Description
width = upper-lower; intervals = width/step; aligned = Number.isInteger(intervals).
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.
width = upper-lower; intervals = width/step; aligned = Number.isInteger(intervals).
When to use this tool
Use Teacher Rating Scale Width when checking an explicit scale or anchor transformation.
How to use the tool and how it works
- Enter lower, upper, step. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read width, intervals, aligned. Inspect aligned before interpreting the associated values.
Require lower <= upper and positive step. width = upper-lower; intervals = width/step; aligned = Number.isInteger(intervals).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| lower | Lower bound under the stated coordinate, derivative or uncertainty convention. | Required. Finite number. |
| upper | Upper bound under the stated coordinate, derivative or uncertainty convention. | Required. Finite number. |
| step | Step | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| width | Width | Required. Finite number. |
| intervals | Intervals | Required. Finite number. |
| aligned | Aligned | Required. Boolean. |
{
"input": {
"lower": 1,
"upper": 5,
"step": 1
},
"output": {
"width": 4,
"intervals": 4,
"aligned": true
}
}Limitations and assumptions
- All scale quantities share one unit. Alignment uses exact floating-point integrality without tolerance, does not count endpoints and does not validate a rating instrument.
- 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
Similar or alternative tools
- Scale Reverse Item Midpoint
midpoint = lower/2+upper/2; reversed = lower+(upper-score).
- Scale Direction Reversal Flag
When reverse is true return lower+upper-value, otherwise preserve value; reversed echoes the flag.