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I have a 200 samples from a population, and I want the p-value to test for significance. What test should I use?

Is t-test ok? How do you determine what test to use?

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Significance of what? What hypothesis do you wish to test? –  onestop Jun 13 '12 at 16:51
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@onestop: If one were to be cynical, one could say that the hypothesis doesn't really matter: you can achieve whatever p-value you need if you're clever enough. That's the problem with p-values. (As I understand it.) –  Wayne Jun 13 '12 at 16:54
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@Wayne The problem with p-values? There are too many problems with p-values to fit in the margin of this post :) –  Michael McGowan Jun 13 '12 at 16:55
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If you ask about a t test it may be that you want to test equality of means. The t test would be appropriate for that if you can assume the two samples come from normal distributions with the same variance. it is robust to mild departures from normality and differences in variances that are not very large. So it can be applied a little more generally than what the required assumptions suggest. If the data are normal and the variances differ you can use Welch's test . This uses the Satterwaite approximate degrees of freedom for the approximating t distribution under the null hypothesis. –  Michael Chernick Jun 13 '12 at 17:00
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You still haven't been specific enough for any of us to give you an intelligent answer. Do you have two columns or more? Are you interested in whether the data in one column come from the same distribution as the data in another column? In that case you do something like a chi square test that the distributions do not differ. If you have two columns and just want to compare means then the t test and the others that I described for comparing means might be appropriate. If yuo have 3 or more columns a one-way analysis of variance or its nonparametric analogue might be appropriate. –  Michael Chernick Jun 13 '12 at 17:18

2 Answers 2

With the amount of information given the only real recommendation I can give is to use SnowsCorrectlySizedButOtherwiseUselessTestOfAnything (implemented in the TeachingDemos package in R, the eponym is more an acceptance of blame than a claim of credit).

If you are interested in testing the population mean then the t-test becomes a possibility (but if you are interested in the median, variance, etc. then you would need something else).

If you are interested in the mean and you know that the population is normal then the t-test is appropriate. If you don't know that the population is normal, but are willing to assume that it is not extremely skewed or has extreme outliers and are willing to live with an approximate p-value (with a sample size of 200 the approximation will be very close) then you can still use the t-test methods.

There are also other tests/tools that could be used as well.

But to really give decent advice we need to know more about what question you are trying to answer, what you know or are willing to assume about your population, and other information.

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+1 for describing an interesting (and amusing) teaching tool (and wrapper of the runif command). –  Jonathan Thiele Jun 13 '12 at 17:45
    
I want to know the p-value for a sample size of 250 with the disease, against those who has the disease and died, about 35 people, this is a subgroup. Is t-test ok? –  user1061210 Jun 14 '12 at 10:47
    
You still have not said anything about the variable that you want to compare (just how you are splitting into 2 groups). The smaller group is going to be much less robust to outliers and skewness than the orginial question suggested. It would probably be best for you to consult with a local statistician who can discuss the important questions with you in detail. –  Greg Snow Jun 16 '12 at 3:51

In your situation, I think the appropriate null hypothesis would be $\mu$=0 or $\mu=k$

The test statistic would be $t$=${\bar X-\mu }\over{s/\sqrt n}$

Let me summarize here, Given the population distribution is normal,

when you have only one group, you can test for the mean or/and the variance.

Test for the population mean will be different according to whether you know the population variance or not.

Test for the population variance will use Chi-squared distribution.

Test for the population mean and variance would use joint distribution of sample mean and variance.

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