What it says really: the mean of the squared deviation of a set of values from the correct value. This is similar to the Standard Deviation (SD) where the mean is of the sum of the differences from the mean value. It’s a measure of dispersion where a “true” or “correct” value is known.
Details #
So the equation is the next. (Look away if you don’t like them, they help some of us but aren’t necessary.)
$$MSE = \frac{\sum (x – correct_{x})^2}{n}$$
Of course this begs the question: “What is the correct value?” Sometimes, where you have a definitive or canonical measure as is the case for some blood tests or perhaps for a very good scales and you are comparing the values you have from a cheaper blood test or a portable scales with those referential measures you use the measure from that definitive measure. So you might have a dataset of 40 people’s weights weighed in the same room, on the same occasion, on the referential scales and on the portable ones. In this case the equation is:
$$MSE = \frac{\sum (weight_{portable} – weight_{referential})^2}{n}$$
(And n here is 40 of course.) This use of the term makes it a measure of unreliability (simplifying slightly).
The term is also used in some analyses, typically multi-level models when the “correct” value is the best fit to the model across all the data and the MSE is the mean squared deviation for each participant/observation from that estimate. Here the MSE is a useful indicator of the variability across the dataset in terms of deviations from the model. For example the model might be that clients’ scores on some measure, say the CORE-10, decrease in some way with the number of sessions they attend. Then the MSE for their CORE-10 scores is the MSE across all participants and all sessions with scores from the model that fits best across all those data points. But this is getting into rather small print.
Try also #
Dispersion
Multi-level models (MLM)
Reliability
Standard Deviation (SD)
Variance: introduction
Variance: detail
Chapters #
Not mentioned in the OMbook.
Online resources #
None yet.
Dates #
First created 5.iv.24.
