Your Chi square test is not correct. You need to provide the counts as a table or matrix, not as two separate vectors. Because you have very small expected values for half of the cells, you need to use simulation to estimate the p-value:
results <- chisq.test(diagnosis[, 2:3], simulate.p.value=TRUE)
The overall table is barely significant at .05. The chisq.test function returns a list including the original data, the expected values, residuals, and standardized residuals. The manual page describes these (?chisq.test) and provides some citations for more details.
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