God I hate hypothesis testing… does anyone out there feel like walking me through the reasoning why a one tail hypothesis test, with a null of less than or equal to and an alternative with a greater than - has a rejection region in the right tail? It seems counterintuitive to me - and both Schweser and CFAI fail to explain it very well. If we want to reject the null (less than), I would think that the reject area would be in the left tail. Thanks in advance for any help.
Because if you are in the right tail, your test statistic (i.e. 2.1) is greater than the critical value (i.e. 1.645). That means that what you are testing (the alternate hypo) is “correct” and the status quo (the null) is “wrong”. However in stats you never say right or wrong, but you get the point. An easy way is always sketch out the normal distro, and plot the crit value (make sure you get the right or left tail correct). Then write on the distribution the Ho and Ha regions. The Ho is always in the middle (the largest part). If you get used to doing this correctly, the rest is cake. Calculate your test stat, and plot that. If it’s in the Ho region, fail to reject the null. If it’s in the Ha region, reject the null. If you try and memorize the “less than means that you reject when blah blah” it is much more difficult than learning to correctly draw out the distribution and visualizing the problem. When you can draw it and know it, you don’t have to bother to memorize (other than the critical values)
Oh forgot to mention… You place the critical value on either side of the normal distribution (for one-tailed tests) based upon the sign in Ho. You read the normal distribution from left to right (like a sentence). So if Ho is , then the crit value goes on the left tail (so that Ho is GREATER THAN the critical value).
also remember that your NULL hypothesis will always have the “=” sign on it.
Thanks for the quick and comprehensive response. I finally “get it.” Gotta love this forum…
I tend to think of the problem in terms of t-stats. If t-stat value > 2 , there is lot of power in the data supporting the conclusion , otherwise it is iffy, i.e. the hypothesis is not strong. We construct the hypothesis by first saying the data is weak . Then when we prove otherwise ( in terms of a big t-stat ) , we are happy and we pat ourselves on the back that we found a causal link. By setting ourselves to fail , and then proving we have not failed , we confirm the alternative . So what we desperately want to prove is put as an alternative , while what we never want to happen ( a weak link ) is stated as the hypothesis . If I say the mean is zero and the t-stat proves high , the mean is NOT zero , and I 'm happy that I did NOT show the lack of power in the independent variable in explaining the dependent variable .
cpk123 Wrote: ------------------------------------------------------- > also remember that your NULL hypothesis will > always have the “=” sign on it. Yeah I thought about opening up Word and getting the greater than or equal to sign out but I’m too lazy 