In one of the tests based on likert scale, the number of respondents are 5, whereas the number of items are 13. However, Cronbach's alpha value is unacceptable. What should be the ratio of items and subjects for reliability analysis?
Dear Amna
You can use the following formula to estimate the sample size according to your information about the population which the sample will be taken from it :
Sample size from finite population can be estimate by :
n= N / ( 1+ N * e^2 )
and from infinite population by :
n= ( Z^2 * S^2) / E^2
where : Z ( 1.96 for 0.05 and 2.58 for 0.01 )
S = standard deviation from previous studies or pilot study
E = significant level
Also, you can use software to calculate sample size ( SPSS , Minitab , Gpower )
also there are online sample size calculator .
For more information you can read the attached files:
Good Luck
Dear Amna,
As an absolute minimum you need more respondents than items and at least 30 respondents, according to the papers I have read. This is much less than the generally received wisdom of at least 300-400 respondents.
Have a look at my guide:
Technical Report Advice on Reliability Analysis with Small Samples
I agree with you Peter, the minimum acceptable observations should be not less than 30 and sometimes 33 to be valid for using statistical tests.
The statistical program will run the reliability, but how much it is meaningful and accurate, here is the doubt!
for example in EFA, it is recommended to have a mimimum of 5 participants for each item. in your case, you have 13 items, thus you may need 65 participants to have trusted result.
Can I perform reliability analysis with small sample size?
Yes you can - but generally & minimally 30 sample size as suggested by some scholars. 5 sample size is too low. Depending on your research model - if it fits into using certain Structural Equation Modeling (SEM) like Partial Least Squares-SEM (sometimes also addressed as Variance-based SEM) that can work well with small sample size, then you can use its statistical software e.g. SmartPLS etc. to generate the Composite Reliability. Some researchers use Composite Reliability to replace Cronbach's Alpha for reliability analysis.
Albeit Cronbach‟s Alpha is widely used as an estimator for reliability tests, it has been criticized for its lower bound value which underestimates the true reliability (Peterson, R.A. and Y. Kim, 2013). Composite Reliability can be used as an alternative as its composite reliability value is slightly higher than Cronbach‟s Alpha whereby the difference is relatively inconsequential (Peterson, R.A. and Y. Kim, 2013).
To know what is the minimum sample size for using PLS-SEM, you can refer to my answer in this RG link:
https://www.researchgate.net/post/What_is_the_minimum_sample_acceptable_for_structural_equation_modelling_using_smartPLS
If you want to know under what conditions you can use PLS-SEM, you can refer to this RG link:
https://www.researchgate.net/post/Can_we_use_structural_equation_modelling_SEM_in_an_exploratory_research
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Sampling Design
- Sample Size