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5.1.7 STEP 7: Find the Critical Value of t in the t-Table

in Appendix E

In the previous chapter where we were dealing with the one-group t-test, you found

the critical value of t in the t-table in Appendix E by ﬁnding the sample size for the

one group in the ﬁrst column of the table, and then reading the critical value of t

across from it on the right in the ‘‘critical t column’’ in the table (see
Sect. 4.1.5
)
.

This process was fairly simple once you have had some practice in doing this step.

However, for the two-group t-test, the procedure for ﬁnding the critical value of

t is more complicated because you have two different groups in your study, and

they often have different sample sizes in each group.

To use Appendix E correctly in this chapter, you need to learn how to ﬁnd the

‘‘degrees of freedom’’ for your study. We will discuss that process now.

5.1.7.1 Finding the Degrees of Freedom (df) for the Two-Group t-Test

Objective: To ﬁnd the degrees of freedom for the two-group t-test and to use it

to ﬁnd the critical value of t in the t-table in Appendix E

The mathematical explanation of the concept of the ‘‘degrees of freedom’’ is

beyond the scope of this topic, but you can ﬁnd out more about this concept by

reading any good statistics book (e.g. Keller
2009
). For our purposes, you can

easily understand how to ﬁnd the degrees of freedom and to use it to ﬁnd the

critical value of t in Appendix E. The formula for the degrees of freedom (df) is:

degrees of freedom
¼
df
¼
n
1
þ
n
2
2

ð
5
:
1
Þ

In other words, you add the sample size for Group 1 to the sample size for

Group 2 and then subtract 2 from this total to get the number of degrees of freedom

to use in Appendix E.

Take a look at Appendix E.

Instead of using the ﬁrst column as we did in the one-group t-test that is based

on the sample size, n, of one group, we need to use the second-column of this table

(df) to ﬁnd the critical value of t for the two-group t-test.

For example, if you had 13 people in Group 1 and 17 people in Group 2, the

degrees of freedom would be: 13 ? 17 – 2 = 28, and the critical value of t would

be 2.048 since you look down the second column which contains the degrees of

freedom until you come to the number 28, and then read 2.048 in the ‘‘critical t

column’’ in the table to ﬁnd the critical value of t when df = 28.

As a second example, if you had 52 people in Group 1 and 57 people in Group

2, the degrees of freedom would be: 52 ? 57 – 2 = 107 When you go down the

second column in Appendix E for the degrees of freedom, you ﬁnd that once you

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