24: Comparing Two Means - T Test Flashcards
A paired t-test is a ratio of:
a. The difference between group means divided by the common standard deviation of
group means.
b. The difference between group means divided by the standard error of the
difference between means.
c. The mean difference divided by the standard error of the mean difference.
d. The mean difference divided by the standard deviation of the mean difference.
c
Rationale: In a paired t-test, there are no group means. The mean difference is the numerator of the ratio divided by the standard error of the mean difference.
Conducting multiple t-tests increases the likelihood of:
a. Finding correct conclusions.
b. Type I error
c. Type II error
d. Measurement reliability
b
Rationale: Repeating t-tests, each at a .05 level of significance, will increase the probability of a Type I error for the overall set of tests.
Which of the following assumptions is not relevant for the unpaired t-test?
a. The dependent variable should be derived from a population with a normal
distribution.
b. The variance in groups being compared should not be significantly different.
c. Data should be at the interval/ratio data.
d. The sample being tested should come from a random sampling of cases.
d
Under which column should you look in output of an unpaired t-test to determine if variances are equal across groups?
a. Levene’s test
b. Confidence intervals.
c. Mean difference
d. Standard Error Difference
a
Rationale: The F column under Levene’s test will indicate if the variances are significantly different. If Sig is less than .05, the variances are significantly different. If Sig is greater than .05, the variances are not different and the line for “Equal variances assumed” can be used.
Which of the following formats is correct for reporting the results of a t-test?
a. t (35) = 12.34, p =.000,
b. t = 3.5, p < .05, d > .5
c. t (24) = –2.5, p = .034, d = .34
d. t (10) = 3.4, p > .05, n = 25 d = .87
c
Rationale: Choice A is not correct because p cannot equal .000. This value is based on a limitation of reporting decimal places in statistical packages, and should be written as p <.001. Choices B and D do not give the specific p value or a correct value for the effect size index, and B does not give degrees of freedom. Choice C includes the value of t, the degrees of freedom, the specific p value, and the effect size.
The effect size index for the t-test is:
a. d
b. s
c. F
d. p
a
Rationale: Cohen’s d is the effect size index used with the t-test. Other values are for standard deviation (s), F value for analysis of variance or Levene’s test, and p for probability. None of these can be used as effect sizes.
A study is done to compare two teaching strategies, A and B, to determine which method students prefer based on questionnaire responses. Which of the following statements is an accurate statement of the null hypothesis for this study?
a. The difference between the means for A and B will equal 1.0.
b. The difference between means for A and B will equal zero.
c. The mean for A will be greater than the mean for B.
d. The difference between means for A and B will be greater than zero.
b
Rationale: The null hypothesis states that there will be no difference between group means, indicating that the difference between them will equal zero.
- A t-test is used to evaluate the difference in pain when individuals with back pain exercise with and without prior pain medication. 30 patients are tested on two consecutive days, with the testing
condition randomly ordered.How many degrees of freedom would be associated with this test?
a. df = 60
b. df = 58
c. df = 28
d. df = 29
d
Rationale: The degrees of freedom for a paired t-test = n – 1, which is 29. There is only one group of subjects.
- A study is done to compare two drugs to improve blood pressure using a sample of 42 patients (21 in each group). The researcher hypothesized that drug 1 would be better than drug 2. The results of a t-test are as follows: t (40) = 1.684, p = .05. Using = .05, the researcher concludes that there is a significant difference. What would be the effect if he had hypothesized that there would be a difference between the two drugs?
a. The test would be significant at a lower p value.
b. There would be no difference in the results.
c. The test would no longer be significant.
d. The test would be significant with a larger effect size.
c
Rationale: This result is based on a one-tailed test (directional hypothesis). When a two-tailed test is applied (nondirectional hypothesis) the same value would be significant at p = .10. This is obtained by looking at Appendix Table A-2, showing that the critical value for t with 40 df = 1.684 for 1 =.05, which is the same critical value for 2 = .10.
- A study was designed to compare the level of wrist pain when using 2 different can openers in patients with arthritis. Participants were asked to use each can opener and estimate their level of discomfort, with the order of use randomly varied. The level of pain was measured on a visual analogue scale. The means for each can opener were Mean 1 = 8.3 (6) and Mean 2 = 4.0 (5). The standard deviation of difference scores was 8.2. What is the effect size for this test?
a. 1.106
b. 0.741
c. 0.782
d. 0.524
b
Rationale: This study uses a repeated measure, and therefore uses the effect size for a paired t-test. The formula is (mean diff/st dev diff)2. For this example it is 4.3/8.21.414 = 0.741.
- An unpaired t-test is used to compare two treatments on a sample of 100 patients, resulting in a mean difference of 98 and a 95% confidence interval of 80 to 115. Which of the following statements is a correct interpretation of this confidence interval?
a. If we performed this study on a different sample of 100 patients, there is a 95%
chance the sample mean difference would be between 80 and 115.
b. 95% of all sample mean differences will fall within the range of 80 to 115.
c. We are 95% confident that the mean difference for patients in this sample is
between 80 and 115.
d. We are 95% confident that the interval 80 to 115 contains the true population mean
difference.
D
Rationale: Confidence intervals provide probability estimates for population parameters, not sample statistics. The population mean is fixed, although we don’t know what it is. Therefore, the confidence interval may be incorrect- although we are 95% confident that it is correct. Choice A- we cannot assume that a different sample will have the same mean and confidence interval. Choice B- The confidence does not reflect the distribution of scores within the sample, only the population parameter. Choice C-the confidence interval does not reflect anything about the distribution of sample screws. We know the mean difference for the sample - it is used tin creating the confidence interval .
