Confidence Intervals from Normalized Data: A correction to Cousineau (2005)
Bibliographic record
Abstract
Presenting confidence intervals around means is a common method of expressing uncertainty in data. Loftus and Masson (1994) describe confidence intervals for means in within-subjects designs. These confidence intervals are based on the ANOVA mean squared error. Cousineau (2005) presents an alternative to the Loftus and Masson method, but his method produces confidence intervals that are smaller than those of Loftus and Masson. I show why this is the case and offer a simple correction that makes the expected size of Cousineau confidence intervals the same as that of Loftus and Masson confidence intervals. Confidence intervals (CIs) are a staple in the presentation of psychological data because they allow researchers to quickly gage the amount of uncertainty in data (Rouder & Morey, 2005). For within-subjects designs, there are several approaches to creating confidence intervals. For a given design it may not be clear which to choose. Consider a simple within-subjects design with two conditions, a pre-test and post-test. For this design, there are multiple methods of generating confidence intervals. I will discuss each in turn. Approaches to confidence intervals The standard way to build confidence intervals is to compute the standard error of the mean for each condition, and multiply it by the appropriate t-distribution quantile. In order to make this concrete, Table 1 lists hypothetical data for N = 10 participants. A paired t-test reveals a significant effect of condition (MSE = 5:19; t(9) = 3:65; p =:005;
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.075 | 0.519 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.005 |
| Bibliometrics | 0.008 | 0.011 |
| Science and technology studies | 0.003 | 0.005 |
| Scholarly communication | 0.005 | 0.007 |
| Open science | 0.007 | 0.006 |
| Research integrity | 0.004 | 0.018 |
| Insufficient payload (model declined to judge) | 0.027 | 0.007 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".