.947
What is the approximate power for a study using the t test for dependent means with an expected small effect size (.20), two-tailed test, N = 40?
24
Approximately how many research participants would be required for 80% power for a study using the t test for dependent means (assume a one-tailed hypothesis with an expected medium effect size of .50):
26
For the following question(s): A researcher conducts a t test for dependent means in which it is predicted that there will be a decrease in unemployment from before to after a particular job-skills training program. The cutoff t needed is 1.833. The standard deviation of the distribution of means of change scores is 2.0 and the mean change score for the sample studied is an increase of 5.2. What is the t score?
5.2/2 = 2.60
For the following question(s): A researcher conducts a t test for dependent means in which it is predicted that there will be a decrease in unemployment from before to after a particular job-skills training program. The cutoff tneeded is 1.833. The standard deviation of the distribution of means of change scores is 2.0 and the mean change score for the sample studied is an increase of 5.2. What is the t score?
5.2/2 = 2.60
Consider a study in which the population variance estimate based on an experimental group of 10 participants is 70, and the population variance estimate based on a control group of 20 participants is 50. Compute the pooled estimate of population variance.
56.4
Suppose you are planning a study involving three groups and you expect a large effect size (and will use the .05 level). For 80% power, how many participants will you need in total?
63
A study has 6 participants in the experimental group and 16 participants in the control group. What is the harmonic mean of these sample sizes?
8.7
Which of the following is TRUE?
A sample's variance is a biased estimate of the population's variance, but a slight change in the variance formula gives an unbiased estimate.
In an experiment involving 50 participants, which study would have the most power?
A study with 25 in the experimental group and 25 in the control group
How do you figure S2Within "assuming sample sizes are equal"?
Add up the population variance estimates figured from within each group, then divide by the number of groups
For the following question(s): Suppose a researcher wants to study the effectiveness of a new reading program for students who have not acquired the necessary reading skills by the time they reach the eighth grade. A randomly selected group of 50 students from a local junior high with poor reading skills will undergo the new reading program. Another group of 50 randomly selected students with poor reading skills will undergo regular reading classes. A month later, the reading skills of all 100 students are assessed to determine whether the program was successful. Which of the following is a population of interest in this study?
Both A and C are correct
What is the appropriate conclusion?
Do not reject null hypothesis
For the following question(s): A research article included the following table: Mean Score on Four Questionnaire Scales Before and After the Experimental Manipulation Which of the following differences was NOT statistically significant?
Dominance
Which of the following would be most likely to appear in a research article?
F(2,44) = 3.4, p < .05
Suppose the counselor tested the null hypothesis that fourth graders in this class were less depressed than those at the school generally. She figures her t score to be −.20. What decision should she make regarding the null hypothesis?
Fail to reject it
Which of the following is the best way to reduce the variances in the distributions of means when conducting a t test for independent means?
Increase the size of the samples
What is the effect size?
It cannot be determined without also knowing the population standard deviation
What can be said about the "Independence" difference score?
It is statistically significant at the .01 level
The t test is sometimes called __________ because its main principles were developed by William Gosset who published his articles anonymously using the name "__________."
Student's t; Student
A local newspaper reports that young women in your town (i.e., a known population) sleep an average of only 5 hours per night. However, you think that women in your town who are enrolled at your college sleep more than that. You randomly select 200 women from your college and ask them to accurately record their hours of sleep. You find that they sleep an average of 7 hours per night. What test would you use to determine whether this mean difference is statistically meaningful?
T test for a single sample
What does the formula Σ (M−GM)2/ dfBetween provide?
The estimated variance of the distribution of means
Which of the following is most likely to be true given the information on this table
The hypothesis testing probably used a t test for dependent means.
Which of the following is TRUE about t distributions
The larger the sample size, the more a t distribution resembles a normal curve.
What is the research hypothesis in this example?
The mean of Population 1 is greater than the mean of Population 2
Which of the following is an assumption for the t test for dependent means?
