Internal Consistency Reliability

Internal consistency reliability describes the extent to which test measurements remain consistent over repeated trials under identical conditions.

Topics

• Split-Half Methodology
• Kuder and Richardson Formula 20
• Cronbach’s Alpha
• Proof of Basic Property

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 r_xt of x and t.

Property 1:

Proof: See Proof of Basic Property

References

Wikipedia (2019) Internal consistency
https://en.wikipedia.org/wiki/Internal_consistency

Navarro, D. J., Foxcroft, D. R. (2023) Internal consistency reliability analysis
https://lsj.readthedocs.io/it/latest/Ch15/Ch15_FactorAnalysis_4.html