Standard deviation of 0,1 variable

[Joseph Hoffman]

Dear SPSSXL members,
  I have a simple question about the standard deviation of a 0,1 dummy
variable. I created a variable X that had only two values, 0 or 1.  Using
SPSS 15, I calculated the mean in my data set to be .7442, N = 172, and
standard deviation .43759.
Shouldn't the standard deviation of a 0, 1 variable with mean p be given
by square root of pq, where q = 1-p? If so, square root of pq for p =
.7442 gives .43631.  Why isn't this equal to the standard deviation given
by SPSS?  What am I forgetting here?

THanks for any suggestions!

Joe Hoffman

Joe Hoffman
Data Analyst
Research Institute on Addictions
State University of New York at Buffalo
1021 Main Street
Buffalo NY 14203
phone [phone]
FAX [phone]
e-mail  [hidden email]

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[Baker, Harley]

Joe,

The formula you use to calculate the SD of a dichotomously scored variable
(0,1), p*q, where q = 1 - p, is a population-based SD with N in the
denominator. SPSS calculates SD with N - 1 in the denominator. To see this,
apply the N/(N-1) correction factor to your calculation of the SD as
follows:

 p*q*sqrt(N/(N-1)), in this case

(.43631)*sqrt(172/171) = (.43631)*(1.00292) ~ .43758, which is what SPSS
delivers after rounding is taken into account.

Harley

Dr. Harley Baker
Associate Professor and Chair, Psychology Program
Chief Assessment Officer for Academic Affairs
California State University Channel Islands
One University Drive
Camarillo, CA 93012

805.437.8997 (p)
805.437.8951 (f)

[hidden email]

> From: Joseph H Hoffman <[hidden email]>
> Reply-To: <[hidden email]>
> Date: Tue, 11 Dec 2007 16:54:18 -0500
> To: <[hidden email]>
> Subject: Standard deviation of 0,1 variable
>
> Dear SPSSXL members,
>   I have a simple question about the standard deviation of a 0,1 dummy
> variable. I created a variable X that had only two values, 0 or 1.  Using
> SPSS 15, I calculated the mean in my data set to be .7442, N = 172, and
> standard deviation .43759.
> Shouldn't the standard deviation of a 0, 1 variable with mean p be given
> by square root of pq, where q = 1-p? If so, square root of pq for p =
> .7442 gives .43631.  Why isn't this equal to the standard deviation given
> by SPSS?  What am I forgetting here?
>
> THanks for any suggestions!
>
> Joe Hoffman
>
> Joe Hoffman
> Data Analyst
> Research Institute on Addictions
> State University of New York at Buffalo
> 1021 Main Street
> Buffalo NY 14203
> phone [phone]
> FAX [phone]
> e-mail  [hidden email]
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD

=====================
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[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
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For a list of commands to manage subscriptions, send the command
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