The population follows a normal distribution.
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.
If not otherwise indicated, one should assume that researchers utilized a __________ test.
Two-tailed
When the research hypothesis is true, the means of the samples are spread out for what reason(s)?
a and b
For a one-way analysis of variance, if the null hypothesis is true, then:
any difference among sample means reflects variance within the populations
In an analysis of variance, if the within-group variance estimate is about the same as the between-group variance estimate, then:
any difference between sample means is probably due to random sampling
The F distribution/ratio:
has a long tail on the right
Gosset discovered the t distribution while attempting to:
improve the quality of beer for Guinness brewers
Other names for the t test for dependent means include all of the following EXCEPT:
independent-sample t test
In what important way does a t distribution differ from a normal curve?
it has slightly more scores at the extremes
When estimating the variance of a population from the sample, you cannot use the sample's variance directly because:
it tends to be slightly too small
According to the effect size conventions for ANOVA, .14 is considered to be a __________ effect.
large
What is the approximate power for a study using the t test for dependent means with an expected large effect size, one-tailed and N = 50?
nearly 1
Analysis of variance should only be done when:
population variances can be assumed to be equal
in a t test for independent means, the square root of the variance of distribution of differences between means is known as the:
standard deviation of the distribution of differences between means
When using a t table, the degrees of freedom you should use for a t test for independent means is the
sum of the two samples' degrees of freedom
A researcher hypothesizes that people of personality type K score higher than people of personality type R on an intelligence test. The SDifference turned out to be .9, while the mean score of type K people was 18.8 and the mean score for type R people was 21.3. What is the t score?
t = (18.8-21.3) / .9 = -2.78
What is the main difference between Z score and t score?
t scores are used when the population variance is unknown
The __________ is a hypothesis-testing procedure used when a sample mean is being compared to a known population mean and the population variance is unknown.
t test for a single sample
The __________ is a hypothesis-testing procedure in which there are two separate groups of people tested and the population variance is not known.
t test for independent means
Suppose a researcher conducted a t test for dependent means using scores from pairs of research participants (i.e., mothers and sons). The researcher considered each pair as if it were one person and calculated a difference score for each pair. In this example, the t test could also be called a:
t test for matched pairs
Which of the following is the most likely way for results of a t test for dependent means to be presented in a research article for a study with 25 participants?
t(24) = 2.94, p < .01
In an analysis of variance, when the null hypothesis is true, then all of the following are true EXCEPT:
the F ratio will generally be significantly larger than 1
If the null hypothesis is true, __________ gives an accurate indication of the variation within the populations (i.e., the variation due to chance factors)
the between-groups estimate of the population variance
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
A research article reports results of a study using a t test for dependent means as "t(38) = 3.11, p < .01." This tells you:
the result is statistically significant
Suppose you wish to compare three medical treatments for bipolar disorder (Treatments A, B, and C). The null hypothesis would be that:
the several populations being compared all have the same mean
A research article reports results of a study using a t test for dependent means as "t(16) = 2.67, p < .05." This tells you
the t score was 2.67
A research article reports results of a study using a t test for dependent means as "t(16) = 2.67, p < .05." This tells you:
the t score was 2.67
in the formula"S2Difference= S2M1 + S2M2" the "S2M1" is:
the variance of the distribution of means for Population 1, based on an estimate of the population variance
Approximately how many research participants would be required for 80% power for a study using the t test for dependent means (assume a two-tailed hypothesis with an expected small effect size of .20):
196
A study has 18 participants in the experimental group and 7 participants in the control group. What is the harmonic mean of these sample sizes?
2)(18)(7)/(18 + 7) = 10.08
For a study using a t test for independent means, the approximate number of participants needed for 80% power for an estimated large effect size and using a two-tailed test is:
26
If a sample has 27 people in it, the degrees of freedom used in the formula to estimate the population variance would be:
26
In an analysis of variance, the between-group estimate of the population variance is 30 and the within-group estimate is 25. What is the F ratio?
