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In Depth Information
If you took a basic algebra course in high school, you may remember the concept
of “absolute value.” In mathematical terms, the absolute value of any number is
always that number expressed as a positive number.
For example, the absolute value of 2.35 is
þ
2.35.
þ
2.35.
This becomes important when you are using the t-table in Appendix E of this
book. We will discuss this table later when we get to Step 5 of the one-group t-test
where we explain how to find the critical value of t using Appendix E.
And the absolute value of minus 2.35 (i.e.
2.35 ) is also
4.1.4 STEP 4: Calculate the formula for the one-group t-test
Objective : To learn how to use the formula for the one-group t-test
The formula for the one-group t-test is as follows:
X
m
s X
t
¼
where
(4.1)
s
s
e
: ¼
S X ¼
p
n
(4.2)
:
This formula makes the following assumptions about the data (Foster, Stine, and
Waterman 1998): (1) The data are independent of each other (i.e., each person
receives only one score), (2) the population of the data is normally distributed, and
(3) the data have a constant variance (note that the standard deviation is the square
root of the variance).
To use this formula, you need to follow these steps:
1. Take the sample mean in your research study and subtract the population mean
m
from it (remember that the population mean for a study involving numerical
rating scales is the “middle” number in the scale).
2. Then take your answer from the above step, and divide your answer by the
standard error of the mean for your research study (you will remember that you
learned how to find the standard error of the mean in Chapter 1; to find the
standard error of the mean, just take the standard deviation of your research
study and divide it by the square root of n , where n is the number of people,
plants, or animals used in your research study).
3. The number you get after you complete the above step is the value for t that
results when you use the formula stated above.
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