Information Technology Reference
In-Depth Information
Ta b l e 2 . 1 .
Notation symbols
Symbol How to verbalize
Meaning and comments
Y
This represents a set of scores or
observations. When we refer to all of the
scores the
Y
is accompanied by a
subscript
i
or
Y
i
. When we refer to a
particular score the subscript
i
is changed
to a number. Thus, the first participant's
score is
Y
1
the second
Y
2
, and so on. Most
of the time, we will eliminate subscripts
to simplify presentation of a formula.
Y
Read as “
Y
-bar.”
This is the symbol for the mean of a
distribution.
The Greek uppercase
letter sigma.
This is a summation instruction and signals
us to add up the scores that follow it.
Y
Read as “summation
Y
.”
This instruction indicates we are to sum
(add up) the
Y
scores.
n
This is the number of scores within a group
or treatment condition. To simplify
computations throughout this topic, we
will always assume equal sample sizes
(equal
n
) across treatment conditions.
The concept of unequal
n
will be dealt
with in Chapter 17. A uppercase
N
is
used to designate the entire sample size.
As we can see from Table 2.2, the couples vary somewhat in their
personal perceptions of matrimonial bliss. By summing the seven scores
we obtain the su
m
(
Y
) of 13. By dividing this sum by
n
(7), we obtain
the group mean
Y
, which equals 1.86. This mean lies between the anchors
very happy
and
happy
and is much closer to the latter. Based on the mean,
we would conclude that as a group these newlyweds appear to be “happy”
with their marriages.
When we perform these calculations
by hand (with a calculator), we typi-
cally report the results to two decimal
places (the nearest hundredth) because
we rarely obtain whole numbers. As a
general heuristic, if the number in the
third decimal place is 5 or greater, round
up. Conversely, if the number in the
third decimal place is less than 5, round
down. Thus, in the present case the actual
mean was 1.857. Hence, we rounded this
value to 1.86. This rounding procedure
may occasionally produce small amounts
of rounding error, but it is usually not
enough to cause concern.
Ta b l e 2 . 2 .
Raw scores for a
two-group example:
Newlywed-rated happiness
Y
i
Happiness score
Y
1
3
Y
2
2
Y
3
2
Y
4
2
Y
5
2
Y
6
1
Y
7
1
Y
13
Y
1.86
