Interpreting p-value < 2.2e-16 in R

Question

I am trying to check variable importance of this gender variable. I know if p value is less than 0.05 then its important otherwise not but what is it's giving p-value < 2.2e-16. I have tried other methods too but giving the same for all of the categorical variable. I have pasted output for only one variable. SO, how to interpret this. (variable to be considered or not).

Frequency of my data points

 table(data$gender,data$target)

 Output: 
          N       Y
  F 2107566 2560932
  M 1307442 1567399
  U       3      16

To test statistical significance score:

chisq.test(table(data$gender,data$target))

Output:

        Pearson's Chi-squared test

    data:  table(data$gender, data$target)
    X-squared = 86.9407, df = 2, p-value < 2.2e-16

Note : I think one of the possible reason might be because of 7.5 million rows. So, will this be solved by sampling the data for checking the significance.

This means $p< 2.2*10^{-16}$ and is effectively close to zero (actually numerically undistinguishable from 0). Do you also ask how to interpret such a small p-value? There are many questions here asking that very thing. — Momo, Sep 23 '15 at 21:29
`<2.2e-16` means $0.00000000000000022$. It is (very much) less than $0.05$. On a different note, what kind of gender is `U`? — gung - Reinstate Monica, Sep 23 '15 at 21:31
Relevant: http://stats.stackexchange.com/questions/78839/how-should-tiny-p-values-be-reported-and-why-does-r-put-a-minimum-on-2-22e-1 — Glen_b, Sep 24 '15 at 02:05
@gung Either it's "unknown" for missing data, or it's some indicator for nonbinary genders. New Zealand officially recognizes several genders, for example. — Sycorax, Sep 24 '15 at 02:53

score -1 · Answer 1 · answered Sep 23 '15 at 22:12

-1

Important parts of the Q is answered. That p-value enables you to undoubtedly report on whether your hypoethsis is true or not. It is far more better than when p-value is at the critical level something like 0.05

answered Sep 23 '15 at 22:12

Ahmed Nur Osman

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1
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hi, Still I am confused about Whether to consider this variable or not. – Vignesh Prajapati Sep 23 '15 at 23:20
@VigneshPrajapati Did you not understand gung's first comment? – Glen_b Sep 24 '15 at 03:53
@Glen_b, I did. But again I have confusion is that if <2.2e-16 is less than 0.05 then why its giving the same value for all of my categorical value. Even I check it for my index no (user_id) its giving me same value. – Vignesh Prajapati Sep 24 '15 at 12:40
The "<2.2e-16" isn't a value but a range of values. Because you have huge sample sizes (7.5 million?) you should not be surprised that the p-values are very low. – Glen_b Sep 24 '15 at 13:10
So, please answer my quick question. Should I consider those variable or not ? – Vignesh Prajapati Sep 24 '15 at 14:40
I am asking because its also giving the same result for some bad/independant variables. – Vignesh Prajapati Apr 02 '16 at 10:28

Interpreting p-value < 2.2e-16 in R

Frequency of my data points

To test statistical significance score:

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