How to calculate probability?

Question

[agata88]

Hi all!

I have some statistics which include diagnostic data. Here is an example of my stats. Women with cancer = 57 (57%) Women without cancer = 43 (43%) The sum = 100 (100%)

Can I calculate the p-value for those results? Is there any statistic test that I can use? Or could I just say that the difference between groups is not statistically significant (p-value =0,57, or p-value = 0,43)? I am very sorry for trivial question. Until today I thought that there is no possibility to do statistics test with calculated p-value for such data. Maybe I am wrong. What do you know about that?

Best,

Agata

[Devon Ryan]

Any p-value would be based off of some model of what one would expect to find. So you'd need to give more information about that.

[agata88]

I don't have any other information. I found that the calculation of Z-score, and then probability can be used to confirm the statistical difference between this two values. Do you agree with that?

[Devon Ryan]

Making a Z score out of that would be meaningless. If you don't have any expectations about what "difference" or "no difference" would look like there you can't determine a p-value.

[russhh]

In this ssetting you'd need to know how many women were in your sample before you can ascribe significance. If you've only screened 7 women, your p-values will be very different than if you've screened 70

[agata88]

No, I screen 100 women, and I have information that 57 of them have cancer and the rest don't have. This is of course the example of data.

[russhh]

Sorry, but since you presented the percentages, that was hardly obvious

Answer 1

[Michael]

Just asking for a p-value without a statistical test and 0-hypotheses or null-distribution in mind is meaningless. There is no p-value for the result itself, that is because the result is a single observation, its singular probability is 1 if you like.

However, you could test for the alternative hypotheses that your sample is different from the prevalence in the general female population using e.g. fisher's exact test, and you will get a very low p-value for obvious reasons, meaning cancer is overrepresented in your sample.

[agata88]

Thank you, you have confirmed my suspicions.

Answer 2

[Carlo Yague]

I understand (I guessed at least) that you want to test the relatioship between the sex (being a woman or a man) and having a cancer. You could try a fisher's exact test then :

>my_data= matrix(c(28,60,47,73), ncol=2, dimnames=list(c("MAN", "WOMAN"), c("CANCER", "HEALTHY")))
>my_data

      CANCER HEALTHY
MAN       28      47
WOMAN     60      73

>fisher.test(my_data)

    Fisher's Exact Test for Count Data

data:  matrix(c(28, 60, 47, 73), ncol = 2)
p-value = 0.308
alternative hypothesis: true odds ratio is not equal to 1

EDIT : frenquencies (the percentages you refer to in your question) and p-values are very different concepts. I suggest you read a bit about it and basic statistics before going further in your analysis.

[Michael]

There is no male in that trial if i understood correctly.

[Carlo Yague]

IMO, the question makes sense only if there are males in the study. Otherwise what is the question the OP wants to answer ? But I might be wrong, this is just my guess.

[Devon Ryan]

My guess would be that either there's a drug trial or some selection of patients and OP is wondering if the high percentage of cancer patients is significant. One would then need a baseline expectation, of course, which isn't exactly forthcoming given OPs lack of details.

[agata88]

Yes, there is no male in situation from the question. And I agree that I cannot calculate probability for that two values. Thank you.

What if we have a population of 394 people,where:

number of woman = 197 number of men = 197

Now I have information that population of woman involve 122 observables with cancer and population of man -125. What test statistic would you use to show significant differences between occurrence of cancer in men and woman in population? Do you suggest in that case to use Fisher Exact test?

And also, is there a meaning for comparing woman population vs whole population etc. ?

[Carlo Yague]

In that case, my answer above can apply. Comparing woman population vs whole population (women vs not women) is usually the same as comparing women vs men (unless your population is composed of more than men and women).

But now I'm confused. Are there males in your data or not ?

[Michael]

I am just guessing, but maybe this is just some hypothetical setting or exam question.

[agata88]

In first question there are not male, in second there are male and woman :) Thanks!