1. One of the assumptions for the t test for independent means is that? a. Sampl
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Question
1. One of the assumptions for the t test for independent means is that?a. Sample means are not significantly different. b. The mean of the distribution of differences between means is 1. c. The variance of each of the parent populations is the same. d. The mean of each of the parent populations vary by no more than 1 standard deviation.
2. Which of the following tactics will reduce the power of a planned study using a t test for independent means?
a. Using a less stringent significance level (such as .10 instead of .05) b. Using more precise measures c. Increasing the size of your samples d. Using unequal sample sizes instead of equal ones (for the same numbe of participants)
3. In an experiment with 50 participants, which division of participants into groups would have the most power?
a. 15 experimental, 35 control b. 40 experimental, 10 control c. 25 experimental, 25 control d. All divisions would have the same power
1. One of the assumptions for the t test for independent means is that?
a. Sample means are not significantly different. b. The mean of the distribution of differences between means is 1. c. The variance of each of the parent populations is the same. d. The mean of each of the parent populations vary by no more than 1 standard deviation.
2. Which of the following tactics will reduce the power of a planned study using a t test for independent means?
a. Using a less stringent significance level (such as .10 instead of .05) b. Using more precise measures c. Increasing the size of your samples d. Using unequal sample sizes instead of equal ones (for the same numbe of participants)
3. In an experiment with 50 participants, which division of participants into groups would have the most power?
a. 15 experimental, 35 control b. 40 experimental, 10 control c. 25 experimental, 25 control d. All divisions would have the same power
a. Sample means are not significantly different. b. The mean of the distribution of differences between means is 1. c. The variance of each of the parent populations is the same. d. The mean of each of the parent populations vary by no more than 1 standard deviation.
2. Which of the following tactics will reduce the power of a planned study using a t test for independent means?
a. Using a less stringent significance level (such as .10 instead of .05) b. Using more precise measures c. Increasing the size of your samples d. Using unequal sample sizes instead of equal ones (for the same numbe of participants)
3. In an experiment with 50 participants, which division of participants into groups would have the most power?
a. 15 experimental, 35 control b. 40 experimental, 10 control c. 25 experimental, 25 control d. All divisions would have the same power
a. Sample means are not significantly different. b. The mean of the distribution of differences between means is 1. c. The variance of each of the parent populations is the same. d. The mean of each of the parent populations vary by no more than 1 standard deviation.
2. Which of the following tactics will reduce the power of a planned study using a t test for independent means?
a. Using a less stringent significance level (such as .10 instead of .05) b. Using more precise measures c. Increasing the size of your samples d. Using unequal sample sizes instead of equal ones (for the same numbe of participants)
3. In an experiment with 50 participants, which division of participants into groups would have the most power?
a. 15 experimental, 35 control b. 40 experimental, 10 control c. 25 experimental, 25 control d. All divisions would have the same power
Explanation / Answer
1) ANS:
c. The variance of each of the parent populations is the same.
The assumptions of the t-test for dependent means focus on sampling, research design, measurement, and distribution. The t-test for dependent means is considered typically "robust" for violations of normal distribution. This means that the assumption can be violated without serious error being introduced into the test in most circumstance. However, if we are conducting a one-tailed test and the data are highly skewed, this will cause a lot of error to be introduced into our calculation of difference scores which will bias the results of the test. In this circumstance, a nonparametric test should be used.
2)ANS:
d. Using unequal sample sizes instead of equal ones (for the same numbe of participants)
When sample size and alpha are held constant, increasing the effect size will always increase power because it is found only in the numerator. Consider an example in which the per-group sample size is n = 60, the standardized effect size is d = .4, = .05, and therefore the critical z1- value is 1.96 with a two-tailed test. Using these values, statistical power is 58.4%. Increasing d from .4 to .5 gives a power value of 77.4%. Similarly, if effect size and alpha are held constant, increasing the sample size will always increase power because it is found in a higher power, or degree, in the numerator than in the denominator. Continuing the example, if instead of increasing d, n is increased from 60 to 70 participants per group, power increases from 58.4% to 65.2%. In order to achieve the same power associated with increasing d from .4 to .5 with n = 40 (77.4%), the per-group sample size would need to be n = 93. Over 100 more participants would need to be collected to achieve the same increase in power associated with an increase in effect size from .4 to .5. A third situation exists in which effect size and sample size are held constant, and alpha is increased, causing an increase in power, or decreased (towards zero), causing a decrease in power. Continuing with the example, suppose we are less willing to make a Type I error, so alpha is decreased from .05 to .01, keeping n constant at 60 and d = .4. The result is an increase in the critical value (z1-), making it more difficult to reject the null hypothesis, and therefore power decreases from 58.4% to 33.9%. Alpha does not often deviate from .05 in the social sciences. However, an unexpected way in which alpha may be modified is in deciding if the researcher will be conducting a one-tailed or a two-tailed test. If the test is one-tailed, the full amount of alpha is placed in one tail of the probability distribution, thus lowering the critical value of the test statistic and increasing power. With = .05 in one tail, as opposed to two, which produced a power value of 58.4%, power has increased to 70.3%.
3)ANS:
d. All divisions would have the same power
we are talking about experimental groups and control groups. Does that mean that you have different experimental and control conditions, or does it simply mean you sample per group of particpants? And do you measure the outcome at the group level or at the individual level? If you measure it at the group level, than you should focus on sampling enough groups, not on sampling individuals.
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