When testing the significance of a coefficient you use a two tail test unless you are testing the coefficient of a dummy variable in which case you use a one tailed test. Is this correct? Also when testing the significance of a dummy variable coeff does T = (coeff-0) / (Std Error)
whether you use a one tailed or a two tailed test depends on what you are trying to test. If you want to test whether some variable is greater (or less) than something else, say, b1 > 0, then you use a one tailed test, but if you want to test whether something is not equal to something else, this is a two tailed test. For example, the test that b1 <> 1. Why is it two tails? Because the mean could be less than one, or greater than one, so you have to test both possibilities. The t test is always t = (coeff- hypothesized value)/stderr, no need to remember something special for testing a dummy variable. Also remmeber that the F test is always a 1 tailed test.
So if you are testing if Men make more than Women with the regression y=0.5 + 3(x1) + 6(x2) where x2 = 1 if its a man and x2 = 0 if its a woman, why do you use a one tailed? B/c you are testing whether or not 6 is greater than 0 not whether or not is equal to 0?
In your example above, you would use a two tailed test(s) H0: x2 = 1 Ha: x2 is not equal to 1 H0: x2 = 0 Ha: x2 is not equal to 0 You would use (x2 - 1)/std error of x2 to find the t value for the first test and compared it with the t crit. For the 2nd test, you would use (x2-0)/std error of x2 and compare it to the t crit. If t calc > t crit, the value is significantly different than the null hypothesis.
Hmmm I am pretty sure QBank answer used a one tail test for that question. Not sure though.
Here it is: In a recent analysis of salaries (in $1,000) of financial analysts, a regression of salaries on education, experience, and gender is run. Gender equals one for men and zero for women. The regression results from a sample of 230 financial analysts are presented below, with t-statistics in parenthesis. Salaries = 34.98 + 1.2 Education + 0.5 Experience + 6.3 Gender (29.11) (8.93) (2.98) (1.58) Holding everything else constant, do men get paid more than women? Use a 5% level of significance. No, since the t-value: A) does not exceed the critical value of 1.65. B) does not exceed the critical value of 1.96. C) exceeds the critical value of 1.96. Your answer: B was incorrect. The correct answer was A) does not exceed the critical value of 1.65. H0: bgender ≤ 0 Ha: bgender > 0 t-value of 1.58 < 1.65 (critical value)
do men get paid more than women… MORE is the key word. this is classic for a 1 tailed test. and they have given you the t-stat of 1.58 for the gender variable.
cpk123 Wrote: ------------------------------------------------------- > do men get paid more than women… MORE is the key > word. > this is classic for a 1 tailed test. > > and they have given you the t-stat of 1.58 for the > gender variable. this does not sound right. MORE is not the keyword. this is one tailed test because dummy variable takes only two values 0 and 1 ( which is greater than one). so dummy variable can go only in one direction away from 0. which is positive side. again we can not test that dummy is not Zero. coz that will include dummy variable being significantly away from ZERO on negative side as well. we can only test if dummy is greater than ZERO, which is one tailed.
no rahulv - u have your concept completely wrong. What if women had been 0 and men had been 1? and then they had asked the same question : Do men earn more than women? Do men earn more than women - means Is men’s salary greater than women’s? which means > on the H0 and <= on the HA.
yeah, I agree with CPK two tailed would be something like do men earn the same as women
So what would the calculation of the t stat be? (6.3-1)/Std error or (6.3-0)/Std error
CP, I think you have your H0 and Ha mixed up. You have to disprove that its not <= so its H0: gender <=0, Ha: gender >0.
they already gave you the value of the t-stat. so no need to calculate it. in this case the 1 and the 0 have no meaning. it is always (6.3 - 0) / std error - bcos H0: Gender > 0 and Ha: Gender <= 0. so you are always comparing against 0.
ok… thank bradleyz.
cpk123 Wrote: ------------------------------------------------------- > no rahulv - u have your concept completely wrong. > What if women had been 0 and men had been 1? and > then they had asked the same question : Do men > earn more than women? > > Do men earn more than women - means Is men’s > salary greater than women’s? > > which means > on the H0 and <= on the HA. yup, i got confused. MORE is the keyword. for MORE, the coefficient needs to be significantly above zero. for LESS, it needs to be significantly below zero. for DIFFERENT, it has to be significantly different than ZERO.
> Salaries = 34.98 + 1.2 Education + 0.5 Experience + 6.3 Gender How do you interpret this? If you are a man, your salary is already ahead by $6300, so how could the test show they don’t get paid more? Caveat: I haven’t done any dummy variable stuff yet.
^^ anyone wants to take a crack at this?
yeah but is the 6300 statistically significant? That is what the test is doing…
something fishy…you have an extremely large slope for gender (much larget than any of the other slopes), yet gender is not significant for detrmining salaries?
Salaries = 34.98 + 1.2 Education + 0.5 Experience + 6.3 Gender Men Salaries = $34,980 + $6,300 *1 = $41,280 Women salaries = $34,980 + $6,300 * 0 = $34,980