Confidence interval

[Hasan Tekin]

Hello Sir/Madams,

When I make an analysis on Stata(12), I get the same results for the level(99), level(95), and level(90). Specifically, the significance of variables does not change.
However, I see the empirical papers that can present different level confidence intervals at the same analysis?

I guess this is very simple, but I could not find an answer about this usage. Could you help how can I overcome this problem?

Regards,
Hasan Tekin

[Marcos Almeida]

Hello Hasan,

Welcome to the Stata Forum,

The p-value is related to the t-score, which is the result of the coefficient divided by its SE. This is the reason why the CI changes according to the level you select, but not the p-value.

Best,

Marcos

[Marcos Almeida]

I hope this example will be helpful:

. sysuse nlsw88.dta
(NLSW, 1988 extract)

. regress  wage south tenure

      Source |       SS           df       MS      Number of obs   =     2,231
-------------+----------------------------------   F(2, 2228)      =     54.66
       Model |  3465.62196         2  1732.81098   Prob > F        =    0.0000
    Residual |  70636.2057     2,228  31.7038625   R-squared       =    0.0468
-------------+----------------------------------   Adj R-squared   =    0.0459
       Total |  74101.8276     2,230  33.2295191   Root MSE        =    5.6306

------------------------------------------------------------------------------
        wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       south |  -1.440695     .24172    -5.96   0.000    -1.914715   -.9666754
      tenure |   .1812466   .0216524     8.37   0.000     .1387857    .2237075
       _cons |   7.313416   .2054015    35.61   0.000     6.910618    7.716214
------------------------------------------------------------------------------

. disp 0.1812466/0.0216524
8.3707395

. disp 0.1812466 +(1.96*0.0216524)
.2236853

. disp 0.1812466 -(1.96*0.0216524)
.1388079

. */ now a 90% CI

. regress  wage south tenure, level(90)

      Source |       SS           df       MS      Number of obs   =     2,231
-------------+----------------------------------   F(2, 2228)      =     54.66
       Model |  3465.62196         2  1732.81098   Prob > F        =    0.0000
    Residual |  70636.2057     2,228  31.7038625   R-squared       =    0.0468
-------------+----------------------------------   Adj R-squared   =    0.0459
       Total |  74101.8276     2,230  33.2295191   Root MSE        =    5.6306

------------------------------------------------------------------------------
        wage |      Coef.   Std. Err.      t    P>|t|     [90% Conf. Interval]
-------------+----------------------------------------------------------------
       south |  -1.440695     .24172    -5.96   0.000    -1.838455   -1.042936
      tenure |   .1812466   .0216524     8.37   0.000     .1456168    .2168764
       _cons |   7.313416   .2054015    35.61   0.000      6.97542    7.651412
------------------------------------------------------------------------------

. disp 0.1812466 +(1.645*0.0216524)
.2168648

. disp 0.1812466 -(1.645*0.0216524)
.1456284

. */ this time, with a 99% CI

. regress  wage south tenure, level(99)

      Source |       SS           df       MS      Number of obs   =     2,231
-------------+----------------------------------   F(2, 2228)      =     54.66
       Model |  3465.62196         2  1732.81098   Prob > F        =    0.0000
    Residual |  70636.2057     2,228  31.7038625   R-squared       =    0.0468
-------------+----------------------------------   Adj R-squared   =    0.0459
       Total |  74101.8276     2,230  33.2295191   Root MSE        =    5.6306

------------------------------------------------------------------------------
        wage |      Coef.   Std. Err.      t    P>|t|     [99% Conf. Interval]
-------------+----------------------------------------------------------------
       south |  -1.440695     .24172    -5.96   0.000    -2.063858   -.8175321
      tenure |   .1812466   .0216524     8.37   0.000      .125426    .2370672
       _cons |   7.313416   .2054015    35.61   0.000     6.783883    7.842949
------------------------------------------------------------------------------

. disp 0.1812466 +(2.576*0.0216524)
.23702318

. disp 0.1812466 -(2.576*0.0216524)
.12547002

.

[Hasan Tekin]

Dear Marcos Almeida,

Thank you for prompt and detailed answer. I know as the basic rule that if the p-value of the variable smaller than 0.05, we show with *, **, or *** regarding with its confidence interval.
But I wonder how people show the different singificant p-values in the same analysis as applied by Ozkan (2002: 23) below and many others in the empirical anlayses ?
If I miss a significant point about this case, could you correct me? I will be very happy.

Regards, Hasan Tekin

[Marcos Almeida]

It seems the table presented in #4 concerns the coefficients plus the SEs of two models. "Nota bene", not the confidence intervals. That said, if I "guessed" correctly, the estimation for the t-scores (for example, 6 for size and 2 for market-to-book) follows the same algebraic formula presented in #3. According to the dfs of both models, a t = 2 would provide a p-value slightly below 0.05 (since it is higher than 1.96), whereas a t = 6 would definitely provide a significant p-value at the 1% level (since it is higher then 2.575). The estimation of the CIs is also according to #3, under a command in Stata or just "by hand" (provided we have the point estimates as well as the SEs).

[Hasan Tekin]

Thank you very much, I understood clearly now.
Regards.