Database Reference
In-Depth Information
SIDEBAR: SO THAT'S WHAT THE LAW OF AVERAGES REALLY MEANS
The numbers in this chapter exhibit the principle that when we average more , rather than fewer ,
results, we tend to have a higher chance of getting a resulting sample mean nearer to the true (popu-
lation) mean. Actually, this is an intuitive way to explain the often heard, not so often understood,
phrase, “the law of averages.” Honestly, we realize that nobody needed this topic to intuitively know
that the more values averaged, the higher the likelihood of obtaining a more accurate result—and a
more accurate result equates to a result that is more likely to be nearer to the true (population) value
we wish to get an idea about. But, sometimes you need to state the obvious!!
1.2.4 THE CENTRAL LIMIT THEOREM
There is another concept that needs some explanation, since it is the primary reason
that the normal distribution is so important—probably 100 times more important
than whatever shaped curve is in second place!
We're talking about the “Central Limit Theorem.” It says, in simpliied terms,
that for any data you would ever see, as we average a larger and larger number of
sample values, the resulting sample mean, denoted “X-bar,” converges to follow a
normal curve, no matter what the shape of the individual X curve before we take
means . (Technically, the data values need to be independent and from the same dis-
tribution, but this is usually the case in UX work, anyway.)
SIDEBAR: X-BAR
A bar over a quanti ty is traditionally used to denote a sample mean. We'll write “X-bar” in this text,
and actually write X in equations.
For example, if we were to take many groups of 10 data values, each—that is,
n = 10—and take the mean of each of these samples, and then draw a histogram of
the means, it would look very much like a normal curve, regardless of what the his-
togram would look like if we drew a histogram of the individual values ( which may
or may not be a normal curve!! ).
We do need to clarify that if the sample size is only 10, the resulting histo-
gram for the means may deviate somewhat from a normal curve, since n = 10 is
not that large a sample, even though it is what you may be dealing with as a UX
researcher; i.e., usability studies are usually conducted with a sample size of 5-8.
However, as a practical matter, you should assume that the mean, even for n = 10,
will follow a normal distribution/curve, since the difference from a normal curve
is unlikely to be material.
 
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