Quiz 9 - Chapter 9: Paired-Samples t-Test Flashcards
A researcher wants to study the effectiveness of a depression treatment. Which of the following research designs would require a paired-samples t-test as the analysis?
A: Recruit a sample of 100 patients with depression, assign half to receive the treatment, and assign the other half to receive a placebo. Compare the average depression level between the two groups.
B: Recruit a sample of 50 patients with depression, measure their depression levels, conduct the treatment, and then measure their depression levels again. Compare the average depression level before and after the intervention.
B: Recruit a sample of 50 patients with depression, measure their depression levels, conduct the treatment, and then measure their depression levels again. Compare the average depression level before and after the intervention.
A researcher conducted a study examining whether a new drug decreased the pain levels of people with a chronic illness. In the study, a sample of 200 people with chronic illness rated their pain levels, then took the new drug for a week, and then rated their pain levels a second time (after the week of taking the drug). What type of t-test would be the best option to analyze this data?
A: One-sample t-test
B: Paired-samples t-test
B: Paired-samples t-test
Researchers at a university collected information about the happiness levels of students in years one and two: At the end of their first year, a sample of students rated their happiness on a scale from 0 to 100. That same sample of students again rated their happiness a year later at the end of their second year. The researchers calculated a 95% confidence interval for the mean difference score (year 2 score minus year 1 score), and found that it ranged from 5 to 15. They want to see whether the happiness levels of students differ at the ends of years 1 and 2 (the null hypothesis is μDiff = 0 and the alternative hypothesis is μDiff ≠ 0). Using this information, what can we infer? CHECK ALL THAT APPLY.
A: We are 95% confident that the interval from 5 to 15 contains the true mean difference score in the population.
B: The p-value for the study is less than 0.05.
C: The t statistic in this study is greater than the critical value.
D: Assuming students are equally happy at the end of years 1 and 2, the probability of obtaining a sample mean difference score at least as extreme as the one obtained in this study is less than 5%.
ALL OF THE ABOVE
A: We are 95% confident that the interval from 5 to 15 contains the true mean difference score in the population.
B: The p-value for the study is less than 0.05.
C: The t statistic in this study is greater than the critical value (this is correct because we can compare a t-statistic to a critical value to determine whether or not we should reject or fail to reject the null hypothesis and since the question makes it clear that we’re rejecting the null hypothesis we know that the t-statistic is outside the range of the critical value. We’re saying that it is greater because we should almost always take the absolute value of a t-statistic to determine our answer).
D: Assuming students are equally happy at the end of years 1 and 2, the probability of obtaining a sample mean difference score at least as extreme as the one obtained in this study is less than 5%.
A small liberal arts college collected a measure of test anxiety from the same group of teens in years 1 and 2. The average decrease in anxiety scores was 5 points, and a paired-samples t-test gave a two-tailed probability value (p-value) of .15 (15%). Which of the following conclusions is correct regarding the probability value? CHECK ALL THAT APPLY.
A: We fail to reject the null hypothesis that there is no change in test anxiety in the population
B: We accept the null hypothesis
C: It is plausible that the population mean anxiety level at year 1 is the same as the population mean anxiety level at year 2
D: It is plausible that there is no change in test anxiety in the population but we cannot say with certainty
E: The change in anxiety scores is consistent with random chance
All of the following are correct:
A: We fail to reject the null hypothesis that there is no change of test anxiety in the population
C: It is plausible that the population mean anxiety level at year 1 is the same as the population mean anxiety level at year 2
D: It is plausible that there is no change of test anxiety in the population but we cannot say with certainty
E: The change in anxiety scores is consistent with random chance (this is correct because “random chance” is the same thing as saying “sampling error” and we already know that sampling error can be the cause of our determination).
An educational psychologist is interested in whether math test scores improve between 5th and 7th grade. She recruits a sample of 80 students and uses a paired-samples t-test to analyze the data. Which of the following is a valid null hypothesis for the study?
A: The change in math scores is 0 in the population
B: The change in math scores is positive (scores improve) in the sample
C: The change in math scores is positive (scores improve) in the population
D: The change of math scores is 0 in the sample
A: The change in math scores is 0 in the population
A researcher studies differences in extraversion between first-born and second-born siblings. They recruit 16 sibling pairs (16 firstborns and 16 second borns) and measure the extraversion of each sibling. They then find the standard deviation of the difference scores to be 8. Find the standard error of the mean difference score (keep no decimals).
