Exam 3
The correct formula for effect size using Cohen's d for a single-sample t test is:
(M - µ)/s
What is the correct formula for Cohen's d for a paired-samples t test?
(M - μ)/s
Twenty-four students were assessed on a mindfulness measure both before and after completing a semester-long meditative yoga class. The critical t values for a two-tailed paired-samples test based on their data, with a p level of 0.05, are:
-1.714 and 1.714
The critical cutoff(s) for a two-tailed, paired-samples t test with 23 participants at a p level of 0.05 is (are):
-2.074 and 2.074
The results of an independent-samples t test were t(18) = -2.11, p < 0.05. In this example, the degrees of freedom are:
18
Psychology students took longer to complete a quiz when music was playing in the background than when there was no background noise: t(19) = -4.01, p < 0.05. What is the sample size in this study?
20
In which situation would it be necessary to use a between-groups ANOVA?
A researcher is interested in the effects of distraction on driving performance and randomly assigns participants to one of three distraction groups
Given a scale dependent variable and a nominal independent variable with three or more levels, a(n) _____ could be used to analyze the data
ANOVA
According to the Consumer Action group, the average credit card interest rate in 2010 was 12.83 percent (based on a sample of 39 cards). A researcher wanted to know if college students at her institution have different interest rates compared to this national statistic. If conducting a single-sample t test, which statement would serve as her research hypothesis?
College students have different interest rates on average compared to the nation
An F statistic calculated on 2 and 26 degrees of freedom equals 2.23. Which decision should be made about a hypothesis tested at the p = 0.05 level?
Fail to reject the null hypothesis and conclude no significant differences are indicated among the groups
Dr. Jameson wanted to know if IQ scores differed between male and female participants in his study. He gave 28 participants an IQ test and then compared IQ scores for gender differences. He hypothesized that there would be a statistically significant gender difference in IQ scores. Contrary to Dr. Jameson's hypothesis, there were no differences in IQ scores between men and women in his study. What is the dependent variable in this study?
IQ scores
What is one benefit of increasing the sample size when using t distributions?
Larger sample sizes reflect the parameters of the population more closely
The formula for the degrees of freedom for the dependent-samples t test is:
N-1
Is it necessary to correct for error when calculating the standard error for a t test? Explain your answer
No; we already corrected the standard deviation and are now reflecting the size of the sample
An F statistic calculated on 3 and 48 degrees of freedom equals 4.23. Which decision should be made about a hypothesis tested at the p = 0.05 level?
Reject the null hypothesis and conclude there are differences among the groups
An effect size of 0.53 was calculated on data after performing a hypothesis test with a single-sample t statistic in which the null hypothesis was rejected. What can be concluded about the results based on this information?
The sample data are significantly different from what was expected based on the population, with the sample mean 0.53 standard deviations greater than the population mean
Dr. Jameson wanted to know if IQ scores differed between male and female participants in his study. He gave 28 participants an IQ test and then compared IQ scores for gender differences. He hypothesized that there would be a statistically significant gender difference in IQ scores. Contrary to Dr. Jameson's hypothesis, there were no differences in IQ scores between men and women in his study. Based on the information provided, does this study meet the assumption of normality? Why or why not?
We do not know whether it is normally distributed and the sample size is not at least 30 participants
Why does correcting the standard deviation to account for error in a t test make a much bigger difference for small samples than it does for larger ones?
