oddsRatio(O11, O12, O21, O22, CL)
Overview
The oddsRatio function calculates the odds ratio for a 2x2 contingency table, along with the confidence intervals and hypothesis testing for independence. It can be particularly useful in epidemiological studies and statistical analysis of categorical data.
Parameters
| Parameter | Type | Description | Default |
|---|---|---|---|
O11 |
Number | Count for group 1 with characteristic A. | - |
O12 |
Number | Count for group 1 without characteristic A. | - |
O21 |
Number | Count for group 2 with characteristic A. | - |
O22 |
Number | Count for group 2 without characteristic A. | - |
CL |
Number | Confidence level for the confidence interval of the odds ratio. | 0.95 |
Returns
| Return | Type | Description |
|---|---|---|
OR |
Number | The calculated odds ratio. |
rejectH0 |
Bool | Whether to reject the null hypothesis of independence. |
lowerCI |
Number | Lower bound of the confidence interval for the odds ratio. |
upperCI |
Number | Upper bound of the confidence interval for the odds ratio. |
Example
local O11 = 13
local O12 = 9
local O21 = 8
local O22 = 6
local CL = 0.95
local result = oddsRatio(O11, O12, O21, O22, CL)
print(result.OR, result.rejectH0, result.lowerCI, result.upperCI) -- Output will vary based on the input
Mathematical Background
The odds ratio OR is calculated as:
OR = \frac{(O11 / O12)}{(O21 / O22)}
The confidence interval for the odds ratio is calculated using:
\text{Lower bound} = e^{\ln(OR) - Z \times \sigma}
\text{Upper bound} = e^{\ln(OR) + Z \times \sigma}
where \sigma = \sqrt{\frac{1}{O11} + \frac{1}{O12} + \frac{1}{O21} + \frac{1}{O22}} and Z is the value from the inverse of the standard normal distribution corresponding to a 1- \alpha/2 confidence level.
The null hypothesis H0 is rejected if the confidence interval does not include 1.