Dear Researcher,
i am developing a Regression Model(Prediction) at a location
Situation A:
Number of n 1100, variable 7.
Situation B:
Number of n 2600, Variable 9.
Question is, do i have to have same number of N at the same location, or the Central limit theorems (CLT) is applicable when dealing with large data for model development ( for normality and validity of the data)
Tuan -
This question isn't clear to me. You have two different regressions: different numbers of regressors and different sample sizes. You ask "...do i have to have same number of N at the same location...?" By "location," are you referring to a mean? Why do these two regressions have anything to do with one another?
I can say two things:
1) sample sizes: Regarding sample sizes, different populations have different standard deviations. Obtaining some level of standard error for a mean involves both sample size and population standard deviation. So in two separate 'situations,' if one standard deviation is larger, then it needs a smaller sample size to achieve the same standard error as for the case of the other population (or subpopulation/stratum). The only time I can think that sample sizes need to be the same is when you have paired observations, and perhaps you are just looking at one dataset, the differences between pairs. But I don't understand your connection to regressions here.
2) normality: If you are considering normality from use of the Central Limit Theorem to always be important for datasets used in regression, that is often not true. I am not very familiar with all kinds of regression, but have worked a great deal with continuous data, and it seems that many people mistakenly think that normality is always important for such dependent variable data, and/or independent variable data, in such cases. This is not true. I long worked with highly skewed data. That is often the case. However, it may be somewhat desirable for the estimated residuals (or, better, for weighted least squares regression, the random factors of the estimated residuals) to be approximately normally distributed. - From your question, it is not clear to me that you understood that.
Best wishes on your project.
Cheers - Jim
Dear Tuan,
When each of your sample sizes are big enough, you are allowed to use CLT. There is no condition for equality of your sample sizes.
Only equality of variances could be important, which is also not discussed in case of large sample sizes.
Thus, you are absolutely allowed to use CLT. However, don't forget this is an approximation and no guarantee for normality of your data.
Good luck