Modified Z Score Calculator
Calculates the common MAD-based modified z score for a selected observation. The form displays 0.6745(x−median)/MAD beside modified z score, using a worked condition that can be recalculated with the labeled inputs.
Enter the source values when the result is reused
Modified z score
The question behind modified z score
The modified z score page calculates the common MAD-based modified z score for a selected observation.
Modified z score is limited to the statistical quantity named by the result panel. The modified z score calculation does not silently add a population, time horizon, causal direction, or decision threshold that is absent from the fields.
How the inputs shape modified z score
- Reference values: For modified z score, the displayed reference values sequence is 12, 15, 18, 18, 21, 24, 27, 30. Preserve reference values order when modified z score depends on pairing, lag, rank, or time position, and distinguish an observed zero from a missing reference values entry.
- Value to score: For modified z score, the worked value for value to score is 30 units. Treat the value to score entry (30 units) explicitly as a count, proportion, rate, estimate, or model parameter before comparing modified z score conditions.
The entries used for modified z score must refer to one coherent analysis condition. Combining incompatible populations, periods, or measurement definitions can produce valid modified z score arithmetic for a nonexistent study.
Following the modified z score relationship
For modified z score, match every symbol in the relationship to a labeled field before substituting numbers. Modified z score is reported in standard deviations.
While checking modified z score, use reference values observations from one defined analysis set rather than totals copied from incompatible groups.
Checking the displayed example
The default modified z score condition is Reference values = 12, 15, 18, 18, 21, 24, 27, 30, Value to score = 30 units.
The example value 30 has a modified z score near 1.57.
The live calculator reports Modified z score 1.5738333 · Median 19.5 · MAD 4.5. Repeating one intermediate step from 0.6745(x−median)/MAD provides a fixed modified z score reference check for later code changes.
What the modified z score arithmetic assumes
MAD equal to zero makes the score undefined; the cutoff used for screening belongs to the analyst, not the calculator.
For modified z score, robust and rank-based methods reduce sensitivity to particular assumptions but do not make the sampling design, independence, ties, or missing values irrelevant.
A nearby method may answer the next question: robust z score.
How to interpret the modified z score output
When interpreting modified z score, document tie handling, score convention, and the population feature the method targets before comparing implementations.
As a second check for modified z score, outliers, ties, ordering, and missing entries can affect modified z score even when the number of observations stays unchanged.
Mistakes to avoid in the modified z score setup
Before accepting modified z score, compare every entered value with its label, unit, and allowed domain after reading the printed relationship from left to right.
For modified z score, do not substitute zero for an unobserved value; missingness and a measured zero describe different data.
Another modified z score failure occurs when a rounded output is reused as though it were the original measurement. Carry guard digits through calculations that depend on modified z score, then round only the reported value.
Reporting modified z score reproducibly
Report modified z score using 0.6745(x−median)/MAD, followed by the entered values, units, exclusions, and analysis date. Name the modified z score population or dataset boundary instead of leaving it implicit.
Keep the full calculator output with the record, including Modified z score 1.5738333 · Median 19.5 · MAD 4.5. A later modified z score review can then distinguish a changed input from a different convention or software implementation.
Questions about modified z score
What should be saved with modified z score?
Save the entered values and units for reference values, value to score, along with the analysis date, exclusions, software or formula version, and the relationship 0.6745(x−median)/MAD. That record is sufficient to rebuild this specific modified z score calculation.
Does modified z score establish a causal or population conclusion?
No. The displayed modified z score value is conditional on the entered data and named method. The modified z score design, measurement process, and assumptions determine what can be concluded beyond those values.