It is advisable to use normal distribution for a large datasets. It is more appropriate for analyzing small datasets as the sample size increases the t distribution becomes Statistically normal.
The short answer is "yes". For large sample sizes the normal distribution and the t distribution with many degrees of freedom are virtually identical.
When the sample size, n is large, the t -distribution is shown to approach the standard normal distribution. The rule of thumb value for a large sample is 30. This may be partly due to the fact that Fisher's and Yate's original tables only had detailed probabilities for up to n=30. Before 'Student' tabulated t values for small samples and somewhat empirically came up with the t -distribution, the researchers are said to have used large sample tests like z-test for the small samples too. While z uses population standard deviation, t is independent of it. Similarly, t-probability curves are slightly different to the normal curve for small samples. Thus, a test based on t- statistic can also be applied to large samples, but the converse is not considered to be true.
- Badges
- Science topic
- Similar topics
- Mathematical Sciences
- Statistics
- Statistical Software
- SPSS