The Statistics - Assignment Example

PART A – MULTIPLE CHOICE Question If other factors remain constant, the larger the sample is, the more likely you are to obtain a significant value for the repeated-measures t. Answer True False  Question 2   For a repeated-measures study, a small variance for the difference scores indicates that the treatment had a consistent effect for all of the participants. Answer True False  Question 3   Compared to independent-measures designs, repeated-measures studies reduce the variance by removing individual differences. Answer True False  Question 4   If a treatment has a consistent effect, then the sample of difference scores will have a large value for variance. Answer True False  Question 5   As the variance of the difference scores increases, the value of the t statistic also increases (farther from zero). Answer True False  Question 6   One concern with a repeated-measures design is that a partcipants performance in one treatment condition may be influenced by previous experience in another treament condition. Answer True False  Question 7   Which of the following studies uses a matched-subjects design? Answer a. A group of twins is tested for visual acuity on one day and then tested again the following day after receiving a drug. b. A sample of children is tested for vocabulary skills at age six and then again at age ten. c. Participants are assigned to one of two treatment groups so that each participant in one group has the same IQ as a participant in the other group. d. None of the other options is a matched-subjects design.  Question 8   In a repeated-measures experiment, each individual participates in one treatment condition and then moves on to a second treatment condition. One of the major concerns in this type of study is that participation in the first treatment may influence the participants score in the second treatment. This problem is called ____. Answer a. individual differences b. order effects c. homogeneity of variance d. bi-treatment effect  Question 9   A research report describing the results from a repeated-measures study states: "The data show no significant difference between the two treatments, t(10) = 1.65, p > .05." Based on this report, you can conclude that a total of ____ individuals participated in the research study. Answer a. 9 b. 10 c. 11 d. 12  Question 10   A research report describing the results from a repeated-measures t test states, " t(22) = 1.71, p > .05." From this report you can conclude that the outcome of the hypothesis test was ____. Answer a. to reject the null hypothesis with a sample of n = 23 participants b. to fail to reject the null hypothesis with a sample of n = 23 participants c. to reject the null hypothesis with a sample of n = 22 participants d. to fail to reject the null hypothesis with a sample of n = 22 participants  Question 11   What is the value of the estimated standard error for the following set of D-scores? Scores: 4, 8, 4, 4 Answer a. 12 b. 2 c. 4 d. 1  Question 12   With α = .05 and a sample of n = 12 participants in a repeated-measures study comparing two treatments, the two-tailed critical region for the t statistic has boundaries of ____. Answer a. t = ±2.228 b. t = ±1.812 c. t = ±2.201 d. t = ±1.796  Question 13   If the null hypothesis is true, on average the expected value for the related-samples t statistic is ____. Answer a. 0 b. 1 c. 1.96 d. t > 1.96  Question 14   A repeated-measures study finds a mean difference of M D = 5 points between two treatment conditions. Which of the following sample characteristics is most likely to produce a significant t statistic for the hypothesis test? Answer a. a large sample size ( n) and a large variance b. a large sample size ( n) and a small variance c. a small sample size ( n) and a large variance d. a small sample size ( n) and a small variance  Question 15   A repeated-measures study produces a sample mean difference of M D = 4.5 with s 2 = 100 for a sample of n = 16 participants. For this study, the estimated value of Cohens d would be ____. Answer a. d = 4.5/100 = 0.045 b. d = 4.5/10 = 0.45 c. d = 4.5/2.5 = 1.80 d. The value of d cannot be determined from the information provided.  Question 16   For a repeated-measures hypothesis test, the null hypothesis states: Answer a. For the individuals in the entire population there is no consistent difference between the two treatments. b. For the individuals in the entire population there is a consistent difference between the two treatments. c. For the individuals in the sample there is no consistent difference between the two treatments. d. For the individuals in the sample there is a consistent difference between the two treatments.  Question 17   What is the value of M D for the following set of difference scores? Scores: 3, -8, 6, -4, -2 Answer a. –1 b. –5 c. 23 d. 23/5 = 4.6  Question 18   The following data were obtained from a repeated-measures research study. What is the value of df for the t statistic? Subject 1st 2nd #1 8 10 #2 6 12 #3 10 7 #4 9 17 #5 7 14 Answer a. df = 4 b. df = 5 c. df = 8 d. df = 9  Question 19   In general, what characteristics of the data (difference scores) are most likely to produce a significant t statistic for the repeated-measure hypothesis test? Answer a. a large mean difference and large variance b. a large mean difference and small variance c. a small mean difference and large variance d. a small mean difference and small variance  Question 20   The data from a repeated-measures research study show that the difference between treatment I and treatment II is large and positive for some subjects, large and negative for some subjects, and near zero for some subjects. These data will produce Answer a. a small sample variance and a large t statistic. b. a small sample variance and a small t statistic. c. a large sample variance and a large t statistic. d. a large sample variance and a small t statistic.  