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Alternately, if you wrote that: ‘‘Female alumni were signiﬁcantly less satisﬁed

than male alumni,’’ the end of this conclusion should be: (4.37 vs. 7.26) since you

mentioned females ﬁrst, and males second.

Putting the two mean scores at the end of your conclusion saves the reader from

having to turn back to the table in your research report to ﬁnd these mean scores to

see how far apart the mean scores were.

Now, let’s discuss FORMULA #1 that deals with the situation in which both

groups have a sample size greater than 30.

Objective: To use FORMULA #1 for the two-group t-test when both groups

have a sample size greater than 30

5.2 FORMULA #1: Both Groups have a Sample Size

Greater than 30

The ﬁrst formula we will discuss will be used when you have two groups with a

sample size greater than 30 in each group and one measurement on each member

in each group. This formula for the two-group t-test is:

t
¼
X
1
X
2

S
X
1
X
2

ð
5
:
2
Þ

s

S
1

n
1

þ
S
2

n
2

where S
X
1
X
2
¼

ð
5
:
3
Þ

and where degrees of freedom = df
¼
n
1
þ
n
2
2

ð
5
:
1
Þ

This formula looks daunting when you ﬁrst see it, but let’s explain some of the

parts of this formula:

We have explained the concept of ‘‘degrees of freedom’’ earlier in this chapter,

and so you should be able to ﬁnd the degrees of freedom needed for this formula in

order to ﬁnd the critical value of t in Appendix E.

In the previous chapter, the formula for the one-group t-test was the following:

t
¼
X
l

S
X

ð
4
:
1
Þ

where s
:
e
:
¼
S
X
¼
S

p

n

ð
4
:
2
Þ

For the one-group t-test, you found the mean score and subtracted the

population mean from it, and then divided the result by the standard error of the mean

(s.e.) to get the result of the t-test. You then compared the t-test result to the critical

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