Statistical Methods for Psychology

they were absent from school (Y). The data and simple summation operations on them are

illustrated in Table 2.4. Some of these operations have been discussed already, and others

will be discussed in the next few chapters.

Double Subscripts

A common notational device is to use two or more subscripts to specify exactly which value

of Xyou have in mind. Suppose, for example, that we were given the data shown in

Table 2.5. If we want to specify the entry in the ith row and jth column, we will denote this

as Thus, the score on the third trial of Day 2 is Some notational systems use

, which translates as “sum the where itakes on values 1 and 2 and jtakes

on all values from 1 to 5.” You need to be aware of this system of notation because some

other textbooks use it. In this book, however, the simpler, but less precise, is used where

possible, with used only when absolutely necessary, and never appearing.

You must thoroughly understand notation if you are to learn even the most elementary

statistical techniques. You should study Table 2.4 until you fully understand all the proce-

dures involved.

gXij ggXij

gX

gi^2 = 1 g^5 j= 1 Xij Xijs

Xij. X2,3=13.

Section 2.6 Notation 31

Table 2.4 Illustration of operations involving summation notation

Anxiety Score Tests Missed

(X)(Y) X^2 Y^2

10 3 100 9 7 30

15 4 225 16 11 60

12 1 144 1 11 12

9 1 81 1 8 9

10 3 100 9 7 30

Sum 56 12 650 36 44 141

(gX)(gY)=(56)(12)= 672

(g(X 2 Y))^2 = 442 = 1936

(gY)^2 = 122 = 144

(gX)^2 = 562 = 3136

g(XY)=(10)(3) 1 (15)(4) 1 (12)(1) 1 (9)(1) 1 (10)(3)= 141

g(X 2 Y)=(7 111111181 7)= 44

gY^2 =(3^2142112112132 )= 36

gX^2 =(10^2115211221921102 )= 650

gY=(3 1411111 3)= 12

gX=(10 115112191 10)= 56

X 2 Y XY

Table 2.5 Hypothetical data illustrating notation

Trial

12345Total

Day^1 876912 42

2 10 11 13 15 14 63

Total 18 18 19 24 26 105