2
> N = 16, that’s because even though we have 16 firstborns and 16 second borns each dyad will only produce one score - so there are only 16 scores
Professor Du is interested in the effect of making a cheatsheet. She asked students to rate their understanding of class materials before making the cheatsheet and asked them again to rate their understanding after making the cheatsheet. The mean difference score is computed by subtracting the post-cheatsheet mean from the pre-cheatsheet mean. If the standardized mean difference obtained by this researcher was -3, what can we know from this number?
A: The students’ self-rated understanding is lower after making the cheatsheet with a large effect size
B: There is a significant effect of making the cheatsheet such that students’ self-rated understanding is significantly lower after making the cheatsheet
C: The students’ self-rated understanding is higher after making the cheatsheet with a large effect size
D: There is a significant effect of making the cheatsheet such that students’ self-rated understanding is significantly higher after making the cheatsheet
C: The students’ self-rated understanding is higher after making the cheatsheet with a large effect size
A researcher is studying the effect of an anxiety medication. She has participants rate their anxiety score once before taking the medication and once after taking the medication. She runs a two-sided paired-samples t-test that involves the following calculation: the difference score is the post-medication anxiety score minus the pre-medication anxiety score. She finds 1) a 95% confidence interval of -1 to -3, 2) a p-value of .017, and 3) a t statistic of -4 with a critical value of -2. Which of the following are sufficient on their own to reject the null hypothesis? CHECK ALL THAT APPLY.
A: The p-value
B: The 95% confidence interval
C: The t statistic compared to the critical value
ALL OF THE ABOVE
A: The p-value
B: The 95% confidence interval
C: The t statistic compared to the critical value
Suppose you have two sample means. Subtract one of the sample means from the other, and then divide the result by the standard deviation of the difference scores. The resulting quantity refers to which of the following?
A: A 95% confidence interval
B: Cohen’s d effect size
C: A two-sample t statistic
D: The p-value of a two-sample t-test
B: Cohen’s d effect size
!!! Make sure you put all formulas on your cheat sheet !!!
True or False: A statistically significant p-value always results in a practically significant effect.
A: True
B: False
B: False
A researcher is interested in whether a new intervention successfully decreases anxiety compared to a standard intervention (new intervention scores minus standard intervention scores). To measure anxiety, they administer a questionnaire with a scale score that ranges from 0 to 100. Which test should they use?
A: One-tailed t-test (difference > 0)
B: Two-tailed t-test (difference ≠ 0)
C: One-tailed t-test (difference < 0)
C: One-tailed t-test (difference < 0)
True or false? A paired-samples t-test is the same as a one-sample t-test of the difference scores.
A: True
B: False
A: True
Suppose that, in a repeated-measures experiment with 25 participants, the standard error of the mean difference scores is 3. What is the standard deviation of the difference scores?
15
!!! Make sure you add all formulas to your cheat sheet !!!
A researcher is interested in studying depression levels before and after administering a new treatment. This treatment is designed to decrease depression levels. In his study, lower scores indicate lower amounts of depression. The way this researcher obtained the mean change score was by doing post-depression mean – pre-depression (post-pre). If the mean difference obtained by this researcher was - 2.17, which group’s mean was larger?
A: The post-depression group’s mean
B: We cannot tell without the data
C: The pre-depression group’s mean
C: The pre-depression group’s mean
The same researcher from the previous question conducts a paired samples t-test to obtain the test statistic. Remember that the researcher’s (or alternative) hypothesis was that the treatment should decrease depression levels. Again, the way this researcher obtained the mean change score was by doing post-depression mean – pre-depression (post-pre). Which of the following t-statistics would provide the MOST evidence in support of the alternative hypothesis?
A: t = 3.5
B: t = 1.25
C: t = 0
D: t = -2.15
D: t = -2.15
This is the correct answer because we’re trying to prove that there is a decrease in depression levels so a negative t-statistic would support that hypothesis. It’s always helpful to draw this stuff out on a test so you can see it more clearly.
