Stats 3
A researcher compares differences in positivity between participants in a low-, middle-, or upper-middle-class family. If she observes 15 participants in each group, then what are the degrees of freedom for the one-way between-subjects ANOVA?
(2, 42)
What are the degrees of freedom for the related samples t test?
(nD - 1)
What is the typical level of significance for a hypothesis test in behavioral research?
.05
Rejecting a true null hypothesis is a Type____________________error.
1
The following is a summary of a one-way between-subjects ANOVA: F(2, 37) = 3.42, p < .05, = .12. How many pairwise comparisons need to be made for this ANOVA result?
3
A researcher assigned participants (n = 8 per group) to read vignettes describing a person engaging in either a helpful, hurtful, or neutral act. Different participants were assigned to each group and asked to rate how positively they viewed the person described in the vignette. What is the critical value for the one-way between-subjects ANOVA at a .05 level of significance?
3.47
A researcher selects a sample of 32 participants who are assigned to participate in a study with one group. What are the degrees of freedom for this test?
31
A researcher conducts a study in which k = 5 and N = 80. What are the degrees of freedom between-groups for the one-way between-subjects ANOVA?
4
47. Which measure of effect size is most commonly reported with a t test?
Cohen's d
Following a significant one-way between-subjects ANOVA in which k > 2, what is the next appropriate step?
Conduct post hoc tests.
When the variability attributed to between-groups is equal to the variability attributed to error, then the value of the test statistic for a one-way between-subjects ANOVA is,
Equal to 1
Which of the following is an assumption for the two-independent sample t test, but not the one-sample t test?
Equal variances
Post hoc tests are computed
Following a significant ANOVA test to make pairwise comparisons.
A researcher has participants rate the likability of a sexually promiscuous person described in a vignette as being male (n = 20) or female (n = 12). The mean likability ratings in each group were 4.0. If the null hypothesis is that there is no difference in likability ratings, then do likability ratings differ at a .05 level of significance?
No, this result is not significant, t(30) = 0.
A researcher computes the following one-way between-subjects ANOVA table. State the decision at a .05 level of significance. (Hint: Complete the table first.)
Reject the null hypothesis.
Two researchers (A and B) compute a two-independent sample t test. For both tests, the mean difference between the two groups is 10, but the standard error is smaller for Researcher A. Which test is more likely to result in a decision to reject the null hypothesis?
Researcher A
The related samples design can ________.
be more practical
is not one of the four steps to hypothesis testing?
evaluate the plan
A method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample, is called
hypothesis testing
The t distribution is similar to the z distribution except
it is associated with greater variability it is characterized by "thicker" tails compared with the z distribution it is associated with scores being more likely in the tails of the distribution
Without changing the value of error variance, the ________ the between-groups variability, the more likely we are to reject the null hypothesis.
larger
The criteria for a decision regarding the value stated in a null hypothesis is set by the
level of significance
When reporting data in a results section, it is ____ necessary to identify the type of t test computed.
not
The term "between-subjects" refers to
observing different participants one time in each group
You read about a study testing whether night shift workers sleep the recommended 8 hours per day. Assuming that the population variance of sleep (per day) is unknown, what type of t test is appropriate for this study?
one-sample t test
One difference between a repeated measures design and a matched samples design is that
only one design involves observing the same participants in each group
Computing a one-sample t test is appropriate when
participants are assigned to only one group the population variance is unknown participants are observed one time
The denominator of the test statistic for a related samples t test
provides an estimate of the error associated with the difference scores
A researcher conducts a study in which the population variance of difference scores between two groups is unknown. What type of t test is most appropriate for this study?
related samples t test
A researcher conducts a study in which the same participants are observed across each level of the independent variable. If there are only two levels of the independent variable, then what type of t test is appropriate for this study?
related samples t test
What are the two decisions that researchers can make in hypothesis testing?
retain or reject the null hypothesis
As_____________________________ increases, the power to detect an effect increases.
sample size
Based on the effect size conventions, d = 0.18 is a
small effect size
Compared to the two-independent sample t test, the related samples design decreases
standard error
Which of the following summarizes a t test that was significant and associated with a large effect size?
t(12) = 2.95, p < .05, d = .82
The power of the decision-making process is
the likelihood of rejecting a false null hypothesis
A lowercase k is used to denote
the number of groups in a study the number of levels of the factor in a study
To compute a related samples t test, a researcher has to know many values. Which of the following is NOT a value that the researcher must know to compute this test?
the population variance of difference scores
For the related samples t test, assuming that all other values remain constant, then as samples size increases,
the value of the test statistic increases the power to detect an effect increases the estimate for standard error decreases
1150±150 ( ). He polls his class of 25 students and finds that the average SAT score is 1200. Suppose he computes a one-sample z test at a .05 level of significance. What is his decision?
to reject the null hypothesis for an upper-tailed test, but to retain the null hypothesis for a two-tailed test
Given the following values: = 6.0, M = 7.6, n = 36, = 6, conduct a one-sample z test at a .05 level of significance. For a one-tailed test, upper-tail critical, what is the decision?
to retain the null hypothesis
A professor gives an exam in which the mean score is 78 points. She gives another exam to test whether or not scores change. In this example, the null hypothesis is
u = 78
The source of variability associated with error variance in the one-way between-subjects ANOVA is called
within-groups variability
Is a one-sample z test reported differently for one-tailed and two-tailed tests?