We subtract 1 from the sample size, which removes a greater proportion of the total and corrects to a greater degree for smaller sample sizes compared to larger ones
What is the confidence interval for a paired-samples t test with a mean difference of 4.6, a standard error of 0.16, and 9 df? (use p < .05 for the significance level)
[4.24, 4.96]
When conducting a paired-samples t test, one can assess the research hypothesis and get a range of mean differences that could be expected in the future using:
a confidence interval
dot plot
a graph that displays all the data points in a sample, with the range of scores along the x-axis and a dot for each data point above the appropriate value
between-groups ANOVA
a hypothesis test in which there are more than two samples, and each sample is composed of different participants
within-groups ANOVA
a hypothesis test in which there are more than two samples, and each sample is composed of the same participants; also called a repeated-measures ANOVA
single-sample t test
a hypothesis test in which we compare a sample from which we collect data to a population for which we know the mean but not the standard deviation
one-way ANOVA
a hypothesis test that includes both one nominal independent variable with more than two levels and a scale-dependent variable
analysis of variance (ANOVA)
a hypothesis test used with one or more nominal (and sometimes ordinal) independent variables (with at least three groups overall) and a scale-dependent variable
Bonferroni test (sometimes called the Dunn Multiple Comparisons test)
a post hoc test that provides a more strict critical value for every comparison of means
F statistic
a ratio of two measures of variance: 1) between-groups variance, which indicates differences among sample means, and 2) within-groups variance, which is essentially an average of the sample variances
post hoc test
a statistical procedure frequently carried out after the null hypothesis has been rejected in an analysis of variance; it allows us to make multiple comparisons among several means; often referred to as a follow-up test
pooled variance
a weighted average of the two estimates of variance--one from each sample--that are calculated when conducting an independent-samples t test
Tukey HSD test
a widely used post hoc test that determines the differences between means in terms of standard error; the HSD is compared to a critical value; sometimes called the q test
According to the null hypothesis, the mean difference for the comparison distribution in a paired-samples t test is:
always 0
The mean of the comparison distribution for the null hypothesis of an independent-samples t test is:
always 0
between-groups variance
an estimate of the population variance, based on the differences among the means
within-groups variance
an estimate of the population variance, based on the differences within each of the three (or more) sample distributions
The z, t, and F distributions have something in common—the numerator of the test statistic:
contains a measure of difference among group means
For the paired-samples t test, the comparison distribution:
contains means difference scores
The symbol df stands for:
degrees of freedom
A paired-samples t test is also known as a:
dependent-samples t test
A psychologist is interested in whether working memory is influenced by sleep loss. The psychologist administers a measure of working memory to a group of subjects at 8 A.M. on Day One of the study and then again at 8 A.M. on Day Two of the study, after keeping the subjects awake the entire night. Does sleep loss affect working memory? What statistical analysis we should be performed to answer this question?
dependent-samples t test
Within-groups degrees of freedom is calculated by:
for each condition, subtracting 1 from the number of subjects in that group and then adding together the totals for all the groups
Dr. Jameson wanted to know if IQ scores differed between male and female participants in his study. He gave 28 participants an IQ test and then compared IQ scores for gender differences. He hypothesized that there would be a statistically significant gender difference in IQ scores. Contrary to Dr. Jameson's hypothesis, there were no differences in IQ scores between men and women in his study. What is the independent variable in this study?
gender
A psychologist is interested in whether working memory is influenced by sleep loss. The psychologist administers a measure of working memory to two groups of subjects. The subjects in one group were kept awake for the entire night and the subjects in the other group maintained their normal sleep schedules. Which statistical analysis should be performed to answer the question "Does sleep loss affect working memory?"
independent-samples t test
Researchers were interested in whether relaxation training decreases the number of headaches a person experiences. They randomly assigned 20 participants to a control group or a relaxation training group and noted the change in number of headaches each group reported from the week before training to the week after training. Which statistical analysis should be performed to answer the researchers' question?
independent-samples t test
Unnithan, Houser, and Fernhall (2006) were interested in whether playing the game Dance Dance Revolution (DDR) affected the heart rate of overweight and non-overweight adolescents differently. A group of 22 adolescents, 10 classified as overweight and 12 as not overweight played DDR for 12 minutes, during which time the researchers measured each participant's heart rate. Which statistical test should the researchers use to analyze their data?
independent-samples t test
t statistic
indicates the distance of a sample mean from a population mean in terms of the estimated standard error
Cohen's d cannot be used as a measure of effect size for ANOVA because:
it can only compare two means
The comparison distribution in a paired-samples t test is a distribution of:
mean difference scores
counterbalancing
minimizes order effects by varying the order of presentation of different levels of the independent variable from one participant to the next
Twenty people participate in a weight-loss program for two months. Their weights after the two months are compared to their starting weights. What kind of mean difference might be expected if the null hypothesis is true for a paired-samples t test?
