Basic Concepts
Internal consistency reliability is the extent to which the measurements of a test remain consistent over repeated tests of the same subject under identical conditions. An experiment is reliable if it yields consistent results of the same measure, i.e. it doesn’t yield random error in measurement. It is unreliable if repeated measurements give different results.
Since there are inaccuracies when taking measurements, even when the same measurements are taken twice there can be differences. We can therefore partition an observed value of x into the true value of x and an error term. Thus we have x = t + e.
Definition 1: The reliability of x is a measure of internal consistency and is the correlation coefficient rxt of x and t.
Property
Property 1:
Proof: Since the covariance is additive (i.e. Property 1 of Correlation – Advanced),
Since ti and ei are independent, cov(t, e) = 0, and so
Thus,
Reference
Furr, R. M. (2021) Chapter 5: Reliability. Psychometrics: An Introduction. Sage
https://www.sagepub.com/sites/default/files/upm-binaries/18478_Chapter_5.pdf
Dear Charles,
Could you please explain to me a little more, why the reliability definition of this page is the same or different from https://en.wikipedia.org/wiki/Reliability_(statistics) where Reliability is the ratio of variances
Thanks
Luis,
Property 1 on this webpage describes reliability as a ratio of standard deviations, which is similar conceptually to a ratio of variances.
Reliability is a pretty broad topic and covers lots of issues such as consistency, agreement, repeatability, etc. What specific topics seem different between the Wikipedia and Real Statistics webpages? I suggest that you look at the webpages on the Real Statistics website that covers the different aspects of reliability.
Charles
Reliability is not available on the Excell Resource Kit. Needing to determine the Reliability Coefficient but the tool is not available. Am I missing something?
Patrick,
Excel Toolpak doesn’t contain reliability data analysis tools. The Real Statistics Resource Pack does contain a number of reliability capabilities.
Charles