Oddsratio Symmetric Table Cell Factor Tool

Description

For positive cells a,b,c,d and a positive scaleFirstRow return oddsRatio=(a*d)/(b*c) and scaledOddsRatio=(a*scaleFirstRow*d)/(b*scaleFirstRow*c).

A binary probability p corresponds to odds p/(1-p). Evidence updates can multiply prior odds by a likelihood ratio, or normalize likelihood-weighted priors. Likelihood densities can exceed one, while event probabilities cannot; compatible observation definitions and measurement bases matter before combining them.

For positive cells a,b,c,d and a positive scaleFirstRow return oddsRatio=(a*d)/(b*c) and scaledOddsRatio=(a*scaleFirstRow*d)/(b*scaleFirstRow*c).

When to use this tool

Use Oddsratio Symmetric Table Cell Factor when you need the stated odds conversion, binary update, or normalization of compatible supplied weights.

How to use the tool and how it works

Enter a, b, c, d, scaleFirstRow. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read oddsRatio, scaledOddsRatio. Use the output convention below.

For positive cells a,b,c,d and a positive scaleFirstRow return oddsRatio=(a*d)/(b*c) and scaledOddsRatio=(a*scaleFirstRow*d)/(b*scaleFirstRow*c).^[1]

Input field	Meaning and units	Accepted input
a	A	Required. Finite number; strictly above 0.
b	B	Required. Finite number; strictly above 0.
c	C	Required. Finite number; strictly above 0.
d	D	Required. Finite number; strictly above 0.
scaleFirstRow	Positive multiplier applied to both first-row cells a and b.	Required. Finite number; strictly above 0.

Output field	Interpretation	Returned shape
oddsRatio	Odds Ratio	Required. Finite number.
scaledOddsRatio	Scaled Odds Ratio	Required. Finite number.

json

{
  "input": {
    "a": 2,
    "b": 3,
    "c": 4,
    "d": 6,
    "scaleFirstRow": 5
  },
  "output": {
    "oddsRatio": 1,
    "scaledOddsRatio": 1
  }
}

Limitations and assumptions

The algebraic row-scaling invariance can be affected by floating-point overflow or underflow. Cell orientation determines the ratio; no contingency-table inference is performed.
Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.

Alternative or Complementary methods

Use a complete likelihood model and an explicit hypothesis space when supplied weights cannot be justified independently. For extreme products, a log-domain calculation can reduce avoidable underflow.

References

Calculation and input contract: probability/oddsratio-symmetric-table-cell-factor — tool.io

Similar or alternative tools

Conditional Odds Joint Cell Crosswalk
Require joint and conditioning within zero through one and conditioning strictly greater than joint, then return odds=joint/(conditioning-joint).
Conditional Independence One Cell Residual
Require joint, leftGiven, rightGiven, and conditioningMass individually within zero through one; return residual=joint-conditioningMass*leftGiven*rightGiven.