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| Format: | Preprint |
| Published: |
2023
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| Online Access: | https://arxiv.org/abs/2308.13811 |
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| _version_ | 1866914009686474752 |
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| author | Ellis, Jules L. |
| author_facet | Ellis, Jules L. |
| contents | It is shown that the psychometric test reliability, based on any true-score model with randomly sampled items and conditionally independent errors, converges to 1 as the test length goes to infinity, assuming some fairly general regularity conditions. The asymptotic rate of convergence is given by the Spearman-Brown formula, and for this it is not needed that the items are parallel, or latent unidimensional, or even finite dimensional. Simulations with the 2-parameter logistic item response theory model reveal that there can be a positive bias in the reliability of short multidimensional tests, meaning that applying the Spearman-Brown formula in these cases would lead to overprediction of the reliability that will result from lengthening the tests. For short unidimensional tests under the 2-parameter logistic model the reliabilities are almost unbiased, meaning that application of the Spearman-Brown formula in these cases leads to predictions that are approximately unbiased. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_13811 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Spearman-Brown Formula and Reliabilities of Random Test Forms Ellis, Jules L. Methodology 62G20 It is shown that the psychometric test reliability, based on any true-score model with randomly sampled items and conditionally independent errors, converges to 1 as the test length goes to infinity, assuming some fairly general regularity conditions. The asymptotic rate of convergence is given by the Spearman-Brown formula, and for this it is not needed that the items are parallel, or latent unidimensional, or even finite dimensional. Simulations with the 2-parameter logistic item response theory model reveal that there can be a positive bias in the reliability of short multidimensional tests, meaning that applying the Spearman-Brown formula in these cases would lead to overprediction of the reliability that will result from lengthening the tests. For short unidimensional tests under the 2-parameter logistic model the reliabilities are almost unbiased, meaning that application of the Spearman-Brown formula in these cases leads to predictions that are approximately unbiased. |
| title | The Spearman-Brown Formula and Reliabilities of Random Test Forms |
| topic | Methodology 62G20 |
| url | https://arxiv.org/abs/2308.13811 |