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Consider the model below:

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In many research papers, significance of statistical results are indicated by *, **, and *** as a significant value at respectively the 1%, 5%, or 10% level.

Does a Sig. value of .047 (forninstance, LAW_LE) mean a significane at the 4,7% level? (So that I may report LAW_LE 0.313**)?

Second, I see many times the Std.Error is also reported in papers. How do I need to interpret the standard error in combination with the significance? For instance, COM_BIK has a standard error of 0.045 and a significance of 0.021; whereas HOF_MAS has a low standard error (0.002) but a significance of .416. What can be said about these two variables based on this information?

Your help is greatly appreciated.

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3 Answers 3

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It depends on the field, but I think this is the most common approach:

  • Report coefficients that have a p-value that is less than 0.05 but greater than 0.01 with one asterisk (*) -- equivalent to the 5% level of significance;
  • Report coefficients that have a p-value that is less than 0.01 but greater than 0.001 with two asterisks (**);
  • Report coefficients that have a p-value that is less than 0.001 with three asterisks (*)

So the LAW_LE would get one asterisk. Usually/often the standard error is also reported, as you suggest. Again, this varies according to the specific field of study, it is fairly standard to see values in a table as the coefficient, the significance level and the standard error in parentheses. So for your LAW_LE you would have

LAW_LE $0.075^{*}$ $(0.037)$

(unless you wanted to report the standardized coefficients in which case $0.075$ would be replaced with $0.313$ -- the decision as to whether you report standardized or unstandardized coefficients is another question and has probably been covered here).

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Most journals won't want to see all of these numbers, and which numbers are preferred vary from journal to journal. You're right that "Sig." is the $p$-value, so a $p$-value of 0.047 would indicate that you should reject the null hypothesis at a confidence level of 0.05

In general, I prefer showing the coefficient values and the $t$-statistic because it contains information on both the standard error and the $p$-value. Most readers have a good intuition that $t$ values above 1.9 are generally significant, and if the reader really wants to see the standard error, it's easy for them to calculate $t/\beta$.

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$\textbf{Answer to part 2}$: If your null hypothesis is that the coefficient on each variable is zero, you can relate the standard error, $t$, and $beta$ as $t=beta/SE(beta)$. A rule of thumb for the significance of coefficient (at 10 %) under two tailed test is that $t$ should be >=2.

$\textbf{Answer to part 1}$: Most of the academic papers report the non-standardized coefficient, so you may want to write $LAW_{LE}= 0.075^{**}$. Also, 1% significance implies significance at $p<=0.01$ and 5 % significance implies significance at $p<=0.05$.

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