No, the same values are reported.
The following is a summary of a one-way between-subjects ANOVA: F(2, 37) = 3.42, p < .05, = .12. How many participants were observed in this study?
40
What is the minimum number of groups that can be observed using the one-way between-subjects ANOVA design?
2
The related samples design can ________ the power to detect an effect by making the standard error ________.
increase; smaller
Eta-squared is computed ______ for the one-sample, and the two-independent sample t tests.
Similarly
Which of the following statements regarding the null hypothesis is true?
The null hypothesis always makes statements about a population parameter.
ANOVA stands for
analysis of variance
When reporting the results of a one-sample z test using APA format, the ________ does not need to be reported.
critical values
A researcher reports that the mean difference in the body weight of rats following a pharmacological versus control treatment is 14 grams, with a pooled sample variance equal to 256. What is the effect size for this test using estimated Cohen's d?
d = 0.88; large effect size
The degrees of freedom for error is called
degrees of freedom error degrees of freedom denominator degrees of freedom within-groups
The test statistic for a related samples t test makes tests concerning a single sample of
difference scores
Each of the following is an advantage for using the related samples design, except
it increases the variability measured in a study
Based on the effect size conventions, d = 0.99 is a
large effect size
A researcher records differences in ratings of emotion among participants watching either a drama or a romance film. Assuming that the population variance is unknown, what type of t test is appropriate for this study?
two-independent sample t test
State the critical value(s) for a t test using a two-tailed test at a .05 level of significance: t(20).
±2.086
A researcher conducts a study using the one-way between-subjects ANOVA. He computes = 120 and = 200. What is the effect size for this test using eta-squared?
.38
In a study with three groups and 13 participants in each group, the sum of squares for the within-groups source of variation is 18. What is the value for the mean square within-groups in this study?
.5
Which of the following statements is the appropriate way to read the degrees of freedom for an ANOVA with 10 participants in each of four groups?
3 and 36 degrees of freedom
Which of the following is an assumption for computing any type of independent sample t test?
Data in the population being sampled are normally distributed. Data were obtained from a sample that was selected using a random sampling procedure. The probabilities of each measured outcome in a study are independent.
________ allows researchers to describe (1) how far mean scores have shifted in the population, or (2) the percentage of variance that can be explained by a given variable.
Effect size
A researcher sampled 16 couples and measured the mean difference in their marital satisfaction. Each couple was paired and the differences in their ratings (on a 7-point scale) were taken. If the mean difference in satisfaction ratings for this sample was 1.8±2.0 ( ), then what is the decision at a .05 level of significance?
Satisfaction ratings significantly differ, t(15) = 3.60.
Using APA format, which value is typically given in parentheses when reporting the results for a t test?
The degrees of freedom
Which of the following post hoc tests is associated with the least power to detect an effect?
Tukey's HSD test
A researcher measures differences in recall between male and female participants following a romantic movie clip. If different participants were in each group, then what type of statistical design is appropriate for this study?
a two-independent sample t test a one-way between-subjects ANOVA
The one-sample z test is a hypothesis test used to test hypotheses
concerning a single population with a known variance
A researcher reports that mean ratings of liking for some food are 0.8±2.4 (M±SD). If the null hypothesis was that the mean equals 0, then what is the effect size for this test using estimated Cohen's d?
d = 0.33; medium effect size
The degrees of freedom for the between-groups variability is called
degrees of freedom numerator degrees of freedom between-groups
Computing a two-independent sample t test is appropriate when
different participants are assigned to each group the population variance is unknown participants are observed one time
94. Computing a one-way between-subjects ANOVA is appropriate when
different participants are observed one time in each of two or more groups for one factor
A measure of the size of an effect in a population is called
effect size
Give the names for two commonly used measures of effect size for t tests that give you the proportion of variance explained in the DV.
eta (^2) omega (^2)
Which measure of proportion of variance tends to overestimate the size of an effect in a population?
eta-squared
Which of the following is not a post hoc test for a one-way between-subjects ANOVA?
eta-squared
All other things being equal, reducing the level of significance from .05 to .01 will ________ the value of the test statistic for a related samples t test.
have no effect on
56. A researcher asks a sample of brothers and sisters to rate how positive their family environment was during childhood. In this study, the differences in ratings between each brother and sister pair were compared. The type of design described here is called a
matched samples design
Which of the following is a type of related samples design in which different participants are actually observed in each group, but treated statistically as if they are the same persons in each group.
matched samples design
Using a between-subjects ANOVA design,
n participants are observed k times
A researcher reports a significant effect with t(14) = 3.24. Compute eta-squared for this result
n(^2) = 0.43 (large effect size)
A researcher compares the difference in the amount of texting by students in class during the first week and last week of classes. The type of design described here is called a
repeated measures design
A type of related samples design in which participants are observed more than once is called a
repeated measures design
The estimated standard error in the t statistic uses the ________ to estimate the ________ when the population variance is unknown.
