PSY 410
A researcher is interested in having as much ability as possible to identify a treatment effect if one really exists. Which of the following strategies should they employ?
change the sample size from n = 25 to n = 100.
For an analysis of variance comparing two treatments with n = 5 in each treatment, the F-ratio will have:
df = 1, 8
An independent-measures research study uses n = 15 participants in one group and n = 12 participants in a second group to compare two treatment conditions. What is the df value for the t statistic computed for the corresponding hypothesis test?
df = 25
Which statement below is not consistent with the benefits of adding an individual difference variable (i.e., gender) to a single factor (i.e., factor A) ANOVA? (i.e., which statement is not correct)
doing so reduces the between treatments variance for the single factor
In a one-way ANOVA, if the sum of squares for error (SSE) (or the sum of squares within) is large relative to the sum of squares for treatments (SST), this is an indication that the
population means are not likely to be different and the null hypothesis should not be rejected.
Which of the following accurately describes the critical region?
sample means that are very unlikely to be obtained if the null hypothesis is true
A researcher uncovers that there is a significant interaction between the factor of marital status (i.e., married or not married) and participant sex (i.e., male or female) with regard to health well-being. A researcher decides to compare the difference in health well-being between married men and married women. This is an example of testing a(n) _____.
simple main effect.
A researcher is examining whether daily exercise influences mood. The researcher assigns n = 12 individuals to exercise for three months and finds an average mood score of M = 22 with SS = 182 after three months for individuals in this group. A second group of n = 7 individuals assigned to a control group for the three months has a mood score of M = 19 with SS = 90. Which of the following is most consistent with the results of conducting a two-tailed independent-measures t test with α = .05?
t = +1.58 and fail to reject the null hypothesis
On average, which value is expected for the t statistic when the null hypothesis is true?
t = 0.00
What is measured by the numerator of the z-score test statistic?
the distance between the sample mean and hypothesized population mean
In a two-factor analysis of variance, a main effect is defined as _____.
the mean differences among the levels of one factor
A treatment effect refers to differences between scores that are caused by the different treatment conditions. The differences (or variability) produced by treatment effects will contribute to __________.
the numerator of the F-ratio
In analysis of variance, the magnitude of the mean differences from one treatment to another will contribute to ____.
the numerator of the F-ratio
Which of the following is consistent with what r2 represents as a measure of effect size?
the portion of variability in a sample attributable to a treatment effect relative to the total variability in the sample
The null hypothesis for an ANOVA states that __________.
there are no differences between any of the population means
A research report states that " F(2, 27) = 5.36, p < .05." Based on this report, with α = .05, you can conclude that the decision from the ANOVA was:
to reject the null hypothesis, conclude there were significant differences between treatments
The between measures differences between the treatments by computing the variability of the treatment means or totals. These differences are assumed to be produced by
treatment effects (if they exist). differences resulting from chance.
The narrower the confidence interval, the more precise it is. Which combination of factors will produce the most precise estimate of the difference between two population means?
two samples of n = 50 and 80% confidence
A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population. If the researcher uses a one-tailed test with a = .01, which of the following correctly identifies the critical region?
z > 2.33
A sample of n = 7 scores is selected from a population with an unknown mean (µ). The sample has a mean of M = 40 and a variance of s2 = 63. Which of the following is the correct 95% confidence interval for µ?
µ = 40 ± 7.341
A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population that is known to have a mean of µ = 80. The results will be examined using a one-tailed hypothesis test. Which of the following is the correct statement for the null hypothesis?
µ ≤ 80
If an analysis of variance produces SSbetween = 20 and SSwithin = 40, then:
η2 = 0.50.
If the null hypothesis is true and there is no treatment effect, what value is expected on average for the F-ratio?
1.00
An experiment compares three treatment conditions with a separate sample of n = 10 in each treatment. If the data are analyzed with ANOVA, the analysis would have dftotal = ____.
29
A researcher reports an F-ratio with df = 3, 36 from an one-way ANOVA research study. Based on the df values, how many treatments were compared in the study and what was the total number of subjects participating in the study?
4 treatments and 40 subjects
One sample has n = 18 with SS = 102 and M = 12. A second sample has n = 5 with SS = 171 and M = 8. Which of the following is the 95% confidence interval for the mean difference in confidence between the two samples?
4 ± 3.7856
A two-factor study with two levels of factor A and three levels of factor B uses a separate group of n = 5 participants in each treatment condition. How many participants are used for the entire study?
n = 30
The results from a two-factor analysis of variance show a significant main effect for factor A and a significant main effect for factor B. Based on this information, what can a researcher conclude about the interaction?
