Database Reference
In-Depth Information
SIDEBAR: THE USABILITY OF USING CHI-SQUARE
The chi-square test of independence was referred to a few decades ago as the chi-square-
contingency-table test. The latter name, not used very frequently nowadays, derives from the
fact that if two entities are not independent (here: having equal success rates), they can be said
to “have a contingency” between them.
Both Excel and SPSS perform the chi-square test of independence; however, each software
package has its own usability problems. In using Excel, you have to perform what are usually some
really simple calculations that Excel could easily have calculated; the calculations are usually not
particularly arduous, but on occasion can be, even though they are still “simple.” And, in SPSS, the
format you need to use to enter the data to implement the test is yet another pain in the you-know-
what. Don't blame the authors—neither one of us worked or consulted for Excel or SPSS. But don't
worry! We'll hold your hand every step of the way.
Let's begin with task 1, where 9 out of 10 participants were successful using the
Behemoth search engine versus the 3 who were successful using the Novix engine.
The hypotheses are now
H0:
p
1N=
p
1B
H1:
p
1N≠
p
1B
where, of course, N stands for Novix and B for Behemoth.
4.3.1
EXCEL
To do the chi-square test of independence in Excel, on any given task, you need to
irst specify what Excel calls your “actual range” and compute what Excel calls your
“expected range.”
SIDEBAR: JUMP RIGHT INTO EXCEL!
The easiest way to compute the “actual” ranges and “expected” ranges is to construct two charts,
as we explain on this page. You can do it in Word, Textedit, or any program that you prefer. But the
easiest might be to just type the simple tables right into Excel, since eventually you must get those
tables into Excel to run the chi-square analysis.
The “actual range” is just the number of successful and unsuccessful completions
for each task, using your task completion data (
Table 4.1
). You need to lesh out
the table by adding the failures for each engine. Of course, to accomplish that, just
subtract the passes from the total number of attempts (in this case, 10) (
Table 4.2
).
Next, we need to construct the “expected range” table. The “expected range” is the
pass/fail values that would be theoretically expected to occur if H0 is true (even though
these theoretical values are unlikely to exactly occur even when H0 is true and the true
p
's are the same.) An analogy would be that if we lip a hundred 50/50 coins, the theo-
retically expected number of heads is 50 (along with 50 tails), but the actual probability
of that exact result is somewhat small, a shade under an 8% chance!
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