(Documentation to be posted tomorrow.)

Characteristics |
Raw Scores and/or Percentages |
Rasch Measurement |

Quantitative hypothesis |
Neither formulated nor tested |
Formulated and tested |

Criteria for falsifying quantitative hypothesis | None | Additivity, conjoint transitivity, parameter separation, unidimensionality, invariance, statistical sufficiency, monotonicity, homogeneity, infinite divisibility, etc. |

Relation to sample distribution | Dependent | Independent |

Paradigm |
Descriptive statistics |
Prescriptive measurement |

Model-data relation |
Models describe data, models fit to data, model with best statistics chosen |
Models prescribe data quality needed for objective inference, data fit to models, GIGO principle |

Relation to structure of natural laws |
None |
Identical |

Statistical tests of quantitative hypothesis | None | Information-weighted and outlier-sensitive model fit, Principal Components Analysis, many other fit statistics available |

Reliability coefficients | Cronbach’s alpha, KR-20, etc. | Cronbach’s alpha, KR-20, etc. and Separation, Strata |

Reliability error source | Unexplained portion of variance | Mean square of individual error estimates |

Range of measurement | Arbitrary, from minimum to maximum score | Nonarbitrary, infinite |

Unit status | Ordinal, nonlinear | Interval, linear |

Unit status assumed in statistical comparisons | Interval, linear | Interval, linear |

Proofs of unit status | Correlational | Axiomatic; reproduced physical metrics; graphical plots; independent cross-sample recalibrations; etc. |

Error theory for individual scores/measures | None | Derived from sampling theory |

Architecture (capacity to add/delete items) | Closed | Open |

Supports adaptive administration and mass customization | No (changes to items change meaning of scores) | Yes (changes to items do not change meaning of measure) |

Supports traceability to metrological reference standard | No | Yes |

Domains scored | Either persons or items but rarely both | All facets in model (persons, items, rating categories, judges, tasks, etc.) |

Comparability of domains scored | Would be incomparable if scored | Comparable; each interpreted in terms of the other |

Unscored domain characteristics | Assumed all same score or random (though probably not) |
No unscored domain |

Relation with other measures of same construct | Incommensurable | Commensurable and equatable |

Construct definition | None | Consistency, meaningfulness, interpretability, and predictability of calibration/measure hierarchies |

Focus of interpretation | Mean scores or percentages relative to demographics or experimental groups | Measures relative to calibrations and vice versa; measures relative to demographics or experimental groups |

Relation to qualitative methods | Stark difference in philosophical commitments | Rooted in same philosophical commitments |

Quality of research dialogue | Researchers’ expertise elevated relative to research subjects | Research subjects voice individual and collective perspectives on coherence of construct as defined by researchers’ questions |

Source of narrative theme | Researcher | Object of unfolding dialogue |

LivingCapitalMetrics Blog by William P. Fisher, Jr., Ph.D. is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.

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Tags: Meaning, measurement, ordinal, performance metrics

July 7, 2009 at 10:45 |

Brilliant – would love permission to share with people I coach / teach about Rasch measurement

July 7, 2009 at 22:39 |

Permission granted to any and all, with the understanding that credit will go where it is due, of course!