Question 1

Sample size affects power because the larger the sample size:

Accepted Answer

The standard deviation of the distribution of means decreases as sample size increases. This makes it easier to detect true differences or relationships between variables, thus increasing the power of the study.

Question 2

A researcher may not be able to change the effect size of a planned study to increase power. Another aspect of a planned study that the researcher can usually change to increase power is:

Accepted Answer

The sample size is one aspect of a planned study that the researcher can usually change to increase power. Increasing the sample size can increase the likelihood of detecting a statistically significant difference between groups or conditions, thereby increasing power. The other options (B, C, and D) are not aspects that a researcher can typically change in a planned study to increase power.

Question 3

One way to increase the power of a planned study by altering the amount of variance within each of the two distributions is to:

Accepted Answer

Increasing the precision of measures can decrease the amount of variance within each distribution, making it easier to detect statistically significant differences between them. Using the variance of the experimental group instead of the comparison distribution's variance would not be valid, excluding outlier scores can distort results, and reducing the number of items on questionnaires would not affect the distribution's variance.

Question 4

Even if the research hypothesis is true, an experiment may not produce significant results because:

Accepted Answer

The sample selected may not be extreme enough to show a significant difference, leading to failure in rejecting the null hypothesis even if the research hypothesis is true.

Question 5

Which of the following is not a direct influence on power?

Accepted Answer

The type of statistical software package used does not directly influence the power of a hypothesis test. The other options all have a direct impact on power. Significance level, one-versus two-tailed tests, and type of hypothesis-testing procedure all affect the likelihood of rejecting the null hypothesis, and thus the power of the test.

Question 6

In the situation where the null hypothesis is true, the population distribution from which the sample was taken is:

Accepted Answer

If the null hypothesis is true, then there is no difference between the sample and the known population. This means that the population distribution from which the sample was taken is the same as the known population's distribution.

Question 7

Standard power tables are useful for:

Accepted Answer

Standard power tables are used to determine the power of an experiment, which is the probability of correctly rejecting the null hypothesis when it is false.

Question 8

Using a two-tailed test makes it __________ to get significance on any one tail. Thus, keeping everything else the same, power __________ with a two-tailed test than with a one-tailed test.

Accepted Answer

Using a two-tailed test makes it harder to achieve significance on either tail because the significance level (alpha) is split between the two tails. Consequently, the power, which is the probability of correctly rejecting a false null hypothesis, is less with a two-tailed test than with a one-tailed test, assuming all other factors are constant. This is because a larger effect size is needed to achieve significance when the alpha is divided.

Question 9

Having a very small amount of overlap between the distribution of population 2 and the predicted distribution of population 1:

Accepted Answer

Having a very small amount of overlap between the distributions indicates that the two populations are distinct from each other, which increases the statistical power of a test to detect a difference between them if one exists.

Question 10

In the meta-analysis described in your text (by Eppley, Abrams, and Shear)on the effect of relaxation techniques on anxiety levels, the authors found that:

Accepted Answer

The authors found clear differences in the effect sizes associated with different relaxation and meditation procedures, indicating that not all techniques yield similar effects.

Question 11

The __________ of a research study is the probability that it will produce a statistically significant result if the research hypothesis is true.

Accepted Answer

Statistical power refers to the ability of a study to detect a statistically significant difference when one exists. It is affected by factors such as sample size, effect size, and alpha level. A high level of statistical power is desirable in research studies as it increases the likelihood of correctly rejecting the null hypothesis when it is actually false.

Question 12

The effect size and the number of participants are two important determinants of:

Accepted Answer

The effect size and the number of participants are two important determinants of power, which is the probability of finding a significant result if the null hypothesis is false. A larger effect size and a larger number of participants increase the power of a study, while a smaller effect size and a smaller number of participants decrease the power of a study. The minimum significant result is determined by the chosen alpha level, which is typically set at 0.05, and is not affected by the effect size or the number of participants. Reliability refers to the consistency and stability of measurements or findings, and is not directly determined by the effect size or the number of participants.

Question 13

It is useful to understand statistical power for which of the following reasons?

Accepted Answer

Understanding statistical power is important for all of the listed reasons. It helps in determining the appropriate sample size for an experiment, interpreting the findings of research articles, and understanding the implications of a study that fails to find statistical significance.

Question 14

In theory, one could increase the power of planned study by:

Accepted Answer

All three options can potentially increase the power of planned study. By increasing the effect size through a larger predicted difference between population means (option A) or a smaller population standard deviation (option B), the study will be better able to detect a significant difference between the groups being compared. Additionally, using a one-tailed test (option C) may increase power because it allows the researcher to focus exclusively on one direction of the hypothesis, rather than having to account for the possibility of the effect going in either direction. However, it is important to note that choosing a one-tailed test should only be done in situations where there is a compelling theoretical or empirical reason to expect a very specific directional effect.

Question 15

What effect will using a one-tailed test over a two-tailed test have on power (presuming the true population difference is in the expected direction)?

Accepted Answer

Using a one-tailed test over a two-tailed test will increase power because all of the α level is concentrated on one tail instead of being split between both tails. This means that less extreme observations will be more likely to fall into the critical region, leading to a higher chance of rejecting the null hypothesis.

Question 16

Effect size is one of the two major factors that contribute to power. Another factor is:

Accepted Answer

The sample size is the other major factor that contributes to power, along with effect size. A larger sample size generally leads to greater power, all other factors being equal. The standard deviation of the sample, minimum meaningful difference, and mean of the known population can all have an impact on power, but they are not as critical as effect size and sample size.

Question 17

In actual practice, the usual reason for determining power before conducting a study is to:

Accepted Answer

The reason for determining power before conducting a study is to determine the number of participants needed to have a reasonable chance of getting a significant result if the research hypothesis is true. This allows researchers to plan their study appropriately and ensure that they have enough participants to detect a significant effect if one exists.

Question 18

When a study has only a small chance of being significant even if the research hypothesis is true, the study is said to have:

Accepted Answer

Low power refers to the likelihood of a study to detect a statistically significant difference or relationship between variables, even if one truly exists. A study with low power has a small chance of being significant, even if the research hypothesis is correct. This can occur for a variety of reasons, including a small sample size or poor study design.

Question 19

If the research hypothesis is true, but the study has a low level of power:

Accepted Answer

A low level of power means that there is a high likelihood of a Type II error (failing to reject a false null hypothesis). Therefore, even if the research hypothesis is true, the probability of obtaining a significant result is low.

Question 20

If statistical power for a given research study is .40, one can say that: "Assuming the researcher's prediction is correct, the researcher has a __________ chance of attaining statistically significant results."

Accepted Answer

Statistical power of .40 means there is a 40% chance of correctly rejecting the null hypothesis (i.e., finding statistically significant results) if the researcher's prediction is correct.

Quiz 7: Making Sense of Statistical Significance: Effect Size and Statistical Power