maomao20010609
Joined: 01 Mar 2013 Posts: 14

I thought i had this straight, but i always get caught. Does anyone has the real solution for when we have a type 1,2 errors ? Here’s what I have until now : n increase > Fstat increase > type 1 decrease > type 2 increase n increase > tstat decrease > type 1 increase > type 2 decrease alpha increase => tstat decrease > type 1 increase > type 2 decrease From the above we can conclude that when t decrease, type 1 increase (and F is the opposite). Now if we move to reading 11, in effects of serial correlation and heteroskedacitty, they say : t, F increase > type 1 decrease > type 2 increase Who’s wrong who’s right ? Please help !!!

yiyi10171218
Joined: 01 Mar 2013 Posts: 20

My interpretation: (caution–I’m learning as I go here and haven’t had any formal training) Your first three conditional statements are referring to the statistics that bound your confidence intervals or make up your testing parameters, onesided for Ftests and two or onesided for tstatistics. An increase in sample size improves the power of both tests. For F, less regression information will now be explained by residuals, prorata. For t, a larger n should decrease your t, because as n increases, your sample’s variance increases proportionately… that means the standard error (the square root of sample variance divided by square root of n) moves in the exact opposite way as t due to n getting bigger (or smaller). Setting an arbitrarily larger alpha means our potential pvalues are increasing, so the probability of rejecting the null hypothesis isn’t so crazy anymore, and we should expect it to happen more often, all things equal. More alpha, more n = more power and, unfortunately, false alarms! Now, to your calculated or observed statistics, which are the empircal data or results: serial/autocorrelation (residuals that are bending/distorting the OLS output in a pattern) or heteroscedasticity (the space between residuals changes from output to output), a few points: 1. Autocorrelated residuals violate the GaussMarkov assumptions. We assumed the OLS output, and thus our slope term, or beta, was more accurate than it really is; that means our standard error is too small (there’s more error than we see per on our vanilla regression model) and that smaller denominator makes our calculated tstatistic too big. It follows that with false confidence our detecting problems that don’t exist (TypeI) would decrease. 2. Heteroscedasticity is common, and your straight regression line will still typically work for the most part, because if the residuals are clustered on the line, or far from the line, but on average an equal distance from the line, your OLS line and hopefully predictions will be useful still. (At least your data’s (and your forecast’s) tendency is to remain straight, rather than in autocorrelation where it bends over time, etc.) Again, tstatistics will be off, since we’re taking an average but s.e. could be more/less in actuality. The Fstatistic could be too big or too small. In short, I think both of those are right. Hope my musings helped.
