Description
Separate total absolute deviations below and above an explicit reference, retaining asymmetric loss evidence without estimating a distribution.
A descriptive statistic depends on what is counted, how observations are weighted, and which reference or denominator is used. Removing observations differs from replacing them at cutoffs, and a ratio of totals differs from a mean of individual ratios. Keep those conventions and measurement units explicit when comparing results.
Separate total absolute deviations below and above an explicit reference, retaining asymmetric loss evidence without estimating a distribution.
When to use this tool
Use this tool to separate total absolute deviations below and above an explicit reference, retaining asymmetric loss evidence without estimating a distribution.
How to use the tool and how it works
- Enter values, reference using the field definitions below.
- Run the operation. Correct input errors before interpreting an output.
- Read result.below, result.above. Use the ordering, boundary rules and absence conditions described below.
Sum reference − value only below the reference, and value − reference only above it, returning separate nonnegative totals.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| values | Finite observations in the measurement units used by reference or cutoffs. | Dense list of at most 128 finite numbers; integer/shape constraints above also apply. |
| reference | Caller-supplied center/reference in the observations’ units. | A finite number satisfying the operation’s stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the named fields below. |
| result.below | Sum of reference-minus-value differences below the reference. |
| result.above | Sum of value-minus-reference differences above the reference. |
{
"input": {
"values": [
1,
2,
9
],
"reference": 3
},
"output": {
"result": {
"below": 3,
"above": 6
}
}
}Limitations and assumptions
- These are unnormalized directional totals; values exactly at the reference contribute zero.
- Use consistent units within each measured list and its reference/cutoffs. Ratios carry numerator units divided by denominator units unless those units cancel. Ordinary floating-point arithmetic is used; input validation does not establish statistical suitability.
- Every declared top-level input field is required and unexpected fields are rejected. Ordinary strings are limited to 8,192 UTF-16 code units and lists to 128 entries, with tighter operation-specific bounds where stated. JSON text has bounded nesting and node counts.
- Numeric outputs must be finite and no larger in absolute magnitude than the safe-integer limit; operations returning exact large integers use decimal text. Positions are zero-based and spans end exclusively unless the operation explicitly states a different convention.
Alternative or Complementary methods
Check the descriptive convention and denominator before comparing results. Use a separate inferential model when you need uncertainty, significance, causal interpretation or population estimates.
References
Similar or alternative tools
- Mean Absolute Deviation from Reference
Compute mean absolute deviation about a caller-supplied reference; existing mean-absolute-deviation centers on the sample mean instead.
- Median Absolute Deviation from Reference
Compute median absolute deviation about an explicitly supplied reference, not automatically the sample median and not normal-consistency scaled.