CHAPTER 6
USING DESCRIPTIVE STATISTICS TO STUDY PROBLEMS OF PRACTICE
TEACHING ACTIVITIES FOR CHAPTER 6
Activity 1. The relationship between constructs, variables, scales, and measures.
Some students have a fear of mathematics or little understanding of what numbers on educational tests and
other measures mean. These students can benefit from instruction in how test scores derive from intuitively
meaningful ideas about constructs, variables, and scales.
You can select a construct to start the class activity. Suppose the construct is reading comprehension. You can
ask students to define this construct. Their definition might be something like this: the ability to understand the
main idea and other information in a text selection.
Then you can ask your students how individuals vary with respect to this construct. If they need help, you can
2. Teaching descriptive statistics.
Students in some education programs take a separate course on statistics. For such students, Chapter 6 might be
redundant. However, our experience is that many students benefit from multiple exposures to statistical concepts
and procedures, especially when it occurs in a research methods course. The course shows them the specific role of
statistics in the research enterprise. Also, each instructor has his or her own way of explaining statistics. One
instructor’s explanations and illustrations might reach some students, while another instructor’s explanations and
illustrations might reach other students.
If students have access to Excel, you can have students practice computing statistics on various data sets.
Students simply need to enter the data in an Excel workbook, open the pull–down menu Tools, and click on the Data
MULTIPLE-CHOICE TEST ITEMS FOR CHAPTER 6
1. Quantitative data
a. are of value in revealing problems of practice in education.
b. can describe longitudinal trends in education..
c. play an important role in medicine, but are not relevant to human service professions like education.
d. All of the above.
2. A particular construct
a. can be measured only by one test or other instrument.
b. can be measured by more than one test or other instrument.
c. manifests itself as one distinctive type of behavior.
d. does not manifest itself in behavioral form.
3. Most variables
a. have an infinite range of values.
b. have five or fewer values.
c. rarely have more than 10 values.
d. differ in their range of values, depending on the construct being measured.
4. The 50 states of the United States
a. constitute an ordinal scale.
b. constitute a nominal scale.
c. constitute an interval scale.
d. cannot be conceptualized as a scale.
5. An ordering of schools from most improved to least improved constitutes a(n)
a. nominal scale.
b. interval scale.
c. ordinal scale.
d. ratio scale.
6. Educational tests and other measures are considered to contain _______ scales for purposes of
statistical analysis.
a. nominal
b. interval
c. ordinal
d. ratio
7. A statistic is best defined as
a. a number that describes a characteristic of a sample’s scores on a measure.
b. the raw score of each individual in a sample
c. a score yielded by an interval or ratio scale.
d. a test that allows inferences about a population.
8. Parameters
a. provide a more precise picture of a sample’s scores than statistics do.
b. can be computed only for scores derived from a ratio scale.
c. can only be computed if a sample’s scores are derived from an interval scale.
d. describe a characteristic of a population’s scores on a test or other measure.
9. The mean and median both
a. describe a point around which all the scores for a variable are distributed.
b. describe the amount of variability in a distribution of scores.
c. identify the most frequent and least frequent score in a sample of scores.
d. All of the above.
10. In statistical analysis, an outlier is an individual who
a. scores extremely high on a measure.
b. scores extremely low on a measure.
c. scores extremely high or low on a measure.
d. has a missing score on a measure.
11. The range is
a. a measure of central tendency.
b. a measure of variability.
c. the difference between the highest and lowest score in a distribution.
d. is computed by summing a sample’s scores on a measure and dividing by the sample size.
12. The sum of squares
a. is the most reliable measure of central tendency for a set of scores.
b. is the sum of all the squared scores in a set of scores.
c. represents the total amount of variability in a set of scores.
d. is used to represent the difference between sample statistics and population parameters in a set of
scores.
13. The most commonly used statistic to represent the variability in a sample’s scores is the
a. range.
b. mean absolute deviation.
c. variance.
d. standard deviation.
14. If a distribution of scores forms a normal curve, we can conclude that
a. the scores are clustered around each side of the mean in a symmetrical pattern.
b. the sample mean equals zero standard deviation units.
c. scores that are one standard deviation above the mean are at approximately the 84th percentile.
d. All of the above.
15. If the mean of a sample’s scores is 30 and the standard deviation is 2, it is reasonable to conclude that
a. the sample’s scores are clustered tightly around the mean.
b. the sample has at least several outliers.
c. the range of scores is large.
d. the mean and the median are substantially different.
16. If you know that a distribution of scores is skewed, the best interpretation is that
a. a majority of the scores are below the sample mean.
b. a majority of the scores are above the sample mean.
c. a majority of the scores are either below or above the sample mean.
d. there are few outliers in the sample.
17. Correlational analysis allows researchers to determine whether
a. a set of scores is clustered symmetrically around each side of the mean.
b. the distribution of scores on one measure is related to the distribution of scores on another measure.
c. the standard deviation units of two distributions of scores are equivalent.
d. two samples were randomly drawn from a population.
18. Correlational analysis provides a description about the relationship between two score distributions that is
a. identical to the results obtained by doing a group comparison.
b. mathematically less precise than the results obtained by doing a group comparison.
c. mathematically more precise than the results obtained by doing a group comparison.
d. easier for the general public to understand than a group comparison.
SHORT-ANSWER TEST ITEMS FOR CHAPTER 6
1. For each of the following measures, indicate whether it is typically regarded as a nominal, ordinal, interval, or
ratio scale.
a. students’ height
b. students’ scores on an Advanced Placement test.
c. students’ rank in a ping-pong competition
d. students’ gender
2. Ten students earned the following scores on a 15-item test:
7
8
8
8
8
9
9
9
10
15
a. What is the mean of these scores?
b. Is there skewness around the mean, and if so, why?
c. Is there an outlier in this set of scores, and if so, what is it?
d. The standard deviation (SD) of this set of scores is 2.24. What is the score represented by +1 SD
for this set of scores?
3. The following are two distributions of scores for a sample of students. One distribution is the students’
scores on a measure of creativity; scores can vary between 0 and 10. The other distribution is their scores
on a recent essay assignment; scores can vary between 1 and 5. Describe the relationship
between the two distributions of scores in non-mathematical terms.
Creativity
9
9
8
8
5
5
4
2
2
2
Essay
Quality
4
5
5
2
4
4
2
2
3
4
CHAPTER 6
USING DESCRIPTIVE STATISTICS TO STUDY PROBLEMS OF PRACTICE
Multiple-Choice Test Items
Short-Answer Test Items