no change in weight or weight gain, indicating that the program does not work
A negatively skewed distribution would most likely violate which assumption?
normality
Researchers were interested in whether relaxation training decreases the number of headaches a person experiences. They randomly assigned 20 participants to a control group or a relaxation training group and noted the change in number of headaches each group reported from the week before training to the week after training. The dependent variable in this study is:
number of headaches
"Degrees of freedom" refers to what on a t table for a single-sample t test?
number of scores that are free to vary in estimating population parameters, N - 1
A clinical researcher was interested in determining whether her interventions for depression were effective in minimizing depression symptoms among her participants. To assess the effectiveness of her treatment program, she administered a depression inventory prior to treatment and after treatment. She hypothesized that depression scores would be lower at time two compared to time one. She then compared the mean differences between the two groups and found that her treatment was effective. Which statistical test was the researcher MOST likely to have used to test her hypothesis?
paired-samples t test
A group of rats ran faster after receiving a steroid drug supplement than they did earlier without any drug supplement. What type of statistical test should be reported with these results?
paired-samples t test
In a(n) _____, a within-groups design with two groups is used to compare the distribution of mean difference scores
paired-samples t test
A researcher studies 45 volunteer citizens from a small community and asks them about the amount of caffeine (in milligrams) they ingest before and after lunch each day, a phenomenon assumed to be normally distributed. Which assumption for the paired-samples t test is NOT met in this research design?
participants are randomly selected
heterscedastic
populations that have different variances
homoscedastic
populations that have the same variance; is also called homogeneity of variance
source table
presents the important calculations and final results of an ANOVA in a consistent and easy-to-read format
square root transformation
reduces skew by compressing both the negative and positive sides of a skewed distribution
order effects
refer to how a participant's behavior changes when the dependent variable is presented for a second time, sometimes called practice effects
In a(n) _____, one sample is used to compare a distribution of means during hypothesis testing
single-sample t test
According to Cohen's conventions, an R2 of 0.02 is considered to be a(n) _____ effect size
small
Between-groups degrees of freedom is calculated by:
subtracting 1 from the total number of groups in the study
When the population mean but not the population standard deviation is known, which statistic is used to compare a sample to the population?
t
A researcher is comparing two groups. The population mean from which the samples come is known, but not the population standard deviation. Which test should be used?
t test because standard deviation for the population must be estimated
When statisticians describe pooling the variances, they mean:
taking the average of the two variances, accounting for sample size
grand mean
the mean of every score in a study, regardless of which sample the score came from
The statement "On average, older adults have the same response time as younger adults" is an example of:
the null hypothesis
degrees of freedom
the number of scores that are free to vary when we estimate a population parameter from a sample
In order to conduct a single-sample t test, one needs to know:
the population mean and the properties of the sample
A researcher can't just run multiple t tests when the independent variable has more than two levels because as more statistical tests are run:
the probability of making a Type I error in one of the tests increases
R^2
the proportion of variance in the dependent variable that is accounted for by the independent variable
Standard error is used in the calculation of both the z and t statistic, with the difference that:
the standard error for the t statistic is estimated using the sample standard deviation
Which of these is NOT an assumption of the paired-samples t test?
there are fewer than 30 sample data
A team of researchers conducted a single-sample t test and found that the 95 percent confidence interval around their sample mean includes the value of the population mean. Based on this, they should conclude that:
they failed to find a significant difference between the sample and population means
A paired-samples t test is reported as t(15) = 0.918, p > 0.05, d = 0.17. What is the effect size for this statistical test?
this is a small effect
Researchers were interested in whether relaxation training decreases the number of headaches a person experiences. They randomly assigned 20 participants to a control group (no relaxation training) or a relaxation training group and noted the change in number of headaches each group reported from the week before training to the week after training. The independent variable in this study is:
training type
independent-samples t test
used to compare two means for a between-groups design, a situation in which each participant is assigned to only one condition
paired-samples t test
used to compare two means for a within-groups design, a situation in which every participant is in both samples; also called a dependent-samples t test
