**Property 1 **(of Cronbach’s Alpha): Let *x _{j} = t_{j} + e_{j}* where each

*e*is independent of

_{j}*t*and all the

_{j}*e*are independent of each other. Also let

_{j}*x*

_{0}= and

*t*

_{0}= . Then the reliability of

*x*≥

_{0}*α*where

*α*is Cronbach’s alpha.

Here we view the *x _{j}* as the measured values, the

*t*as the true values and the

_{j}*e*as the measurement error values.

_{j}Proof: By Property 5 of Basic Concepts of Correlation, *var*(*t _{i}–t_{j}*)

*= var*(

*t*)

_{i}*+ var*(

*t*)

_{j}*(*

*–*2 cov*) , and since*

*t*,_{i}*t*_{j}*var*(

*t*)

_{i}–t_{j}*≥ 0, it follows that*

*var*(

*t*)

_{i}*+ var*(

*t*) ≥

_{j}*2 cov*(

*). Since for each*

*t*,_{i}*t*_{j}*i*there are

*k –*1

*j*for which

*j ≠ i*, it follows that

It now follows by Property 5 of Basic Concepts of Correlation

IT is v.nice

Hello ,

I used a questionnaire of five Likert scale and the questionnaire itself has many categories and each category has many subsets .is it possible to use Cronbach’s alpha to assure the reliability of the questionnaire and how can i use it ?if you could clarify that for me, I would be grateful

thanks a lot

Bekhal /Iraq

Bekhal,

As long as all the questions in the questionnaire are measuring the same concept you can calculate Cronbach’s Alpha. If each of the categories is measuring a different concept then you need to calculate a separate Cronbach’s Alpha for each concept/category.

Charles

Hello ,

How do I know that my questionnaire is reliable after I use Cronbach’s alpha for that purpose ? I mean the result of the process should be around what number?

Bekhal

Hello Bekhal,

This issue is discussed on the following webpage:

Cronbach’s Alpha

Charles

Hello Sir,

I have collected the data of 128 respondents by survey. Each questionnaire contains 37 questions in YES and NO format. Now, how i can calculate Cronbach’s alpha to check the reliability of questionnaire? Is 37 items (37 questions) are sufficient for Cronbach’s alpha?

Pankaj,

The Real Statistics website explains how to perform these calculations. Alternatively you can use the Real Statistics software to do the calculations for you.

Cronbach’s alpha can certinly be calculated with 37 items.

Charles