Observed Expected Ratio Calculator

Calculate the O/E ratio, confidence intervals, and statistical significance for your research data

Data Input

Observed Events (O):

The actual number of events observed in your study

Expected Events (E):

The expected number of events based on reference rates

Confidence Level:

Custom Z-Score:

Calculation Method:

Advanced Options

Population Size (for rates):

Enter if you want to calculate rates per 1000 or similar

Rate Multiplier:

E.g., 1000 for rates per 1000 population

Decimal Places:

O/E Ratio Results

Observed/Expected Ratio

Standardized Ratio

Statistical Significance
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Confidence Interval

Enter your data to calculate the confidence interval.

Interpretation Guide

O/E = 1

Observed equals expected. No difference from reference.

O/E > 1

Observed exceeds expected. Possible excess risk.

O/E < 1

Observed is less than expected. Possible protective effect.

📊 Statistical Reference

Z-Score	Confidence Level	p-value Threshold
1.645	90%	0.10
1.960	95%	0.05
2.576	99%	0.01
3.291	99.9%	0.001

Note: These are common thresholds for statistical significance testing.

📚 Methodology Notes

📉

Poisson Distribution

Appropriate for rare events. Assumes variance equals mean. Best for small expected counts.

📊

Normal Approximation

Good for larger counts (O > 10). Uses z-scores for CI calculation. More conservative.

🧮

Exact Binomial

Most accurate for small samples. Computationally intensive. Provides exact p-values.

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Note: This calculator provides statistical estimates for research purposes. Results should be interpreted by qualified professionals familiar with the specific context of the data. The tool assumes appropriate study design and accurate input data.