Re: Standard Deviation and "False Alarm" Rate

On 8 Sep 2006 15:12:57 -0700, bodybuilder@xxxxxxxxxxxxxx wrote:

Hello. I am a stats novice and have a question regarding how the
percentages quoated in the following statement were derived:

"It is important to note that even when there is no significant
difference between a student's score and the class average, tehse two
values will still differ by 0.5 or more standard deviations 35 percent
of the time, and by 1 or more standard deviations 24 percent of the
time. This represents a high percentage of "false alarms," which can
lead to inaccurate conclusions."

No additional information is provided. I am trying to determine how to
derive the 35% and 24% quoted above. Any assistance you can provide
would be greatly appreciated! Thank you!

Usually, such claims make use of the normal distribution.

This one misuses the normal distribution in a unique way -
I think I found where the writer got his number

The proper numbers would be that 31% score more than
0.5 SD above the mean, and another 31% score that much
below it, 62% in all. And 16%+16%, or 32% score, more
than 1 SD from the mean.

A handy table of the normal distribution shows me that the
numbers from the writer, 0.35 and 0.24, happen to be the
y-ordinates for the normal curve, at 0.50 and 1.0 respectively.
It seems that he looked them up, and used the wrong column.


--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.

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