Table Of ContentTEST SCORES
AND
W HAT THEY MEAN
HOWARD B. LYMAN
TEST SCORES
AND
WHAT THEY MEAN
second edition
HOWARD B. LYMAN
University of Cincinnati
PRENTICE-HALL, INC., Englewood Cliffs, New Jersey
This
2nd
Edition
Is Affectionately
Dedicated
to
2,
too
© 1971, 1963 by Prentice-Hall, Inc.
Englewood Cliffs, N.J.
All rights reserved. No part of this book
may be reproduced in any form or by any means
without permission in writing from
the publisher.
P-13-903781-0
C-l3-903799-3
Library of Congress Catalog Card Number: 71-121726
Printed in the United States of America
Current printing (last number):
10 9 8 7 6 5 4 3 2 1
PRENTICE-HALL INTERNATIONAL, INC., London
PRENTICE-HALL OF AUSTRALIA, PTY. LTD., Sydney
PRENTICE-HALL OF CANADA, LTD., Toronto
PRENTICE-HALL OF INDIA PRIVATE LIMITED, New Delhi
PRENTICE-HALL OF JAPAN, INC., Tokyo
PREFACE
Standardized testing is a fascinating study. The number of tests being used
increases by millions each year. New tests are constantly being published—
and new applications for tests are constantly being found.
Back in 1963, when the first edition of Test Scores and What They Mean
was published, I stated the belief that there was need for a book which could
be used by people who have access to test results but who have had little
training in the meaning of test scores. I thought that such a book would be
most helpful to those people whose professional training had not included
much about testing (even though they might make occasional or even fre-
quent reference to test results): school teachers, psychiatrists, social workers,
pediatricians, academic deans, and admissions counselors, among others. I
suggested also that the book might be used in connection with courses
in introductory psychology, educational psychology, counseling, psycholog־
ical testing, educational measurement and evaluation, guidance, individual
differences, and the like—in the training of psychologists, counselors, per-
sonnel workers, and others who may use tests often.
The reception given to the first edition was gratifying. The book was used
as a text or supplementary text for a wide variety of courses in colleges and
universities throughout the United States and Canada, and at some institu-
tions elsewhere. It was translated into Japanese. At least one consulting
firm urged personnel from client companies to consider its use. At least two
test publishers advertised it in their own catalogs as a service to their respec-
tive customers. Reviews were generally favorable, as were the comments of
professional colleagues. One Past President of the American Psychological
Association wrote: “The book is a beautiful job of matching information to
the need for it.”
There have been some improvements in the testing field since 1963.
iii
iv Preface
Test manuals are generally better. Test publishers seem to have made some
technical improvements in their tests, their selection of norms groups, etc.
And there has been a great increase in the use of sophisticated (and, generally,
more accurate) electronic scoring services. It’s even possible that there is
some improved test interpretation. But the job is far from complete, for there
is still too much test misuse and misinterpretation.
Criticism of standardized testing is louder than ever. Intelligence tests,
critics maintain, do not measure creativity. The tests do not give unvarying
results, and they are unfair to minority groups. Personality tests, they
contend, are an unfair invasion of privacy. Although tests are being used in
ever-increasing numbers, the critics are making ever-stronger adverse com-
ments. My views on these and related issues form the basis for Chapter
Eleven.
The difficulties with testing, of course, lie more with the users of tests and
of test results than with the tests themselves. The evidence seems clear:
more tests are going to be used by more people who have access to test results
without knowing as much as they should about the meaning of test scores.
Is it too much to hope that the critics may have the beneficial effect of
encouraging greater responsibility in the use and interpretation of test infor-
mation?
The second edition, like the first, is intended primarily for students of
testing and for the test-naive. For this reason, I have written informally in
an effort to make the book interesting and intelligible to any intelligent
adult.
My philosophy of testing is dynamic and still evolving. It has been in-
fluenced by my own teachers, both undergraduate and graduate: J. Me-
Vicker Hunt, Donald Lindsley, Donald G. Paterson, Howard P. Longstaff,
C. Gilbert Wrenn, Walter Cook, W. S. Miller, E. G. Williamson, John
G. Darley, Ralph F. Berdie, Herbert Sorenson, Robert North, Lysle Croft,
and others. My views have developed through years of research with tests,
through teaching and interacting with students in testing courses, and
through consultation on testing problems with a wide variety of clients.
The most distinctive feature of the first edition was the original classifica-
tion of types of test score. It has been retained almost unchanged. The con-
version table which enables the reader to convert from one type of score to
another (under certain assumptions) has been completely reset by the pub-
Usher to enable the reader to use it more easily. This table was used more
widely by professional psychologists and counselors than any other feature
of the first edition.
Most features of the first edition have been retained. Numerous minor
changes have been made throughout the book in the interest of clarity, but
there has been little change just for the sake of change.
Preface V
There arc two completely new chapters, “The Test Manual” and “Test-
ing Today and Social Responsibility.” In the former, I have tried to give the
reader some idea of what a good test manual is like and some suggestions for
reading the manual intelligently.
