Exam 3, 311
________ 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 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 z test reported differently for one-tailed and two-tailed tests?
No, the same values are reported.
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
Compared to the two-independent sample t test, the related samples design decreases
standard error
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
What is the typical level of significance for a hypothesis test in behavioral research?
.05
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
State the critical value(s) for a t test using a two-tailed test at a .05 level of significance: t(20).
±2.086
When reporting the results of a one-sample z test using APA format, the ________ does not need to be reported.
critical values
A researcher selects a sample of 36 dog owners and measures their responsiveness to two types of pictures: one depicting the humane treatment of dogs and one depicting the inhumane treatment of dogs. The researcher finds that responsiveness significantly differed, t = 3.243. Use eta-squared to compute the proportion of variance for this result.
= 0.23
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, all of the above
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.
Which of the following statements regarding the null hypothesis is true?
The null hypothesis always makes statements about a population parameter.
A method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample, is called
hypothesis testing
(EXTRA CREDIT) 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
Which of the following is an assumption for the two-independent sample t test, but not the one- sample t test?
Equal variances
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)
The mean crying time of infants during naptime at a local preschool is 12 minutes (that's the population mean). 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. Calculate t.
-4.35
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
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
= 78
Which measure of effect size is most commonly reported with a t test?
Cohen's d
(4 pts) 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. (Be sure you give the exact terms)
Eta-Squared and Omega-Squared (Eta-squared estimate of proportion of variance; used for all t tests) This can overestimate the proportion of variance accounted for by the independent variable. (Omega-squared estimate of proportion of variance; used for all t tests) Variability explained by the treatment (DV) divided by the total variability observed. Subtracting 1 from the t allows for a smaller effect size and more conservative estimate for the proportion of variance
Post hoc tests are computed
Following a significant ANOVA test to make pairwise comparisons.
(2 points) Rejecting a true null hypothesis is a Type____________error.
I
(4 pts) A researcher computes some of the values in this F table for a one-way between-subjects ANOVA. Fill in all of the missing values (hint: there are four) Source of variation SS df MS F Between groups 32 4 X X Within groups (error) 90 45 X X Total 122
MSbetween = 8, MSerror = 2, F = 4, df total = 49
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 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.
Using APA format, which value is typically given in parentheses when reporting the results for a t test?
The degrees of freedom.
(4 pts) Give the definition of "power" in statistics usage.
The likelihood of rejecting a false null hypothesis. Give points if students describe the relationship between alpha, sample size and effect size.
The one-sample z test is a hypothesis test used to test hypotheses
concerning a single population with a known variance
A researcher runs an independent groups design and 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
The test statistic for a related samples t test makes tests concerning a single sample of
difference scores
(EXTRA CREDIT) Using a two-way between-subjects ANOVA with Factor A (Gender: male, female) and Factor B (Type of employment: blue collar, white collar), a researcher found that salary for men and women significantly varied across the levels of the second factor (type of employment). That is, the effect of gender depended on type of employment. In this study, the researcher found a significant
interaction
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, all of the above
(2 points). One type of ANOVA design is a(n)_________________ design, which is defined as the situation when at least one independent variable is between groups and at least one independent variable is within groups.
mixed
Using a between-subjects ANOVA design,
n participants are observed k times
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, all of the above
A researcher records the time it takes (in seconds) for participants to respond (by pressing a key) to a familiar versus an unfamiliar word flashed onto a computer screen. In this study, the difference in response time for each participant is compared. 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 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, all of the above
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
(4 pts). A professor finds that the average SAT score among all students attending his college (i.e., in that population) is 1150±150 (). He polls his class of 25 students and finds that the average SAT score is 1200. Compute a one-sample z test. Also, state whether he would reject the null hypothesis with a two-tailed test with a .05 level of significance. (Be sure to show your work).
z= 1.67, No: do not reject the null hypothesis
