Question

distinguish between big sample and small sample

Answer 1

The basic difference is that big sample have more number of sample while the small sample only restricted to few.

There less changes of error in big sample result while in case of small sample the original may variate.

Additionally, Big samples are often times consuming and need much effort as compared to the small sample. The big sample generally required more amount of money for it's collection as compared to the small sample.

Answer 2

Usually a candidate population less than 50 is considered a small sample for multiple choice exams. Indeed, the concept of the multiple choice exam was developed to test large samples of candidates effectively and efficiently. However, the multiple choice format has become so well accepted that it is now often applied to small as well as large samples. In order to better understand the impact of candidate sample size on test item performance, a test with a large sample of over 1,000 candidates and a test with a small sample of less than 20 candidates were analyzed using the Rasch model. The criteria for reviewing item performance were 1) item separation reliability, 2) item discrimination and 3) the error associated with the calibrated difficulty of each item.

Item separation reliability is an indication of the reproducibility of the item difficulties. High item separation reliability means that there is a high probability that items will maintain the same difficulty estimates across examinations. For the large sample test, the item separation reliability was 1.00, while for the small sample test it was .75 indicating that the test item variable is less well defined when a small sample is used to calibrate the items.