I am indebted to Dr. Robert Walker, of The Personnel Press (a subsidiary
of Ginn and Company) for the idea of including such a chapter; and I am
indebted to several test publishers (California Test Bureau, Consulting
Psychologists Press, Educational Testing Service, Houghton Mifflin Com-
pany, Personnel Press, Science Research Associates, and The Psychological
Corporation) for permission to use the illustrative material which made the
chapter possible. It is an interesting commentary on the status of testing, I
think, that I find it more difficult to select the material than to find the exam-
ples; i.e., I could easily have used other illustrations for every example in
this chapter.
Chapter Eleven, “Testing Today and Social Responsibility,” is a state-
ment of some of the present concerns about testing. Here, I have discussed
the cultural and racial fairness of tests, the charge that tests are an invasion
of privacy, and other issues.
The bibliography has been updated and greatly expanded. New items
include audio and video tapes, testing monographs, and books of readings.
The section on reliability has been almost completely rewritten in an
effort to explain that concept in a manner that will be most meaningful to
the beginning tester. In doing so, I have developed a five-dimensional model
of reliability which I believe will make this important test attribute a little
easier for the student to appreciate.
I want to thank the many users of the first edition of Test Scores and What
They Mean, especially those who were thoughtful enough to express their
comments. I want to thank Professor Saburo Iwawaki, who contributed many
thoughts while preparing his excellent Japanese translation of the book.
I want to thank my colleagues in Cincinnati (most especially Venus Blue-
stein, Goldine Gleser, Richard Melton, and Joan Bollenbacher) for permit-
ting me to throw occasional questions their way while writing this manuscript.
Thanks are due, too, to my wife, Pat, for her encouragement and her counsel,
as well as for her typing of the manuscript. Thanks, too, to my own students
for their free expressions of opinions—not always favorable—which have
helped me to write intelligibly for future users of this book.
Howard B. Lyman
CONTENTS
CHAPTER ONE
SCORE INTERPRETATION 1
Testing Today, 2 A Pretest, 5
Answers to Pretest Questions, 6
CHAPTER TWO
THE LANGUAGE OF TESTING 9
Maximum-Performance Versus Typical-Performance
Tests, 9 Differentiating Types of Maximum-Performance
Tests, 11 Typical-Performance Tests, 12
This Book, 20
CHAPTER THREE
BASIC ATTRIBUTES OF THE TEST 21
Validity, 21 Criterion-Related Validity
(Empirical Validity), 23 Reliability, 25
Usability, 32
VI
Contents VI1
CHAPTER FOUR ״
A FEW STATISTICS 34
Introduction, 34 Descriptive Statistics, 41
The Normal Probability Curve, 49 Inferential
Statistics, 51 Expectancy Tables, 59
An Omission and an Explanation, 62
CHAPTER FIVE ,
THE TEST MANUAL 63
The Test Catalog and Other Sources, 63
Test Publishers, 64 Manuals and the Like, 65
CHAPTER SIX
DERIVED SCORES 88
A Classification Scheme, 88 The Scores, 94
Type I : Comparison With an Absolute Standard, or Content
Difficulty, 94 Type II: Interindividual Comparisons, 96
Type III: Intra-Individual Comparison, 120
Type IV: Assorted Arbitrary Bases, 122, A Final Word, 124
CHAPTER SEVEN
PROFILES 126
Specific-Test Profiles, 127 General
Profiles, 141
Contents
CHAPTER EIGHT
COMMON SENSE 145
CHAPTER NINE
WHAT CAN WE SAY? 150
Who Is Entitled to Test Information, 150
Communicating the Results, 153 In Summary, 160
CHAPTER TEN
EXPERTS STILL NEEDED 161
CHAPTER ELEVEN
TESTING TODAY AND SOCIAL RESPONSIBILITY 163
CHAPTER TWELVE
CONCLUDING REMARKS 173
CONVERSION TABLE 176
BIBLIOGRAPHY 182
APPENDIX 186
GLOSSARY OF TERMS 186
INDEX 197
SCORE
INTERPRETATION
Chapter One
“When am I going to start failing?” a student asked me several years ago.
Upon being questioned, he told me this story: “My high school teacher told
me that my IQ is only 88. He said that I might be able to get into college
because of my football, but that I’d be certain to flunk out—with an IQ like
that!” I pointed out to Don that he had been doing well in my course. I
found out that he had had a B+ average for the three semesters he had com-
pleted. I reminded him that the proof of a pudding lies in its eating—and
that the proof of scholastic achievement lies in grades, not in a test designed
to predict grades.
Last June, Don graduated with honors.
This little story, true in all essential details, illustrates many points; for
example:
1. Was the test score correct? I suspect that an error was made in adminis-
tering or scoring the test. Or, perhaps that score was a percentile rank
instead of an /()—which would make a lot of difference.
2. Regardless of the accuracy of the score, the teacher should not have told
him the specific value of his IQ on the test.
3. The teacher went far beyond proper limits in telling Don that he would
“. . . be certain to flunk out. . . .” The teacher should have known that
test scores are not perfect.
4. Furthermore, test scores do not determine future performance; demon-
strated achievement is more conclusive evidence than is a score on a test
intended to predict achievement. Both the teacher and Don should have
known that!
If Don’s case were unusual, I might have forgotten about it; however,
mistakes in interpreting tests occur every day. Here are three other examples
that come quickly to mind:
