Description
Calculate a paired difference under an explicit reference direction.
Statistical summaries depend on weights, reference origins, denominator definitions and sign conventions. A squared deviation about an arbitrary origin is not automatically a variance, and a scale label does not studentize a residual. Keep the stated measurement and model conventions attached to a quantity before comparing or interpreting it.
Calculate a paired difference under an explicit reference direction.
When to use this tool
Use Paired Difference Reference Sign when you already have firstObservation, secondObservation, secondMinusFirst and need to calculate a paired difference under an explicit reference direction.
How to use the tool and how it works
- Enter firstObservation, secondObservation, secondMinusFirst. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read difference. Use the output convention below.
Return second-first when secondMinusFirst=true, otherwise first-second, using compatible units.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstObservation | First Observation | Required. Finite number. |
| secondObservation | Second Observation | Required. Finite number. |
| secondMinusFirst | Second Minus First | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| difference | Difference | Required. Finite number. |
{
"input": {
"firstObservation": 3,
"secondObservation": 8,
"secondMinusFirst": true
},
"output": {
"difference": 5
}
}Limitations and assumptions
- No pairing, uncertainty, effect standardization or statistical significance is established.
- 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Calculate the full weighted statistic from all observations and its defined centering and normalization. Consult the original model or reporting method for studentization and effect-size conventions, keeping a supplied scale label separate from a computed statistical quantity.
References
Similar or alternative tools
- Effect Size Signed Reference Change
Reverse a supplied effect size's reference sign when requested.
- Proportion Observation Denominator Type
Record the denominator-type convention of a proportion statistic.