Question

In: Statistics and Probability

In a study to determine whether an association exists between maternal rubella and congenital cataracts, samples...

In a study to determine whether an association exists between maternal rubella and congenital cataracts, samples of 20 children with congenital cataracts and 25 children without congenital cataracts were selected. The mother of each child was asked whether she had rubella while carrying the child. The data are given below. Assume that all z-based methods are valid.


RUBELLA	CATARACTS
Frequency Row Pct	1_YES	2_NO	Total
1_YES	14 58.33	10 41.67	24
2_NO	6 28.57	15 71.43	21
Total	20	25	45

Statistic	DF	Value	Prob
Chi-Square	1	4.0179	0.0450
Likelihood Ratio Chi-Square	1	4.0979	0.0429
Continuity Adj. Chi-Square	1	2.9029	0.0884
Mantel-Haenszel Chi-Square	1	3.9286	0.0475
Phi Coefficient		0.2988
Contingency Coefficient		0.2863
Cramer's V		0.2988

Column 1 Risk Estimates
	Risk	ASE	95% Confidence Limits		Exact 95% Confidence Limits
Row 1	0.5833	0.1006	0.3861	0.7806	0.3664	0.7789
Row 2	0.2857	0.0986	0.0925	0.4789	0.1128	0.5218
Total	0.4444	0.0741	0.2993	0.5896	0.2964	0.6000

Difference	0.2976	0.1409	0.0215	0.5737
Difference is (Row 1 - Row 2)

What are the null and alternative hypotheses? Be sure to define any symbols that you use.

Expert Solution

The Chi-Square test of independence is used to determine if there is a significant relationship between two nominal (categorical) variables. The frequency of each category for one nominal variable is compared across the categories of the second nominal variable.

First we have to calculate the expected value of the two nominal variables. We can calculate the expected value of the two nominal variables by using this formula:

Where

= expected value

= Sum of the ith column

= Sum of the kth row

N = total number

After calculating the expected value, we will apply the following formula to calculate the value of the Chi-Square test of Independence:

= Chi-Square test of Independence
= Observed value of two nominal variables
= Expected value of two nominal variables

Null hypothesis: Assumes that there is no association between maternal rubella and congenital cataracts

Alternative hypothesis: Assumes that there is an association between maternal rubella and congenital cataracts

orchestra answered 2 years ago

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