Student t distribution function

[Jared Greathouse]

I am translating some R code (lines 92-96 for the curious) to calculate some confidence intervals, and I'm gifted with the following syntax

lb <- att - qt(1-alpha/2,df=K-1)*se

The thing to focus on here is everything in the parentheses. According to Statology . com,

The function qt returns the value of the inverse cumulative density function (cdf) of the Student t distribution given a certain random variable x and degrees of freedom df.

I'm only vaguely familiar with Stata syntax for distributions and that sort of thing. Might there be an equivalent for this function in Stata?

[Clyde Schechter]

I think this would be -invt(K-1, 1-alpha/2)- in Stata. [I don't know R, I'm relying here on the description you show from Statology.com.]

[Andrew Musau]

The related function is

help invttail()

sysuse auto
regress mpg weight disp
di _b[weight] - invttail(e(df_r),0.05/2)*_se[weight]

Res.:

. regress mpg weight disp

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     66.79
       Model |  1595.40969         2  797.704846   Prob > F        =    0.0000
    Residual |  848.049768        71  11.9443629   R-squared       =    0.6529
-------------+----------------------------------   Adj R-squared   =    0.6432
       Total |  2443.45946        73  33.4720474   Root MSE        =    3.4561

------------------------------------------------------------------------------
         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |  -.0065671   .0011662    -5.63   0.000    -.0088925   -.0042417
displacement |   .0052808   .0098696     0.54   0.594    -.0143986    .0249602
       _cons |   40.08452    2.02011    19.84   0.000     36.05654    44.11251
------------------------------------------------------------------------------

.
. di _b[weight] - invttail(e(df_r),0.05/2)*_se[weight]
-.00889252

Note: Crossed with #2.

[Clyde Schechter]

If you use -invttail()- instead of my proposal of -invt()-, you will, for typical values of alpha, get a negative number returned, which will mean that the value of lb (which I'm guessing from context stands for lower bound of a confidence interval) will be higher than the value of att. You could, however, use -invttail(K-1, alpha/2)-, which would give the same result as -invt(K-1, 1-alpha/2)-.

[Jared Greathouse]

lower bound of a confidence interval) will be higher than the value of att

Indeed you are correct, I was perplexed at first when my lower bounds were higher than the counterfactual, and my higher bounds were lower than the counterfactual. Either way, this helps, so thank you both so much!