Likelihood Ratios and Statistical Tests
In the first question, we make valid conclusions on the given likelihood ratio tests. The question that follows involves using a sample size to estimate parameters like the mean, standard deviation, and the standard error of the mean. What's more, we find the confidence interval of the mean and recommends a sample size suitable for finding the mean value under given conditions
Likelihood Ratios
Q4.1 The following table shows the Likelihood ratio for test positive and likelihood ratio for test negative of 3 biomarkers to diagnose Disease A. Answer the following question.
Likelihood Ratio
| Test | Test Positive | Test Negative |
| Biomarker 1 | 2.4 | 0.3 |
| Biomarker 2 | 5.7 | 0.6 |
| Biomarker 3 | 1.07 | 0.9 |
- (i) Which test/biomarker would be the best to rule in Disease A?
Biomarker 2
(ii) Which test/biomarker would be the best to rule out Disease A?
Biomarker 1
(iii) Which test/biomarker is the least useful test for both rulings in and ruling out disease A?
Biomarker 3
Statistical Estimation Using Tests
Q5.1 You would like to estimate the birth weight and rate of low birth weight(<2.500kg) of Chinese male babies in Hong Kong. Worksheet A provides the birthweight of boys delivered in Hospital A in Hong Kong. Provide answers for the following. Give answers to 3 decimal places.
- (i) What is the sample size?
The sample size is 200
(ii) What is the mean and its standard deviation?
The mean is 3.077 and the standard deviation is 0.467
(iii) Standard Error of the mean
The standard error of the mean is 0.033
(iv) Margin of error for the mean at the 95% confidence level
Margin of error = 1.96 * 0.467/√200
= 1.96 * 0.033
= 0.065
(v) 95% confidence interval of the mean
95% C.I for mean
= (3.077 – 0.065, 3.077+0.065)
= (3.012, 3.142)
(vi) What is the sample size required in a survey to assess the mean value with an error at half of the current error?
The sample size is based on confidence level, the larger the required confidence level, the higher the sample size.