Question

Authors in the New England Journal of Medicine investigated a possible link between Zika virus and microcephaly (or other fetus developmental abnormalities) and researchers collected the following data from Rio de Janeiro state in Brazil (data from March 2016):

	Baby with microcephaly	Baby without microcephaly	Row totals
Pregnant mum with Zika	12	30	42
Pregnant mum w/o Zika	0	16	16
Column totals:	12	46	58

Test for independence between maternal Zika virus infection and a baby’s microcephaly. Report here the test you are using, the p-value you get, and the conclusion you come to

Answer 1

H_o: Maternal Zika virus infection and a baby’s microcephaly are independent.

H_a: Maternal Zika virus infection and a baby’s microcephaly are not independent.

For this analysis, let the significance level be 0.05. Using sample data, we will conduct a chi-square test for independence.

Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the  degrees of freedom, we determine the P-value.

DF = (r - 1) * (c - 1) = (2 - 1) * (2 - 1) = 1 (r and c denotes the row and column).

Expected frequencies are,

E_r,c = (n_r * n_c) / n
E_1,1 = (42 * 12) / 58 = 8.689655
E_1,2 = (42 * 46) / 58 = 33.31034
E_2,1 = (16 * 12) / 58 = 3.310345
E_2,2 = (16 * 46) / 58 = 12.68966

Chi-square test statistic,

Χ² = Σ [ (O_r,c - E_r,c)² / E_r,c ]
Χ² = (12 - 8.689655)²/8.689655 + (30 - 33.31034)²/33.31034 + (0 - 3.310345)²/3.310345 + (16 - 12.68966)²/12.68966
= 5.764

P-value = P(Χ² > 5.764, df = 1) = 0.0164

Since p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that there is significant evidence that Maternal Zika virus infection and a baby’s microcephaly are not independent.