Significance of Handwashing Frequency

Date: 02/23/2002 at 01:11:30
From: Adam
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!

- Adam

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

Hi Adam,
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
From: Adam
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.!