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4.1.5 STEP 5: Find the Critical Value of t in the t-Table

in Appendix E

Objective: To ﬁnd the critical value of t in the t-table in Appendix E

Before we get into an explanation of what is meant by ‘‘the critical value of t,’’

let’s give you practice in ﬁnding the critical value of t by using the t-table in

Appendix E.

Keep your ﬁnger on Appendix E as we explain how you need to ‘‘read’’ that

table.

Since the test in this chapter is called the ‘‘one-group t-test,’’ you will use the

ﬁrst column on the left in Appendix E to ﬁnd the critical value of t for your

research study (note that this column is headed: ‘‘n’’).

To ﬁnd the critical value of t, you go down this ﬁrst column until you ﬁnd the

sample size in your research study, and then you go to the right and read the

critical value of t for that sample size in the critical t column in the table (note that

this is the column that you would use for both the one-group t-test and the 95 %

conﬁdence interval about the mean).

For example, if you have 27 people in your research study, the critical value of t

is 2.056.

If you have 38 people in your research study, the critical value of t is 2.026.

If you have more than 40 people in your research study, the critical value of t is

always 1.96.

Note that the ‘‘critical t column’’ in Appendix E represents the value of t that

you need to obtain to be 95 % conﬁdent of your results as ‘‘signiﬁcant’’ results.

The critical value of t is the value that tells you whether or not you have found a

‘‘signiﬁcant result’’ in your statistical test.

The t-table in Appendix E represents a series of ‘‘bell-shaped normal curves’’

(they are called bell-shaped because they look like the outline of the Liberty Bell

that you can see in Philadelphia outside of Independence Hall).

The ‘‘middle’’ of these normal curves is treated as if it were zero point on the

xaxis (the technical explanation of this fact is beyond the scope of this topic, but any

good statistics book (e.g. Zikmund and Babin
2010
) will explain this concept to

you if you are interested in learning more about it).

Thus, values of t that are to the right of this zero point are positive values that

use a plus sign before them, and values of t that are to the left of this zero point are

negative values that use a minus sign before them. Thus, some values of t are

positive, and some are negative.

However, every statistics book that includes a t-table only reprints the positive

side of the t-curves because the negative side is the mirror image of the positive

side; this means that the negative side contains the exact same numbers as the

positive side, but the negative numbers all have a minus sign in front of them.

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