From: phunt@interpac.net
Subject: Re: Comparing Mean
Date: Fri, 23 Apr 1999 02:32:46 GMT
Newsgroups: sci.math
To: pjlee@cyberway.com.sg
Keywords: t-test

In article <7fm7od$h52$1@nnrp1.dejanews.com>,
  pjlee@cyberway.com.sg wrote:
> Hi all, I was thought in school that you could never take two mean look at
> them and then make a judgement that one is higher than the other one without
> considering the standard deviation (performing a t-test).
>

I don't understand this.  Where is the other mean that you want to
compare with your sample mean?

The t-test will compare two means assuming that each distribution
is approximately normal, and that you know both means and variances,
along with the number of items in each sample.

>
> I conducted a survey which would require a group of people to respond to a yes
> or a no answer. At the end of the day I compiled the result and realized that
> there are more yes than no answer. Could I take this result at face value or
> should I perform a t-test?
>

The t-test can yield a confidence interval for the true population
mean based on your sample mean, when the sample variance is given,
and the underlying distribution is assumed to be approximately
normal.

If you are taking binomial samples, and the number of samples is
greater than 20, then the binomial approximation to the normal
distribution is excellent.  More exactly you'll want n*p >= 5,
where n is the number of samples, and p is the sample proportion
(successes).  The sample variance will then be var = p*q/n, where
q = (1 - p).

Then, your problem is to estimate the true population proportion
(probability) P, and to do so you'll have to assume that the true
population variance is the same as var, your sample variance.

The t-test is appropriate when the conditions above are satisfied.

/ph

- - - - - -

> Secondly, I used to read in magazines and papers that this year we saw a 17%
> increase in the number of...could I safely assume that they had performed a
> statistical significance test? Or are they reading the result at face value
> using only the mean and paying no attention to the standard deviation?
>
> Thanks in advance guys/gals.
>
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