Workbook for Introductory Statistics for the Behavioral Sciences

215 Pages·1976·5.611 MB·English

by  Robert B. Ewen (Auth.)

WORKBOOK FOR
Introductory
Statistics
for the Behavioral
Sciences.
Second Edition
Robert B. Ewen
Florida International University
®
ACADEMIC PRESS New York San Francisco London
A Subsidiary of Harcourt Brace Jovanovich, Publishers
COPYRIGHT © 1976, BY ACADEMIC PRESS, INC.
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Introduction
Many students of the behavioral and social sciences approach
the study of statistics with fear and trepidation, regarding it as a
necessary evil encountered in the course of pursuing their major
field of study. While statistics is vitally important for behavioral and
social sciences majors, you will probably not have much chance to
apply what you learn in introductory statistics until later in your
academic career, when you will have had enough exposure to
various content areas in your field to design and carry out research
of your own and read and critically evaluate experiments and statis-
tical procedures carried out by others.
Therefore, though it is possible that statistics will be of im-
mediate practical value to you, it is more likely that you will simply
have to "take on faith" the great importance of this area of study
until such time as you can make use of what you have learned.
Statistics is not an end in itself, but rather a means to the end of
proper data analysis, and your work in statistics should be under-
taken with this goal in mind.
Although the development of "table-top" computers may
ultimately do away with the need for carrying out most statistical
computations by hand, homework practice in a first course in
statistics is essential to learning and understanding the material;
statistics cannot be well learned simply by listening to lectures.
The purpose of this workbook is to help you obtain the necessary
practice. In particular, the following objectives have guided the
development of this workbook :
/. The workbook should be interesting. No one can make
a statistics workbook as entertaining as a popular novel, but a dry
and lifeless approach can only lead to boredom and distaste for
statistics and should be avoided insofar as is possible.
ix
X INTRODUCTION
2. Numerical computations should be kept within rea-
sonable bounds. Burdening introductory statistics students with
hours of laborious mathematical calculations can hardly be con-
sidered a meaningful educational experience. All too often, students
lose sight of the general procedures and underlying rationales when
faced with endless masses of computations. Also, any enthusiasm
the student may have had for statistics is likely to be lost in the
process. Computations are necessary to develop understanding of
the material, but there is no reason why the computations cannot
be relatively simple and involve a relatively small number of figures.
Therefore, it is important for you to understand that many
numerical examples in this workbook are designed with the goal
of ready computation in mind. On page 1, you will see some hypo-
thetical data that will be used in many of the homework problems.
In actual practice, it would not be a good idea to draw small samples
of only five or ten cases, as is done with the "University C" and
"University D" data. Similarly, other problems in this workbook
often involve a smaller sample than would be desirable in a real
situation. If you can deal correctly with the problems in this work-
book, you will have no difficulty with real problems that involve
exactly the same statistical operations but have more data to be
analyzed.
3. The workbook should stress understanding as well
as computation. Carrying out computations correctly is highly
commendable, but leaves something to be desired if you do not
understand the reasons for what you are doing. Therefore, this
workbook includes questions that are designed to help you evalu-
ate your understanding of the various procedures, as well as
questions designed to give you practice in performing the necessary
calculations.
4. There should be some continuity across different
units. If a workbook consists of a potpourri of problems, where
those in one chapter have nothing to do with those in the next, it
is difficult for students to appreciate the relationships among
different areas. Therefore, the hypothetical "University" data are
provided in order to establish some continuity across the various
topics covered in this workbook. These data will not be suitable for
all problems, so new data will be introduced at various points.
INTRODUCTION xi
However, the "University" data should allow you to get a fairly
good idea of how the researcher goes from a mass of numbers to
various descriptive statistics, the purpose of which is to make the
data more understandable, and to various inferential statistics, the
purpose of which is to permit the researcher to test his scientific
hypotheses.
5. The workbook should highlight formulas and key
ideas for ready reference. At the beginning of each chapter,
you will find a "reminder" to provide a ready reference to the
formulas and important ideas for that chapter. This workbook is
not intended to stand by itself, and you should use the reminders
