Odds Ratio Calculator With P Value and Standard Deviation

Odds Ratio Formula:

\[ OR = \frac{a/b}{c/d} = \frac{ad}{bc} \]

Odds Ratio (OR):

Standard Error (log OR):

P-value:

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1. What is Odds Ratio?

The odds ratio (OR) is a measure of association between an exposure and an outcome. It represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\[ OR = \frac{ad}{bc} \] \[ SE(\ln(OR)) = \sqrt{\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d}} \] \[ \chi^2 = \sum \frac{(O - E)^2}{E} \]

Where:

a — Exposed with outcome
b — Exposed without outcome
c — Unexposed with outcome
d — Unexposed without outcome
O — Observed value
E — Expected value

Explanation: The odds ratio compares the odds of the outcome in two different groups, while the p-value assesses the statistical significance of this association.

3. Interpretation of Results

Details:

OR = 1: No association
OR > 1: Positive association (higher odds with exposure)
OR < 1: Negative association (lower odds with exposure)
P-value < 0.05: Statistically significant

4. Using the Calculator

Tips: Enter counts for all four cells (a, b, c, d) in the 2×2 contingency table. All values must be non-negative integers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between odds ratio and relative risk?
A: Odds ratio compares odds, while relative risk compares probabilities. They're similar for rare outcomes but differ for common ones.

Q2: How do I interpret the standard error?
A: The SE is for the natural log of OR. 95% CI = exp(ln(OR) ± 1.96×SE).

Q3: When should I use Fisher's exact test instead?
A: When sample sizes are small (any cell <5) or the data are very unbalanced.

Q4: Can I calculate OR for continuous variables?
A: No, OR is for categorical data. For continuous variables, consider logistic regression.

Q5: What if I have zero in one cell?
A: Add 0.5 to all cells (Haldane-Anscombe correction) to allow calculation.