False Chi-Square Significance? I am a newcomer to Chi-Square analysis. I have the following dataset:
            Healthy      Disease
Females     537653       4467
Males       362013       3365

My goal is to calculate whether there is any significant difference between the Females and Males in terms of getting the Disease.
But the Chi-square results confuse me (p=1.026e-06) because initially, when I was looking at the actual numbers, I couldn’t imagine there would be any significant difference between the groups, but obviously there is. How come the p value is so low? The expected numbers are:
            Healthy      Disease
Females     537441.33    4678.67
Males       362224.67    3153.33

By just looking at the datasets, I would say that the difference between high significance (the first dataset) and low significance (the second dataset) is extremely small. Can this be explained?
 A: Conducting a hypothesis test --- that is, determining the p-value --- is only one part of a statistical analysis.
Another important part is looking at the effect size.  Here, you might use  phi, which is an effect size statistic used for a 2 x 2 contingency table (where you might use a chi-square test of association).  Here, phi is about 0.01. According to a standard interpretation †, this would be a very small value. 
This is what your intuition is noting:  The p-value suggests that there is a small probability that data as extreme as yours would occur by chance, but phi is telling you that the counts don't differ much from expected values.  This might be conveyed with a bar plot of proportions of disease for each of Females and Males.  
Another effect size statistic that would be appropriate in this case is odds ratio.
A third part of the broader analysis is thinking about the practical implications.  This might include external information, such as costs.  Here, you would need to consider if the difference in proportions between Females and Males (0.92% vs. 0.82%) is meaningful in this context.     

† Jacob Cohen, 1988, Statistical Power Analysis for the Behavioral Sciences, is often cited for standard interpretations of common effect size statistics.  But it should be understood that the interpretation is always relative to the discipline and the specific problem.  A small change in proportions may matter a lot in matters of life and death, or, for example, in politics.
See also, "Measures of Association for Nominal Variables". (Caveat: my own webpage).

R code:
Input =("
            Healthy      Disease
Females     537653       4467
Males       362013       3365
")

Matrix = as.matrix(read.table(textConnection(Input),
                   header=TRUE,
                   row.names=1))

chisq.test(Matrix, correct=TRUE)

   # Pearson's Chi-squared test
   #
   # X-squared = 23.879, df = 1, p-value = 1.026e-06

library(psych)

phi(Matrix)

   # [1] 0.01

prop.table(Matrix, margin=1)

   #           Healthy     Disease
   # Females 0.9917601 0.008239873
   # Males   0.9907904 0.009209640

