Database Reference
In-Depth Information
We now describe the way to ind these conidence intervals, but must say that we
lament the fact that neither Excel nor SPSS has built-in modules that will compute
them for you (weep!).
The formula that is used for the adjusted Wald method is the standard normal
approximation formula for large sample sizes, with adjustments as described below.
SIDEBAR: BINOMIAL CONFIDENCE INTERVALS SHORTCUT
As much as enjoying calculating binomial conidence intervals, we'll admit it can be time consuming.
Therefore, you'll ind a nifty table at the end of this chapter that speed things up if your sample size is
anywhere from 1-15. (Lab usability tests are usually conducted with anywhere from 3-12 participants,
so you should be covered.) Simply ind your sample size (number of participants) along the top and work
your way down that column until you reach the number of successes for a particular task. For example,
say you have 6 out of 10 successful completions for a particular task. Work your way down from the
“10” column until you reach the “6” row. Find your binomial conidence interval, which is 0.31-0.83.
If you have a sample size over 15 (for example, while running a unmoderated usability study), you
can do the calculations as we've explained in this chapter. Sorry; the table had to stop somewhere! ☺
The standard normal approximation formula, with a sample size of “n” and a
sample proportion that passed of “p-bar” (analogous to X-bar of earlier chapters) is
depicted in expression (1)
1
:
p-bar±Z*SQRT([p-bar] * [1−p-bar]/n)
(4.1)
where
n = total number of trials (people)
p-bar = proportion of trials that were successes
Z = the Z-value corresponding to the desired conidence level (e.g., 95%, 90%)
And we will use this formula for conidence intervals when we have large sample
sizes. It should be noted that Z = 1.96 for a 95% conidence interval, which, tradi-
tionally, is the conidence level nearly always chosen. For a 99% conidence interval,
Z = 2.57, and for a 90% conidence interval, Z = 1.64.
However, when you have a small sample size, you adjust the values of p-bar and
n (as described below); this is the adjusted Wald method.
The adjustments are as follows:
First, we compute the adjusted proportion:
p
ADJ
=(n*p-bar+Z
2
/2)/(n+Z
2
)
Then, compute the adjusted sample size:
n
ADJ
=n+Z
2
The reader may note that the adjustments make a meaningful difference when
n is “small” but make virtually no difference when n is “large.” For example, with
n = 10 and p-bar = .4,
1
Traditionally, a sample size is considered suficiently large to use the routine normal distribution
formula (i.e., without the Wald adjustment) if both n*(p-bar) > 5 and also n*(1 - [p-bar]) > 5.
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