sample variance; population variance
The ________ is an inferential statistic used to determine the number of standard deviations in a t distribution that a sample mean deviates from the mean value or mean difference stated in the null hypothesis
t statistic
Homogeneity of variance is an assumption for the one-way between-subjects ANOVA. What does this assumption mean?
that the variance is equal in each population from which samples are selected
For an analysis of variance, the term "one-way" refers to
the number of factors in the design
To compute a two-independent sample t test, a researcher has to know many values. Which of the following is NOT a value that the researcher must know to compute this test?
the pooled population variance
"Elementary school children spent significantly more time reading the presence of a teacher than when the teacher was absent, t(7) = 2.804, p < .05 (2 = 0.46)." In this related samples t test, how many participants were observed?
8
A researcher conducts a study, but has low power to detect an effect. Which of the following is one way in which the research can increase power?
Increase the sample size.
A researcher reports that the size of an effect in some population is d = 0.88. Which of the following is an appropriate interpretation for d?
Mean scores shifted 0.88 standard deviations in the population.
Is a one-sample t test reported differently for one-tailed and two-tailed tests?
No, the same values are reported
A researcher assigns 21 adolescents to rate the likability of a person described in a vignette as having one of three personality traits. An equal number of participants are assigned to each group. If = 4.08 for this study, then what was the decision at a .05 level of significance for a one-way between-subjects ANOVA
Reject the null hypothesis.
Two researchers (A and B) compute a one-sample t test. For both tests, the mean difference between the sample and value stated in the null hypothesis is 5, but the standard error is smaller for Researcher A. Which test is more likely to result in a decision to reject the null hypothesis?
Researcher A.
A researcher randomly assigned 32 children to observe a short clip depicting either their favorite superhero, a parent, a teacher, or no person at all (n = 8 per group). If = 30 and = 104, then what was the decision at a .05 level of significance for a one-way between-subjects ANOVA?
Retain the null hypothesis.
A researcher tests how well participants know their spouse while under hypnosis, and again without hypnosis. It was hypothesized that participant responses would be more accurate (greater number of correct responses) when under hypnosis. The mean number of correct responses was M = 5.30 under hypnosis and M = 3.40 without hypnosis in a sample of 30 participants. If the estimated standard error for difference scores was 2.52, then what is the decision at a .05 level of significance (two-tailed test)?
Retain the null hypothesis; responses were not more accurate under hypnosis
A researcher measures deviant behavior in a sample of 12 children from abusive homes (Sample A). Another researcher measures the same behavior in a sample of 18 children from abusive homes (Sample B). Which sample is associated with larger degrees of freedom?
Sample B
Which of the following is an advantage for selecting related samples compared to selecting independent samples in behavioral research?
Selecting related samples can be more practical. Selecting related samples minimizes standard error. Selecting related samples increases power.
A researcher conducts two studies. Each study was a one-sample z test. Both studies placed the rejection region in both tails and measured the same sample mean. The alpha level in Study 1 was larger than the alpha level used in Study 2. Which study is associated with greater power to detect an effect?
Study 1
A researcher conducts two t tests. Test 1 is a one-tailed test with a smaller sample size at a .05 level of significance. Test 2 is a one-tailed test with a larger sample size at a .05 level of significance. What do you know about the critical values for each test?
Test 2 is associated with smaller critical values
All other things being equal, as the sample size increases, what happens to the critical value for a related samples t test (or for any t test, for that matter)?
The critical value decreases.
The mean crying time of infants during naptime at a local preschool is 12 minutes. The school implements a new naptime routine in a sample of 25 infants and records an average crying time of 8±4.6 (M±SD) minutes. Test whether this new naptime routine reduced crying time at a .05 level of significance.
The new naptime routine significantly reduced crying time, t(24) = -4.35, p < .05.
Which of the following is an assumption for computing a one-way between-subjects ANOVA?
The population being sampled from is normally distributed. Participants were selected to participate using a random procedure. One observation has no effect on the likelihood of another observation.
Two researchers analyze the same data set. Researcher A uses a two-independent sample t test and decides to retain the null hypothesis. Researcher B uses a related samples t test and decides to reject the null hypothesis. Which of the following is a likely explanation for the disparity in the decisions made.
The related samples t test had greater power to detect the effect.
A researcher computes a test statistic and finds that the p value for this test is .03. What does this result mean?
There is a 3% likelihood of obtaining the test statistic value, if the null were true
A researcher directly controls for the probability of a ________, but does not directly control for the probability of a ________.
Type I error; Type II error
A researcher reports that the mean difference in response time to an auditory versus a visual cue is 0.83 seconds, with a pooled sample variance equal to 2.45. What is the effect size for this test using estimated Cohen's d?
d = 0.53; medium effect size
A researcher obtains z = 1.45 for a one-sample z test. What is the decision for this test at a .05 level of significance?
to retain the null hypothesis
A researcher matched 30 participants on intelligence (hence 15 pairs of participants), and then compared differences in emotional responsiveness to two experimental stimuli between each pair. For this test, what are the critical values, assuming a two-tailed test at a .05 level of significance?
±2.145