Question 21   A researcher conducts a repeated-measures study comparing two treatment conditions with a sample n = 10 participants and obtains a t statistic of t = 2.01. Which of the following is the correct decision about the null hypothesis using a two‐tailed test? Answer a. Reject the null hypothesis with α = .05 but fail to reject with α = .01. b. Reject the null hypothesis with either α = .05 or α = .01. c. Fail to reject the null hypothesis with either α = .05 or α = .01. d. cannot determine the correct decision without more information PART B – SHORT ANSWER QUESTIONS 1.a. D D2 -5 25 -1 1 -4 16 -3 9 -6 36 -8 64 0 0 1 1 -1 1 = -27 = 153 1.b. Step 1: The null and alternate hypotheses are (There is no difference.) (There is a difference.) Step 2: α = .05 df = n – 1 = 9 – 1 = 8 Critical region: t beyond ±2.306 Step 3: The test statistic is SS = 72 Step 4: Reject the null hypothesis, , as the t value obtained falls in the critical region. Yes, the the results indicate a significant difference. 1.c. About 52.94% of variance accounted for by relaxation training. The effect is large. 2.a. Step 1: The null and alternate hypotheses are (There is no change.) (There is a change.) Step 2: α = .05 df = n – 1 = 9 – 1 = 8 Critical region: t beyond ±2.306 Step 3: The test statistic is Step 4: Reject the null hypothesis, , as the t value obtained falls in the critical region. Yes, these data indicate a significant change in depression. 2.b. estimated The effect is medium. 3.a. The null and alternate hypotheses are 3.b. α = .05 df = n – 1 = 16 – 1 = 15 Critical region: t beyond ±2.131 3.c. SS = 6000 3.d. Reject the null hypothesis, , as the t value obtained falls in the critical region and conclude that the drug had a significant effect on the activity. 3.e. About 54.04% of variance accounted for by drug. The effect is large. 4.a. Step 1: The null and alternate hypotheses are (No difference.) (There is a difference.) Step 2: α = .05 This is an independent measure design. Critical region: t beyond ±2.306 Step 3: The pooled variance is The estimated standard error is The test statistic is Step 4: Fail to reject the null hypothesis, , as the t value obtained falls in the non-critical region. No, the data do not indicate a significant difference between treatments. 4.b. Step 1: The null and alternate hypotheses are (There is no difference.) (There is a difference.) Step 2: α = .05 df = n – 1 = 5 – 1 = 4 Critical region: t beyond ±2.776 Step 3: The test statistic is SS = 4 Step 4: Reject the null hypothesis, , as the t value obtained falls in the critical region. Yes, the data indicate a significant difference between treatments. 4.c. The 2-point mean difference is significant for the repeated-measures and not significant for the Independent-measures test. The reason for this is that for the Independent-measures test, the variance is large because of big differences between treatments. However, when we get the difference score for the treatments, this big difference between treatments eliminated and the variance for the difference scores is small. In other words, compared to independent-measures designs, repeated-measures studies reduce the variance by removing individual differences and thus t statistic is large. Treatment 1 Treatment 2 D D2 10 11 1 1 2 5 3 9 1 2 1 1 15 18 3 9 7 9 2 4 = 10 = 24 5.a. Step 1: The null and alternate hypotheses are (There is no change.) (There is a change.) Step 2: α = .05 df = n – 1 = 10 – 1 = 9 Critical region: t beyond ±2.262 Step 3: The test statistic is Step 4: Fail to reject the null hypothesis, , as the t value obtained falls in the non-critical region. No, this is not a statistically significant change. 5.b. Step 1: The null and alternate hypotheses are (There is no change.) (There is a change.) Step 2: α = .05 df = n – 1 = 10 – 1 = 9 Critical region: t beyond ±2.262 Step 3: The test statistic is Step 4: Reject the null hypothesis, , as the t value obtained falls in the critical region. Yes, this is a statistically significant change. 6. Step 1: The null and alternate hypotheses are (There is no difference.) (There is a difference.) Step 2: α = .05 df = n – 1 = 6 – 1 = 5 Critical region: t beyond ±2.571 Step 3: The test statistic is SS = 34.833 Step 4: Reject the null hypothesis, , as the t value obtained falls in the critical region. Yes, the data indicate a significant difference. Participant During Heartbeats Between Heartbeats D D2 A 93 98 5 25 B 90 94 4 16 C 95 96 1 1 D 92 91 -1 1 E 95 97 2 4 F 91 97 6 36       = 17 = 83 7.a. The null hypothesis is “the ability to empathize-the capacity to understand and experience the emotional states of another person does not increase with age”. (No difference.) or (1-sixth graders and 2-first graders) 7.b. We would analyze the data with the t test for two independent samples, as there are two different groups. The researcher could not reasonably conclude that the difference in the independent variable was causally responsible for differences in the dependent variable. This is because the two groups are different and difference may be because of some other factor. 8.a. The null hypothesis is “the ability to empathize-the capacity to understand and experience the emotional states of another person does not increase with age”. (No difference.) or (D = sixth graders - first graders) 8.b. We would analyze the data with the t test for two related samples, as there is one group measured at two different times. The researcher could reasonably conclude that the difference in the independent variable was causally responsible for differences in the dependent variable. This is because the same group is measure at two different age, thus, other factors effect is reduced. Read More