for review and reference only and use your textbook to learn the
material. In a few cases where the computation of a statistic is
moderately complicated, a numerical example has been included
to further clarify the procedures involved.
6. The workbook should deal with the choice of the
correct procedure. All too often, writers in the area of statistics
ignore the fact that the selection of the appropriate statistic is often
as much of a problem to the beginning student (and to the more
experienced one as well!) as is the proper computation of that
statistic. Therefore, exercises are included which deal with which
procedure to use in a given situation.
The behavioral or social scientist with a competent understand-
ing of statistics has at his grasp a collection of quality tools, which
when applied correctly will aid in the development of proper data
analysis. I hope that you will develop an appreciation and liking
for the techniques of statistics, and that they will serve you well in
the years to come.
Note to the Instructor
The second edition of this workbook includes a chapter on nonpara-
metric statistics, and problems on multiple comparisons in one-way
analysis of variance, in accordance with corresponding changes in the
textbook. In addition, most chapters now consist of three sections :
7. Reminder. A summary of important formulas and concepts.
2. Problems. Basic calculational problems, and thought problems
designed to test the student's understanding of statistical concepts and
issues.
3. Additional Computational Practice. Problems that provide
more extensive calculational practice. Often, statistically significant and
statistically nonsignificant sets of data are presented in pairs to help
students develop more of a "feel" for real data. These problems may be
assigned to all students, or just to those who have had difficulty with
the problems in the preceding section.
xiii
Glossary of Symbols
Numbers in parentheses indicate the chapter in which the symbol first appears.
a Y intercept of linear regression line for predicting /from X (11 )
YX
a criterion (or level) of significance; probability of Type I error (9)
b slope of linear regression line for predicting Y from X (11 )
YX
ß probability of Type II error (9)
1 — p power (13)
cf cumulative frequency (2)
χ2 chi square (16)
D difference between two scores or ranks (10)
D mean of the Ds (10)
df degrees of freedom (9)
df degrees of freedom between groups (14)
B
dfyj degrees of freedom within groups (14)
df degrees of freedom for factor 1 (1 5)
y
df degrees of freedom for factor 2(15)
2
dfy x 2 degrees of freedom for interaction (1 5)
δ delta (13)
ε epsilon (14)
£R epsilon applied to ranks (17)
f frequency (2)
f expected frequency (1 6)
e
f number of negative difference scores (17)
m
f observed frequency (1 6)
Q
f number of positive difference scores (17)
p
F statistic following the F distribution (14)
G Mdn grand median (17)
γ effect size, gamma (13)
h interval size (3)
H Kruskal-Wallis H (17)
H% percent of subjects in all intervals higher than the critical one (3)
H null hypothesis (9)
0
Η alternative hypothesis (9)
Λ
XV
xvi GLOSSARY OF SYMBOLS
/ case number (1 )
/% percent of subjects in the critical interval (3)
k a constant (1 )
k number of groups (or the last group) (14)
L% percent of subjects in all intervals below the critical one (3)
LRL lower real limit (3)
LSD Fisher protected t test (14)
Mdn median (4)
MS mean square (14)
MS mean square between groups (14)
B
MS mean square within groups (14)
W
MS·! mean square for factor 1 (15)
MS mean square for factor 2 (1 5)
2
MS^ x 2 mean square for interaction (1 5)
μ population mean (4)
N number of subjects or observations (1 )
NG number of observations or subjects in group G (14)
π hypothetical population proportion (9)
p observed sample proportion (9)
P(A) probability of event/\ (7)
PR percentile rank (3)
φ phi coefficient (16)
r matched-pairs rank biserial correlation (17)
c
r Glass rank biserial correlation (17)
G
r sample Pearson correlation coefficient between X and Y (11 )
XY
r Spearman rank-order correlation coefficient (12)
s
r point-biserial correlation coefficient (12)
pb
Rj mean of ranks in group / (17)
PXY population correlation coefficient between X and Y (11 )
5 sample standard deviation (5)
s2 population variance estimate (5)
SQ variance of the Ds (10)
Spooled pooled variance (10)
s~ standard error of the mean (9)
sx 1-x standard error of the difference (10)
Score score corresponding to thepth percentile (3)
p
SFB sum of frequencies below the critical interval (3)
SS sum of squares (14)
SS sum of squares between groups (14)
B
SS total sum of squares (14,)
T
SS sum of squares within groups (14)
W
SS, sum of squares for factor 1 (1 5)
SS sum of squares for factor 2 (1 5)
2
GLOSSARY OF SYMBOLS xvii
S5-! sum of squares for interaction (1 5)
x2
Σ sum or add up (1 )
σ standard deviation (5)
σ2 variance (5)
standard error of a sample proportion (9)
Ρ
σ^ standard error of estimate for predicting Y (11 )
ΐ statistic following the t distribution (9)
Τ T score (6)
τ expected sum of ranks (17)
Ε
τ, sum of ranks in group / (17)
θ theta (13)
X deviation score (4)
X' predicted X score (11 )
X sample mean (4)
XG mean of group G (14)
Y' predicted /score (11 )
ζ standard score based on a normal distribution (8)
Ζ standard score (6)