30/25 = 1.20
Consider a study in which the population variance estimate based on a treatment group of 14 participants is 8, and the population variance estimate based on a control group of 17 individuals is 9. Compute the pooled estimate of population variance.
8.55
Which of the following shows how the results of an analysis of variance would usually be reported in a research article?
F(3,50) = 4.33, p < .01
You do a t test for dependent means in exactly the same way as a t test for a single sample, except that you use something called:
difference scores
Typically, after getting a significant result with an ANOVA, researchers will go on to compare:
each population to each other population (using a protected t tes
It takes a slightly __________ sample mean to get a significant result when using a t distribution than when using a normal curve.
more extreme
In an analysis of variance where sample sizes are equal, when you go from the estimated variance of the distribution of means to an estimated variance of the population of individual scores you:
multiply the estimated variance of the distribution of means by the number of participants in each sample
Which of the following is an assumption for the t test for dependent means?
The population follows a normal distribution
Presume the counselor wants to examine whether there is a change (either an increase or decrease) in procrastination after attending his workshop. If the counselor tests 10 students using the .05 level of significance, what cutoff t score(s) will he use? (You should be able to figure this out without a table.)
−2.262, +2.262
What is often a limitation of research using a repeated-measure design?
lack of control group
If the null hypothesis is false, the between-groups estimate of population variance will not give an accurate estimate of the variation within the populations because it also will be affected by:
the variation among the populations
In an analysis of variance, if the null hypothesis is true, then:
there is less variance among the sample means than if the null hypothesis was not true
If not otherwise indicated, one should assume that researchers utilized a __________ test
two-tailed
The shape of a t distribution:
will vary according to the degrees of freedom in the sample you used to estimate population variance
If you know the sample's variance but not the population's variance
you can estimate the population's variance from the scores in the sample
If you know the sample's variance but not the population's variance:
you can estimate the population's variance from the scores in the sample
Because of the assumption that the population variances are equal, when you do an analysis of variance:
you figure an averaged estimate of the population variance
When conducting a t test for independent means:
you reject the null hypothesis if the t score is more extreme than the cutoff t score
What is considered a medium effect size for a t test for dependent means?
.50
When utilizing t tests, __________ would be considered an adequate amount of power.
80%
The within-groups degrees of freedom is also known as the:
denominator degrees of freedom
A study has three groups, each with an equal number of participants. The population variance is estimated from the variance within each group, giving three estimates, 54.4, 48.6, and 50.9. What is the within-group estimate of the population variance?
(54.4 + 48.6 + 50.9)/3 = 51.3
With a t test for dependent means, Population 2 will ordinarily have a mean of:
0
For a study using a t test for independent means, the approximate number of participants needed for 80% power for an estimated small effect size and using a one-tailed test is:
310
Suppose you were conducting an ANOVA with 6 groups of 10 participants each. What are your between-groups and within-groups degrees of freedom, respectively?
5;54
Another name for difference scores is:
Change scores
Suppose the counselor tested the null hypothesis that fourth graders in this class were less depressed than those at the school generally. She figures her t score to be −.20. What decision should she make regarding the null hypothesis?
fail to reject it
n a t test for independent means, when the number of scores in the two groups differs, the __________ is used as the equivalent of each group's sample size when determining power.
harmonic mean
A "distribution of differences between means" can be thought of as a distribution of as:
the differences you get when you repeatedly draw a sample mean from one population and a sample mean from another population and subtract one mean from the other
You conduct a t test for independent means and reject the null hypothesis. This means that:
the mean of one sample is so far from the mean of the other sample that you decide the samples must come from populations with different means
In the formula for estimating the population variance from the scores in a sample, the sum of squared deviations is divided by:
the number of participants in the sample minus one
In the formula [t = M1-M2 /SDifference], "SDifference" is:
the standard deviation of the distribution of differences between means
