Question 1

The mode is the most common value in a data set. It is a measure of:

Accepted Answer

The mode is a measure of central tendency, as it indicates the value that occurs most frequently in the data set. Range is a measure of the spread of the data, kurtosis measures the degree of peakedness of a distribution, and correlation measures the relationship between two variables. None of these relate specifically to the mode.

Question 2

Which of the following information can you get from inferential statistics that you cannot obtain from descriptive statistics?

Accepted Answer

Inferential statistics allow you to make predictions or inferences about a population based on a sample, such as determining how much the data differs from an expected value, which is not possible with descriptive statistics.

Question 3

In Alison's study, the Pearson's r of participants' caffeine consumption (milligrams) and their reaction time (milliseconds) on a computer task is -0.22. This means that…

Accepted Answer

A negative Pearson's r value (-0.22) indicates an inverse relationship between the two variables. In this case, as caffeine consumption increases, reaction time decreases, suggesting that participants were quicker on the computer task with higher caffeine intake.

Question 4

Cohen's d is seen as advantageous over calculating the difference in means of two groups as a measure of effect size because:

Accepted Answer

Cohen's d takes into account the variability within groups by dividing the difference between means by the standard deviation, allowing for a more meaningful interpretation of effect size. Option B is incorrect because Cohen's d does not influence the likelihood of obtaining statistically significant results. Option C is incorrect because reliability refers to the consistency of results over time, and Cohen's d does not necessarily improve this aspect. Option D is incorrect because calculating Cohen's d requires additional steps compared to simply taking the difference between means.

Question 5

Which of the following groups of data can you compute a confidence interval for?

Accepted Answer

Confidence intervals can be computed for data that are at least at the interval level of measurement because they require numerical data with meaningful differences between values. Interval and ratio data meet these criteria, while ordinal data can sometimes be used depending on the context and the specific statistical methods applied. Nominal and categorical data, which do not have a meaningful order or numerical difference between categories, are not suitable for computing confidence intervals.

Question 6

Which of the following is true about confidence intervals?

Accepted Answer

The answer of Which of the following is true about...

Question 7

Stephanie is designing an experiment to investigate the effect of listening to calming music on positive emotions. Even though the usual alpha level is 0.05, Stephanie feels that she wants to adopt more stringent criteria for her study, so she chooses an alpha level of 0.01. This strategy reduces the probability of:

Accepted Answer

By choosing a more stringent alpha level of 0.01, Stephanie is reducing the probability of Type I error, which is the probability of falsely rejecting the null hypothesis when it is actually true. This means she is being more cautious and ensuring that any significant findings are less likely to be due to chance.

Question 8

Jessica wants to ensure that her study has sufficient statistical power so that she has a good chance of rejecting the null hypothesis in the event that it is actually false. She would like to reduce the chances of a:

Accepted Answer

A Type II error is failing to reject a null hypothesis that is actually false. By ensuring sufficient statistical power, Jessica can reduce the chances of a Type II error and increase her chances of correctly rejecting a false null hypothesis.

Question 9

Which of the following is true about Type II error of a test?

Accepted Answer

Type II error is a conditional probability, which means it depends on the true effect size or difference between groups. It is the probability of accepting the null hypothesis when it is actually false. The probability of a Type II error can be reduced by increasing sample size or decreasing the level of significance (alpha), but it cannot be completely eliminated. Option A is incorrect because researchers can take steps to minimize Type II error by increasing sample size, improving measurement tools, and using appropriate statistical methods. Option B is incorrect because Type II error is not the summation of Type I error and statistical power; rather, it is complementary to statistical power. Option D is incorrect because the probability of a Type II error and the alpha level of a test are not the same; they are inversely related.

Question 10

What is meant for data to be normally distributed?

Accepted Answer

Normal distribution, also known as Gaussian distribution, is a statistical distribution in which the data tends to cluster around the mean, and the frequency of values higher or lower than the mean decreases as the distance increases from the mean.

