Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

30 CHAPTER 1 | Introduction to Statistics
experimental condition (15)
nonequivalent groups study (16)
pre–post study (17)
quasi-independent variable (17)
construct (19)
operational definition (19)
discrete variable (19)
continuous variable (19)
real limits (20)
upper real limit (20)
lower real limit (20)
nominal scale (21)
ordinal scale (22)
interval scale (23)
ratio scale (23)
SPSS ®
The Statistical Package for the Social Sciences, known as SPSS, is a computer program that performs
most of the statistical calculations that are presented in this book, and is commonly available
on college and university computer systems. Appendix D contains a general introduction to SPSS.
In the Resource section at the end of each chapter for which SPSS is applicable, there are stepby-step
instructions for using SPSS to perform the statistical operations presented in the chapter.
FOCUS ON PROBLEM SOLVING
It may help to simplify summation notation if you observe that the summation sign is always
followed by a symbol or symbolic expression—for example, ΣX or Σ(X + 3). This symbol
specifies which values you are to add. If you use the symbol as a column heading and list all
the appropriate values in the column, your task is simply to add up the numbers in the column.
To find Σ(X + 3) for example, start a column headed with (X + 3) next to the column of Xs.
List all the (X + 3) values; then find the total for the column.
Often, summation notation is part of a relatively complex mathematical expression that
requires several steps of calculation. The series of steps must be performed according to the
order of mathematical operations (see page 26). The best procedure is to use a computational
table that begins with the original X values listed in the first column. Except for summation,
each step in the calculation creates a new column of values. For example, computing Σ(X + 1) 2
involves three steps and produces a computational table with three columns. The final step is
to add the values in the third column (see Example 1.4).
DEMONSTRATION 1.1
SUMMATION NOTATION
A set of scores consists of the following values:
7 3 9 5 4
For these scores, compute each of the following:
X X 2
7 49
3 9
9 81
5 25
4 16
ΣX
(ΣX) 2
ΣX 2
ΣX + 5
Σ(X – 2)
Compute ΣX To compute ΣX, we simply add all of the scores in the group.
ΣX = 7 + 3 + 9 + 5 + 4 = 28
Compute (ΣX) 2 The first step, inside the parentheses, is to compute ΣX. The second step is
to square the value for ΣX.
ΣX = 28 and (ΣX) 2 = (28) 2 = 784