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### Significance of Handwashing Frequency

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Date: 02/23/2002 at 01:11:30
Subject: Determining Significance of Handwashing Frequency

I'm doing an experiment for Psychology class. I went to a public
restroom and took data on how many people washed their hands both when
there was an observer present and when there wasn't. 25 people were
observed with a visible observer present, and 25 without. Out of the
people accompanied by an observer, 23 washed their hands and 2 did
not. When an observer was not present, 12 washed their hands and 13
did not.

I need to determine whether the absence of an observer (i.e. if the
bathroom-user is alone) makes a statistically significant difference.
I think I need to use a chi-squared test for this, but I don't know
how to do one. Could you please show me the procedure for doing one?
Thanks a lot!

```

```
Date: 02/23/2002 at 03:33:58
From: Doctor Schwa
Subject: Re: Determining Significance of Handwashing Frequency

your null hypothesis in this case is that people are equally likely to
wash their hands whether or not an observer is present.

Based on your data, the overall probability of handwashing is 35/50 or
70%.

Thus, in each case, you'd predict 70% of 25 would wash their hands:
17.5 people.

You can make a table:

ACTUAL    wash   not wash
observed   23       2
not obs.   12      13

PREDICTED wash   not wash
observed  17.5    7.5
not obs.  17.5    7.5

Now, in each of the 4 spaces, calculate (actual - predicted)^2, and
divide the result by the predicted number for that space. Then add up
those 4 numbers, and you'll have the chi-squared statistic.

In this case, there's one degree of freedom (once we figured out that
one 70% number, we could fill in the whole PREDICTED table). So, to
find out if the result is significant, compare it to a table of values
for chi-squared with one degree of freedom.

I hope that helps clear things up. If not, you should try searching
our Dr. Math archives for the keyword  chi-square .

http://mathforum.org/mathgrepform.html

You'll find a few more, different explanations of how to do this.

If that doesn't help, please write us back.

Enjoy,

- Doctor Schwa, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 02/24/2002 at 00:38:22
Subject: Determining Significance of Handwashing Frequency

Thank you very much for your help. My results turned out to be
significant at the 95% (p=.05) level. As a bonus, I can now boast to
my math and psychology teachers that I know something they don't.
Thanks a lot, Dr.!
```
Associated Topics:
High School Statistics

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