Confidence Intervals from Normalized Data: A correction to Cousineau (2005)
By Richard D. Morey. 2008
1,983 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Statistics and Probability
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Citations in the corpus
- Do Better ImageNet Models Transfer Better? (2018, methodology): “We computed error bars for model accuracy averaged across datasets, using the procedure from Morey [50] to remove variance due to inherent differences in dataset difficulty.”
- The Comprehension of Counterfactual Conditionals: Evidence From Eye-Tracking in the Visual World Paradigm (2019, background): “Error bars are 95% confidence intervals within participants (see Morey, 2008; O’Brien and Cousineau, 2014).”
- Reminders and repetition of misinformation: Helping or hindering its retraction? (2017, background): “Error bars depict within-subject standard errors of the mean (Morey, 2008).”
- The shifting boxplot. A boxplot based on essential summary statistics around the mean. (2010, background): “Such computation basically removes the between-groups variance since it is of no avail in the statistical analysis of dependent-measures designs (Cousineau, 2005; Jarmasz & Hollands, 2009; Loftus & Masson, 1994; Masson & Loftus, 2003; Morey, 2008).”
- That sounds sweet: using cross-modal correspondences to communicate gustatory attributes (2015, background): “Error bars indicate 95% within-subjects confidence intervals (Morey, 2008).”