Astrometric Reduced Chi Square
Evaluate weighted astrometric residual chi-square and a supplied reduced-chi-square criterion; independent correctly estimated errors are assumed.
Description
Reduced chi-square compares error-normalized residuals with the fit's degrees of freedom.
Reduced chi-square compares error-normalized residuals with the fit's degrees of freedom. Its interpretation depends on independent residual errors and a correctly stated fitted-parameter count.1
Evaluate weighted astrometric residual chi-square and a supplied reduced-chi-square criterion; independent correctly estimated errors are assumed.
When to use Astrometric Reduced Chi Square
Use this tool to evaluate weighted astrometric residual chi-square and a supplied reduced-chi-square criterion; independent correctly estimated errors are assumed.
Prepare the source, detector or coordinate measurements. Confirm frame, epoch, angular units, axis directions and the stated RA proper-motion convention before entering values.
How to use Astrometric Reduced Chi Square and understand its results
- Prepare the source, detector or coordinate measurements. Confirm frame, epoch, angular units, axis directions and the stated RA proper-motion convention before entering values.
- Enter residuals, standardErrors, fittedParameters, maximumReducedChiSquare using the field table and calculation rules, then run the tool.
- Read chiSquare, degreesOfFreedom, reducedChiSquare, passesSuppliedCriterion. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| residuals | Residuals | list of number | Required |
| standardErrors | Standard errors | list of number | Required |
| fittedParameters | Fitted parameters | integer | Required |
| maximumReducedChiSquare | Maximum reduced chi square | number | Required |
Enter aligned nonempty finite residuals and positive errors in matching units, a nonnegative integer parameter count and positive reduced-chi-square maximum. n−parameters must be positive. Return chi-square, degrees of freedom, reduced value and inclusive passesSuppliedCriterion.
Paired lists must be nonempty and have equal lengths.
chiSquare=Σ(residual_i/error_i)²; reduced=chiSquare/(n−parameters) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| chiSquare | Chi square | number |
| degreesOfFreedom | Degrees of freedom | number |
| reducedChiSquare | Reduced chi square | number |
| passesSuppliedCriterion | Passes supplied criterion | boolean |
{
"input": {
"residuals": [
1,
2
],
"standardErrors": [
1,
2
],
"fittedParameters": 1,
"maximumReducedChiSquare": 2
},
"output": {
"chiSquare": 2,
"degreesOfFreedom": 1,
"reducedChiSquare": 2,
"passesSuppliedCriterion": true
}
}Limitations and assumptions
It does not fit a model, estimate errors, correct correlations or provide a p-value. Passing a supplied cutoff alone does not establish unbiased parameters or model adequacy.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.
Alternative or Complementary methods
Use Ruwe From Fit Normalization: Derive RUWE from chi-square, fit degrees of freedom, and caller-supplied magnitude/color normalization; no catalog calibration table is embedded. For a complementary task, use Five Parameter Design Rank: Audit rank of a position/proper-motion/parallax design from supplied epoch offsets and RA*/Dec parallax factors; conditioning and measurement weights are not assessed.
References
-
Astrometric Reduced Chi Square — tool.io
Similar or alternative tools
- Ruwe From Fit Normalization
Derive RUWE from chi-square, fit degrees of freedom, and caller-supplied magnitude/color normalization; no catalog calibration table is embedded.
- Five Parameter Design Rank
Audit rank of a position/proper-motion/parallax design from supplied epoch offsets and RA*/Dec parallax factors; conditioning and measurement weights are not assessed.