In a normal distribution, the mean, median, and mode are equal, and the data is symmetrically distributed around this central point. Therefore, choice B is the correct answer.

Question 11

The sampling distribution of a mean with a sample size of 50…

Accepted Answer

The standard deviation of the sampling distribution of the mean decreases as the sample size increases, assuming the population standard deviation is known or the sample size is sufficiently large to estimate the standard deviation using the sample. Therefore, a sample size of 50 will have a smaller standard deviation than a sampling distribution with the same mean of sample size 30.

Question 12

The central limit theorem states that:

Accepted Answer

The central limit theorem states that the sampling distribution of the mean will approach a normal distribution as the sample size increases, even for populations that do not have a normal distribution. This means that for sufficiently large sample sizes, the shape of the population distribution becomes less important and normality can be assumed.

Question 13

The sampling distribution of means with a sample size of 1000 obtained from a population with a trimodal distribution (i.e., three modes) will…

Accepted Answer

According to the central limit theorem, for large sample sizes, the sampling distribution of means becomes approximately normal regardless of the shape of the population distribution. Therefore, the sampling distribution of means with a sample size of 1000 obtained from a population with a trimodal distribution will be approximately normal and unimodal.

Question 14

The p value measures…

Accepted Answer

The p value measures the probability of obtaining a result as extreme as the data if the null hypothesis were true.

Question 15

When comparing two studies measuring the same phenomenon, the study with a statistical power of 0.5 is more likely to ________________________ than the study with a statistical power of 0.8.

Accepted Answer

Statistical power refers to the ability of a study to detect a true effect if it exists. A study with a statistical power of 0.5 has a lower ability to detect a true effect, meaning it is more likely to result in a Type II error, which is failing to reject a false null hypothesis. Therefore, the study with a statistical power of 0.8 is more likely to produce a statistically significant finding, but it does not necessarily give a more precise estimate of the effect.

Question 16

The disadvantage of a small sample size in psychology experiments that expect to measure a small to medium effect is that…

Accepted Answer

A small sample size in psychology experiments that expect to measure small to medium effects may result in an underpowered study, leading to an increased likelihood of a Type II error, which is failing to detect a significant effect when one truly exists. A Type II error is also known as a false negative. A Type I error, on the other hand, is rejecting a null hypothesis that is actually true, also known as a false positive. Overpowering a study refers to having a sample size that is larger than necessary, which can increase the risk of a Type I error.

Question 17

Why should a power analysis be done while designing the study (i.e., before data collection)?

Accepted Answer

A power analysis done before data collection can help determine the sample size needed to have a good chance of detecting an effect if it exists. This can save time and resources by avoiding collecting an insufficient sample size or unnecessary data.

Question 18

Which of the following is a valid reason for focusing on effect size instead of p values when analyzing your results?

Accepted Answer

Effect sizes are not dependent on the sample size of your data, whereas p values are influenced by the size of your sample. Focusing on effect size allows for a more meaningful interpretation of the results beyond statistical significance.

Question 19

Which of the following piece(s) of information is/are available from a stem-and-leaf plot?

Accepted Answer

A stem-and-leaf plot provides a visual representation of data that allows for the determination of the mean, median, and mode. The mean can be calculated by adding all the values and dividing by the number of values, the median can be found as the middle value when the data is ordered, and the mode is the most frequently occurring value(s), all of which can be identified from a stem-and-leaf plot.

Question 20

Consider the histogram below. Which of the following statements is necessarily true?

Accepted Answer

The median of a data set is the value that divides the data into two equal halves. In this histogram, the middle bar represents the range from 15 to 20, which means that approximately 50% of the data falls within this range. Therefore, the median must lie between 15 and 20. Choice A is not necessarily true as we do not know the specific values in the data set. Choice C is incorrect as a histogram and a stem-and-leaf plot both represent the same data but in different visual forms. Choice D is incorrect as there is only one mean in a data set.

Quiz 13: Analyzing Your Data I: an Overview