A researcher cannot make any conclusion about the statistical significance of the interaction.
Which of the following statements comparing one-tailed with two-tailed hypothesis tests is correct?
All else equal, a less extreme z-score is needed to obtain statistical significance for a one-tailed than two-tailed hypothesis test.
Describe the similarities between an F-ratio and a t statistic.
Both the F-ratio and the t statistic compare the actual mean differences between sample means (numerator) with the differences that would be expected if there is no treatment effect (the denominator if is true). If the numerator is sufficiently larger than the denominator, we conclude that there is a significant difference between treatments.
For an experiment comparing more than two treatment conditions you should use analysis of variance rather than separate t tests because __________.
Conducting several t tests would inflate the risk of a Type I error.
For a two-factor experiment with 2 levels of factor A and 3 levels of factor B and n = 10 subjects in each treatment condition, how many participants are in each level of factor A?
n = 30
What is the critical value of F for the interaction in a two-factor analysis of variance hypothesis test with two levels in each factor and n = 7 individuals in each level using an alpha level of α = .05.
F = 4.26
A researcher administers an IQ test to a random sample of n = 16 of high school students and obtains a sample mean IQ of M = 115 with s = 25. Test H0: µ = 100, using a two-tailed test with α= .01.Based on this test you conclude:
Fail to reject the null hypothesis, there is not significant evidence of a difference in IQ scores.
How does sample variance influence the estimated standard error and measures of effect size such as r2 and Cohen's d?
Larger sample variance increases the estimated standard error but decreases measures of effect size.
If other factors are held constant, which set of sample characteristics is most likely to lead a researcher to reject a null hypothesis stating that µ = 80?
M = 90 and s2 = 9
For an experiment with k = 3 treatments, MSbetween = 10. For this analysis,
SSbetween = 20.
A researcher is interested in the effect of positive affirmations on self-confidence. What is the most likely consequence of adding gender as a factor in the ANOVA?
The MSbetween treatments value will decrease.
Two samples from the same population both have M = 84 and s2= 20, but one sample has n = 10 and the other has n = 20 scores. Both samples are used to evaluate a hypothesis stating that µ = 80 and to compute Cohen's d. How will the outcomes for the two samples compare?
The larger sample is more likely to reject the null hypothesis, but the two samples will have the same value for Cohen's d.
Consider that the results of a research study conclude that the "effect of social media use on anxiety depends on gender." Which statement below is correct based on this conclusion?
The research study uncovered an interaction between social media use and gender, but we don't know about the main effects of social media use or gender.
Explain why t distributions tend to be flatter and more spread out than the normal distribution.
The sample variance or sample standard deviation (s) used to compute t changes from one sample to another and contributes to the variability of the t statistics. A z-score uses the population variance, which is constant from one sample to another.
A researcher selects a sample and administers a treatment for anxiety to the individuals in the sample. If the sample is used for a hypothesis test, what does the null hypothesis (H0) put forth about the treatment?
The treatment has no effect on anxiety.
Two parallel lines in a graph pertaining to separate factors (i.e., A & B) in a two-factor analysis of variance indicate which of the following?
There is no interaction between factors A and B.
What is the relationship among the separate F-ratios in a two-factor ANOVA?
They may have different df values, but they all have the same denominator.
What value is expected for the F-ratio, on average, if the null hypothesis is true in an ANOVA? Explain why.
When there is no treatment effect, the numerator and the denominator of the F-ratio are both measuring the same sources of variability (random and unsystematic differences from sampling error). In this case, the F-ratio is balanced and should have a value near 1.00.
Why should you use ANOVA instead of several t tests to evaluate mean differences when an experiment consists of three or more treatment conditions?
With three or more treatment conditions you need three or more t tests to evaluate all the mean differences. Each test involves a risk of Type I error. The more tests you do, the more risk there is of a Type I error occurring in any of the tests. The ANOVA performs all of the tests simultaneously with a single, fixed level for .
When there are more than two treatments in an ANOVA, rejecting the null hypothesis means that
at least one of the treatment means is different from the others.
Which combination of factors is most likely to produce a large value for the F-ratio for ANOVA?
large mean differences and small sample variances
A researcher reports t(22) = 5.30, p < .01, two tails for an independent-measures experiment. How many individuals participated in the entire experiment?
n = 24
