Is my parameter estimate significant or not? - Cross Validated most recent 30 from stats.stackexchange.com 2019-07-21T10:48:26Z https://stats.stackexchange.com/feeds/question/67998 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://stats.stackexchange.com/q/67998 1 Is my parameter estimate significant or not? Herman Haugland https://stats.stackexchange.com/users/15978 2013-08-21T17:07:16Z 2013-08-21T17:29:42Z <p>DISCLAIMER: This question was sent to Stata list today, but so far nobody has answered.</p> <p>NOTE: I use Stata here, but actually I don't think the question is software-specific.</p> <p>Hi,</p> <p>I would appreciate someone could provide me an answer to the following question:</p> <p>I am estimating the following model:</p> <pre><code>. areg beta L.lev group#cL.lev i.year, absorb(group) </code></pre> <p>Group is a categorical variable: 1, 2 Lev is a continuous variable Year are year effects Group are group effects</p> <p>Under that specification of the model, I get the following results:</p> <pre><code> . areg beta L.lev group#cL.lev i.year, absorb(group) Linear regression, absorbing indicators Number of obs = 285 F( 17, 266) = 4.04 Prob &gt; F = 0.0000 R-squared = 0.3540 Adj R-squared = 0.3103 Root MSE = 0.3038 ------------------------------------------------------------------------------ beta | Coef. Std. Err. t P&gt;|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- lev | L1. | .059685 .014907 4.00 0.000 .0303342 .0890358 | group#cL.lev | 2 | -.0451045 .0178834 -2.52 0.012 -.0803155 -.0098936 </code></pre> <p>What I would like to highlight from here, is the fact that the P value for group#cLlev 2 is significant at the 5% level.</p> <p>If I run the same model in a different way (not including the variable Lev by itself), like this:</p> <pre><code>. areg beta group#cL.lev i.year, absorb(group) Linear regression, absorbing indicators Number of obs = 285 F( 17, 266) = 4.04 Prob &gt; F = 0.0000 R-squared = 0.3540 Adj R-squared = 0.3103 Root MSE = 0.3038 ------------------------------------------------------------------------------ beta | Coef. Std. Err. t P&gt;|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- group#cL.lev | 1 | .059685 .014907 4.00 0.000 .0303342 .0890358 2 | .0145805 .0114004 1.28 0.202 -.0078661 .037027 </code></pre> <p>The P value for group 2 is not significant at the 5% level.</p> <p>So the question is, which P-value should I consider as correct? In other words, is my parameter estimate significant or not?</p> <p>(Please note that I get exactly the same parameter estimates from both methods, but the associated P-values and t-values change).</p> https://stats.stackexchange.com/questions/67998/-/68000#68000 4 Answer by Andy for Is my parameter estimate significant or not? Andy https://stats.stackexchange.com/users/26338 2013-08-21T17:29:42Z 2013-08-21T17:29:42Z <p>The two regression results are the same but leaving out the main effect (lev) changes the baseline for comparison of the two groups.</p> <p>In the first regression <code>lev L1. = 0.059685</code> is the coefficient for group 1 and <code>group#cL.lev 2 = -0.0451045</code> is the deviation of group 2 from the baseline (group 1). This means that the coefficient for group 2 is <code>-0.0451045</code> smaller than the coefficient of group 1.</p> <p>In the second regression this is exactly what you get again just that the coefficient of group 2 is not expressed as the difference between the two groups. To see this go back to the first regression and subtract <code>0.059685 - 0.0451045 = 0.0145805</code>, which is your group 2 coefficient in the second regression.</p> <p>This means that the effect of <code>lev</code> on the outcome variable <code>beta</code>for group 2 is not significantly different from zero (p-value = 0.202) in the second regression. The first regression on the other hand tells you that the effect on group 2 compared to group 1 is <code>-0.0451045</code> smaller and this difference is significant.</p>