Achievement Score Scale Mean Shift Tool

Description

z = (rawScore-sourceMean)/sourceSd; scaledScore = targetMean+z*targetSd.

Numeric score transformations can reverse a scale, map anchors or change its mean and standard deviation. Such arithmetic does not establish equal category spacing, comparable constructs or statistical equating between assessments.

z = (rawScore-sourceMean)/sourceSd; scaledScore = targetMean+z*targetSd.

When to use this tool

Use Achievement Score Scale Mean Shift when checking an explicit scale or anchor transformation.

How to use the tool and how it works

Enter rawScore, sourceMean, sourceSd, targetMean, targetSd. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read z, scaledScore. Use the output convention below.

Require positive sourceSd and targetSd. z = (rawScore-sourceMean)/sourceSd; scaledScore = targetMean+z*targetSd.^[1]

Input field	Meaning and units	Accepted input
rawScore	Raw Score	Required. Finite number.
sourceMean	Source Mean	Required. Finite number.
sourceSd	Source Sd	Required. Finite number; strictly above 0.
targetMean	Target Mean	Required. Finite number.
targetSd	Target Sd	Required. Finite number; strictly above 0.

Output field	Interpretation	Returned shape
z	Z	Required. Finite number.
scaledScore	Scaled Score	Required. Finite number.

json

{
  "input": {
    "rawScore": 70,
    "sourceMean": 50,
    "sourceSd": 10,
    "targetMean": 100,
    "targetSd": 15
  },
  "output": {
    "z": 2,
    "scaledScore": 130
  }
}

Limitations and assumptions

This is a linear mean/SD transformation, not percentile mapping, nonlinear equating or proof the source and target tests measure the same construct.
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

Use appropriate measurement validation or equating methods before treating transformed scales as interchangeable.

References

Calculation and input contract: educational-psychology/achievement-score-scale-mean-shift — tool.io

Similar or alternative tools

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