Question 1

In a distribution with a mean of M = 36 and a standard deviation of SD = 8, a score of 40 would be considered an extreme value.

Accepted Answer

An extreme value in a distribution is typically one that is very far from the mean. To determine whether a score of 40 is extreme in this particular distribution, we can calculate its z-score:

z = (40 - 36) / 8 = 0.5

A z-score of 0.5 indicates that the score is only half a standard deviation above the mean, which is not particularly extreme. In fact, we would typically consider scores with z-scores of 2 or more (or -2 or less) to be extreme. Therefore, a score of 40 would not be considered extreme in this distribution.

Question 2

Without some correction, the percentage of agreement between two observers will tend to overestimate the true level of interrater reliability.

Accepted Answer

This is because the observers may agree on certain aspects of the observation by chance, leading to a higher percentage of agreement that does not necessarily reflect true interrater reliability. Correction methods such as Cohen's kappa or intraclass correlation coefficients can provide a more accurate estimate of interrater reliability.

Question 3

In a distribution with a mean of M = 76 and a standard deviation of SD = 7, a score of 91 would be considered an extreme value.

Accepted Answer

An extreme value is typically defined as a score that falls more than 2 standard deviations above or below the mean. In this distribution, 2 standard deviations above the mean would be M + 2SD = 90, so a score of 91 would be considered an extreme value.

Question 4

One concern with measuring split-half reliability is that many different correlations are possible depending on how you decide to split the test items in half.

Accepted Answer

Splitting the test items in different ways can lead to different subsets of items being included in each half, which can affect the reliability coefficient obtained. Therefore, it is important to use a systematic method for splitting the items, such as randomly dividing them or dividing them based on content or difficulty.

Question 5

The median is the most commonly used measure of central tendency.

Accepted Answer

The mean is actually the most commonly used measure of central tendency. The median is often used as an alternative when the data is skewed or has outliers.

Question 6

For data that consist of two or more groups of scores with each score a numerical value measuring the same variable, the most common statistics are those that measure and evaluate the mean differences between groups.

Accepted Answer

The most common statistics used for data consisting of multiple groups with numerical values are measures of central tendency and variability, such as means, standard deviations, and ranges. These statistics can be used to evaluate the differences between groups.

Question 7

A summary value, usually numerical, that describes a sample is called a parameter.

Accepted Answer

A summary value that describes a sample is actually called a statistic. A parameter refers to a numerical value that describes a population.

Question 8

Without some correction, such as the Spearman-Brown formula, a correlation measuring split-half reliability will tend to overestimate the reliability for the full test.

Accepted Answer

The Spearman-Brown formula is used to correct for the underestimation of reliability when using split-half methods, by predicting the reliability of the full test based on the split-half reliability.

Question 9

In general, a sample with large variance is more likely to produce a significant result than a sample with small variance.

Accepted Answer

A large variance in a sample often indicates more spread in the data, which can make it harder to detect a true effect or difference, thus potentially reducing the likelihood of finding a significant result.

Question 10

A Type I error means that the hypothesis test has failed to detect a real treatment effect.

Accepted Answer

A Type I error means that the hypothesis test has falsely detected a treatment effect that is not actually there.

Question 11

In general, a correlation obtained from a large sample is more likely to be significant than a correlation obtained from a small sample.

Accepted Answer

This is true because a larger sample size increases the power of the analysis, making it more likely to detect significant correlations. Conversely, a smaller sample size decreases the power of the analysis and increases the chance of obtaining a non-significant correlation even if a true correlation exists.

Question 12

The goal of descriptive statistics is to simplify, summarize, and organize data.

Accepted Answer

Descriptive statistics involves methods for summarizing and organizing data in order to make it more easily interpretable and understandable. This can include calculating measures of central tendency (such as mean, median, and mode), measures of variability (such as range, variance, and standard deviation), and graphical representation of data (such as histograms, scatter plots, and box plots). All of these techniques aim to simplify the data in some way and make it more manageable for analysis and interpretation.

Question 13

A researcher reports a significant correlation using an alpha level of .01. The probability that the researcher is making a Type I error is p

Accepted Answer

The alpha level of .01 indicates the probability of making a Type I error, which is rejecting a true null hypothesis.

Question 14

When a research report demonstrates a significant treatment effect at the .05 level, you can be more confident that the effect is real than if the researcher had reported a significant effect with an alpha level of only .01.

Accepted Answer

A significant effect at the .01 level indicates a stronger level of statistical significance compared to the .05 level, meaning there is a lower probability that the observed effect is due to chance, thus increasing confidence in the reality of the effect.

Question 15

The mode is the best way to measure central tendency for data from a nominal scale of measurement.

Accepted Answer

The mode is the only measure of central tendency that can be used with nominal data, as it only identifies the most frequently occurring category or value. Other measures such as the mean and median cannot be used with nominal data as it does not make sense to average or order categories without meaningful numeric values.

Question 16

A negative correlation means that as the X values decrease, the Y values also tend to decrease.

Accepted Answer

A negative correlation means that as the X values increase, the Y values tend to decrease, and vice versa.

Question 17

The goal of a hypothesis test is to demonstrate that the patterns observed in the sample data represent real patterns in the population and are not simply due to chance or sampling error.

Accepted Answer

The statement accurately describes the goal of hypothesis testing. By conducting a hypothesis test, researchers aim to confirm that any patterns or differences observed in a sample are likely representative of the larger population, rather than being random or due to chance.

Question 18

A researcher records the average age for a group of 25 preschool children selected to participate in a research study. The average age is an example of a statistic.

Accepted Answer

The given statement is true. The average age of the 25 preschool children is a statistic because it represents a numerical summary of the sample data.

Question 19

In a frequency distribution graph, the frequencies are listed on the vertical axis.

Accepted Answer

The frequencies are typically listed on the vertical axis of a frequency distribution graph, while the values or categories being counted are listed on the horizontal axis.

Question 20

It is always possible that patterns observed in sample data do not accurately represent patterns in the population.

Accepted Answer

This statement is a fundamental concept in statistics known as the "sampling error," which states that samples are inherently subject to random fluctuations and may not perfectly represent the larger population from which they are drawn.

Quiz 15: Statistical Evaluation of Data