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identiiably “paired” with a data point from the other alternative. As we stated earlier,
this makes a difference in the precise way we perform the t-test. The hypotheses are
the same as in the previous chapter:
H0:μ1=μ2
H1:μ1≠μ2
Another way to notate the “pairing” of the data is by changing the above notation to
H0:μ1−μ2=0
H1:μ1−μ2≠0,
and deine D = μ1 − μ2, where D stands for “true average difference” (for the same
person using the two alternatives) and writing
H0:D=0
H1:D≠0
In other words, is the (true) average difference (D) between the time it takes
a person to perform the two tasks zero (H0 is true) or not zero (H0 is false, H1 is
true)? Recall from Chapter 1 that if we accept H0 (concluding that H0 is true), this
really is saying that there is insuficient evidence to reject H0.
Let's illustrate the “paired-data t-test” using our job posting timing data for design
1 (“The Long Scroller”) and design 2 (“The Wizard”). The particular data set has 10
people using each of two designs, and to ensure there is no “learning curve effect,”
we randomly had 5 of the participants use design 1 irst and 5 of the participants use
design 2 irst. The 20 data points—recall that these data represent 10 participants
using each of the two designs—are in
Table 3.1
.
As you can see in
Table 3.1
, some of the participants were very quickly illing out
the form (e.g., participants 1 and 10, who required relatively little time to perform
Table 3.1
Task Completion Data (in minutes) for Two Competing Designs
Participant #
Design 1
“The Long Scroller”
Design 2
“The Wizard”
1
5.5
6.2
2
8.8
9.2
3
27.2
29.7
4
12.9
13.8
5
13.8
15.9
6
5.1
4.9
7
10.4
15.7
8
15.6
16.3
9
25.6
27.2
10
3.9
3.7
Mean
12.88
14.26
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