Editing Cronbach's alpha (section)

===If there is no measurement error, the value of Cronbach's alpha is one.===
This anomaly also originates from the fact that <math>\rho_{T}</math> underestimates reliability. 

Suppose that <math>X_2</math> copied the value of <math>X_1</math> as it is, and <math>X_3</math> copied by multiplying the value of <math>X_1</math> by two. 

The covariance matrix between items is as follows, <math>\rho_{T}=0.9375</math>.
{| class="wikitable" style="text-align: center;"
|+ Observed covariance matrix
|-
!
! <math>X_1</math>
! <math>X_2</math>
! <math>X_3</math>
|-
! <math>X_1</math>
| <math>1</math>||<math>1</math>||<math>2</math>
|-
! <math>X_2</math>
| <math>1</math>|| <math>1</math>|| <math>2</math>
|-
! <math>X_3</math>
| <math>2</math>|| <math>2</math>|| <math>4</math>
|}
For the above data, both <math>\rho_{P}</math> and <math>\rho_{C}</math> have a value of one.

The above example is presented by Cho and Kim (2015).<ref name = ChoKim/>