Microsoft Office Tutorials and References

In Depth Information

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
:

X

m

S
X

t

¼

(4.1)

where s.e.

¼

S

S
X
¼

p

n

(4.2)

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 value of

t to see if you either accepted the null hypothesis, or rejected the null hypothesis and

accepted the research hypothesis.

The two-group t-test requires a different formula because you have two groups,

each with a mean score on some variable. You are trying to determine whether to

accept the null hypothesis that the
population means of the two groups are equal
(in

other words, there is no difference statistically between these two means), or

whether the difference between the means of the two groups is “sufﬁciently

large” that you would accept
that there is a signiﬁcant difference
in the mean

scores of the two groups.

The numerator of the two-group t-test asks you to ﬁnd the difference of the

means of the two groups:

X
1

X
2

(5.4)

The next step in the formula for the two-group t-test is to divide the answer you

get when you subtract the two means by the standard error of the difference of the

two means, and
this is a different standard error of the mean that you found for the

one-group t-test because there are two means in the two-group t-test.

The standard error of the mean when you have two groups is called the ”standard

error of the difference of the means” between the means of the two groups. This

formula looks less scary when you break it down into four steps:

1. Square the standard deviation of Group 1, and divide this result by the sample

size for Group 1 (n
1
).

2. Square the standard deviation of Group 2, and divide this result by the sample

size for Group 2 (n
2
).

3. Add the results of the above two steps to get a total score.

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