CHAPTER 8
THE PRACTICAL SIGNIFICANCE OF STATISTICAL RESULTS
TEACHING ACTIVITIES FOR CHAPTER 8
1. Tables of norms.
Your students might have heard of tables of norms, but not actually seen such a table. Therefore, you might
wish to locate a familiar standardized test and the test manual that accompanies it. The manual should contain tables
of norms, such as age equivalents, grade equivalents, or percentile ranks. You can project these tables onto a screen
2. Effect size.
Effect size has become an important statistic in educational research and reviews of quantitative research
studies. Therefore, it is worthwhile to develop your students’ understanding of this concept. One way is to show
students a set of 10 scores, such as: 2, 3, 3, 4, 4, 6, 7, 7, 8, 9. We will designate these scores as the performance of a
group on an achievement test prior to instruction.
You can tell students that the mean of these scores is 5.3 and the standard deviation (SD) is 2.41. Next, you can
tell them to suppose that each student improves by 2 points on the test after instruction. The posttest mean is thus
7.3, and the SD is still 2.41. Ask students to explain why the SD has not changed. They should be able to infer that
3. Student achievement gains.
You can ask your class to read the reprinted article by James Popham and be prepared to discuss it in class. In
class, you can review the weaknesses of two approaches to assessing students’ intellectual growth described in the
TEST ITEMS FOR CHAPTER 8
1. The total score of an individual on a test with ten items, each scored 0 or 1, is called a _________ score.
a derived
b. standard
c. z
d. raw
2. Curriculum standards typically
a. are helpful in determining the practical significance of test scores.
b. are more useful in creating test scores that have practical significance than in developing
curriculum materials .
c. have greater theoretical value than practical value.
d. have meaning in statistical interpretation only if they include an ideal standard of performance.
3. One limitation of rankings is that they
a. have no practical significance.
b. require complex statistical calculations.
c. have unequal intervals.
d. apply only to a particular range of individuals in a group.
4. A norming group is intended to represent
a. the sample whose scores on a test are being interpreted for practical significance.
b. a group that scores very high on a test and therefore sets an ideal standard against which other
groups can be compared.
c. a population whose scores on a test provide a set of norms to which other groups’ raw scores can be
compared.
d. a population whose scores on a test are at a particular level of a curriculum standard.
5. Norms can take the form of
a. grade equivalents
b. age equivalents.
c. percentile ranks.
d. All of the above.
6. Standard scores represent a transformation of raw scores based on
a. the rankings of the individuals in a sample.
b. the standard deviation of the sample’s score distribution.
c. a table of norms.
d. test levels keyed to curriculum standards.
7. An individual with a standard score of 0 would be at the ___ percentile of the score distribution.
a. 50th.
b. 99th.
c. 66th.
d. 1st.
8. The normal curve
a. cannot be used to interpret z scores.
b. can be used to interpret any z score.
c. can be used to interpret z scores only if the sample’s standard deviation on a measure is 1.0 or
higher.
d. is used to calculate z scores.
9. Educators can use z scores to determine
a. where a student stands relative to a group on a particular test.
b. how well a student has done on various tests, each having a different number of items.
c. how different the average performance of one group is from the average performance of another
group on a particular test.
d. All of the above.
10. The Stanford-Binet Intelligence Scale relies primarily on __________ for interpretation of an
individual’s performance on the test.
a. raw scores
b. age equivalents
c. standard scores
d. the normal curve
11. Effect sizes can be used to determine whether
a. a sample’s raw scores on a test have practical significance.
b. it is appropriate to use a table of norms in interpreting test results.
c. z scores should be used instead of another type of standard score to interpret the practical
significance of a group’s performance on a test.
d. the difference between the means of two samples has practical significance.
12. There is general consensus among researchers that an effect size of ___ or larger has practical
significance.
a. .10
b. .20
c. .33
d. .50
13. A meta-analysis of research results across studies on the same problem makes use of
a. effect sizes.
b. tables of norms.
c. standard scores.
d. the normal curve.
14. Ceiling effects occur in testing when
a. a student has a lower level of achievement than that measured by the test.
b. a student has a higher level of achievement than that measured by the test.
c. the raw scores do not fit on a normal curve.
d. an achievement test has many test items that are too difficult for the students who will take it.
15. The use of ratios to represent research data
a. is not useful for determining the practical significance of the data.
b. is more helpful for research purposes than for explaining test results to the general public.
c. is more informative than the reporting of percentage gains and losses.
d. is less informative than the reporting of percentage gains and losses.
16. In a status model of school improvement, students in the third grade of a school would be tested, and
a. then the same students would be tested the following school year.
b. their performance would be compared with the performance of third graders in another, similar
school.
c. their test scores would be interpreted by using a table of norms based on the population of third
graders.
d. their performance would be compared with the performance of next year’s third graders.
17. One of the main advantages of growth models of school improvement is that they
a. determine gains in learning for a particular group of students as they progress through school.
b. require fewer testing sessions than other models of school improvement.
c. require simpler statistical analysis than other models of school improvement.
d. do not require statistical analysis of gains or losses in test performance.
SHORT-ANSWER TEST ITEMS FOR CHAPTER 8
1. Describe two transformations of an individual student’s raw score on a test that can help educators determine
the practical significance of the raw score.
2. Describe one problem with the use of gain scores to measure increases in students’ academic achievement.
3. What is a tables of norms useful for interpreting a student’s score on a standardized test?
4. State two reasons why it is useful to convert students’ raw scores on a measure to standardized scores, such as
z-scores.
CHAPTER 8
THE PRACTICAL SIGNIFICANCE OF STATISTICAL RESULTS
Multiple-Choice Test Items
Short-Answer Test Items
