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  • One tailed and two tailed t test in a fixed effect panel data set

    Dear Statalist
    (I use Stata 11)
    I want to calculate the significance of a coefficient using a two tailed t-test and another using a one tailed t-test in the following regression model:

    y= a+ b1 pos_special items + b2 BV

    I use a fixed effect panel data technique to estimate the model and run the following commands:

    xtreg y pos_special items BV, fe

    **I obtain the following output:
    Fixed-effects (within) regression Number of obs = 15457
    Group variable: firmid Number of groups = 5449

    R-sq: within = 0.0021 Obs per group: min = 1
    between = 0.0053 avg = 2.8
    overall = 0.0010 max = 19

    F(2,10003) = 10.60
    corr(u_i, Xb) = -0.0627 Prob > F = 0.0000

    ------------------------------------------------------------------------------
    F.dcesur | Coef. Std. Err. t P>|t| [95% Conf. Interval]
    -------------+----------------------------------------------------------------
    pos_siW | .2312587 .1271344 1.82 0.069 -.0179504 .4804678
    bv | -.0056147 .0013331 -4.21 0.000 -.0082279 -.0030015
    _cons | .0659563 .0020179 32.69 0.000 .0620009 .0699117
    -------------+----------------------------------------------------------------
    sigma_u | .13057331
    sigma_e | .19472136
    rho | .31018181 (fraction of variance due to u_i)
    ------------------------------------------------------------------------------
    F test that all u_i=0: F(5448, 10003) = 1.01 Prob > F = 0.3696

    ** My aim is to use a two tailed t-test for the coefficient on BV. Since the t statistics reported by Stata, by default, are based on two sided test , then BV is staistically significant at all conventional levels. For pos_siW , the predicted value is (+) and I use a one tailed t test (right side) to test its significance, therefore I run the following commands to calculate critical values based on a one tailed test and a degree of freedom 15454 that I calculate as N-K ( where N=15457 based on the number of observations from the output above , and K is the number of the regression coefficients 3 (including the constant, right ? ) :

    . display invttail(15454, 0.01)
    2.3265892

    . display invttail(15454, 0.05)
    1.6449522

    . display invttail(15454, 0.10)
    1.2816063

    Since t statistics for pos_special items is 1.82 > 1.6449522 and also > 1.2816063 , pos_special items is both positive and significant in the model


    my questions are:
    1- Do I calculate the df correctly ?
    2- Is this the right way to determine the significance of the variable using a one tailed test ?
    3- Are there any other methods?

    Thanks

  • #2
    Sorry , I forgot to add that pos_special items is both significant and positive at both 0.05 and 0.10 levels and positive and insignificant at the 0.01 significance level.
    Ahmed

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