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I have a question related to the significance of the dummy variable. Some background context: I am writing my thesis and I have hypothesized the following. My first hypothesis hypothesizes that the independent variable (IP) which is the institutional pressure has a positive relationship with CSR (my dependent variable). I was able to find statistical evidence to support the hypothesis. For my second hypothesis, I wanted to compare the CSR performance of companies in two countries, Russia and China. And my second hypothesis hypothesized that the dependent variable's score would be higher in Russia compared to China as Russia has a higher institutional pressure compared to China. In order to do so, I created a country dummy variable where 1 denotes Russia and 0 denotes China and ran the GLS regression analysis. I was able to find a positive relationship however there was no statistical significance that was found ( p-value < 0.0509). I am struggling with understanding how to interpret the result in this context. If the first hypothesis is statistically significant, shouldn't the second hypothesis also deliver the same result? How do I interpret the statistical insignificance in relation to the dummy variable? I'd really appreciate it if anyone could shed some light on this. Thank you so much in advance!

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p-value < 0.0509

Incredible, this is the closest I've seen someone get to the nominal value. Please keep in mind that The Difference Between “Significant” and “Not Significant” is not Itself Statistically Significant. Though you have failed to reject the null (by a hair's worth) I would look at the confidence interval for the effect to see what sorts of effects are consistent with the observed data.

I am struggling with understanding how to interpret the result in this context. If the first hypothesis is statistically significant, shouldn't the second hypothesis also deliver the same result?

No, not necessarily. The differences between China and Russia could be too small to detect reliably with your dataset.

How do I interpret the statistical insignificance in relation to the dummy variable?

If the model is

$$ CSR = \beta_0 + \beta_1 \mbox{IP} + \beta_2I(\mbox{Country=Russia}) $$

Then a failure to reject the null means that, from these data, we can no conclude that $\beta_2\neq0$. That does not mean that $\beta_2=0$, only that from these data we could not find evidence to the contrary.

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  • $\begingroup$ Thank you very much for your very helpful answer! Regarding the confidence interval, at (95% confidence interval)= (-0.377) to 19.619. How would I interpret these values? And, I saw a post earlier that suggested that p-value means the country dummy variable seems to account for other country-specific factors, what does this mean in this context? How do I discuss this "marginal significance" in the results sections? Thank you so much in advance! $\endgroup$
    – Sarah
    Jan 7, 2022 at 17:09
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    $\begingroup$ @Sarah regarding interpretation of the confidence interval, I think you're going to find this resource very useful. That interpretation of the p-value is incorrect, and I would encourage you to search for highly upvoted answers on the interpretation of the p value. "Marginal significance" is not a term I condone. I would simply report a failure to reject the null and interpret the effects consistent with the data from the CI (see link for more). $\endgroup$ Jan 7, 2022 at 17:40

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