1) My null hypothesis (H0) is: The size of the board shall not influence the firm's performance. My alternative hypothesis (H1) is: The size of the board shall have a positive influence on the firm's performance

I have run a t-test in Stata between Board Size and Return on Assets (which, in this case, is my measure of firm performance)

The results look a bit weird. I am unsure which of the alternative hypothesis I am meant to pick. They are as follows:

Ha: diff < 0

Pr(T < t) = 1.0000


Ha: diff > 0

Pr(T > t) = 0.0000

I am convinced it should be the first. But doesn't this imply statistical insignificance?

2) My second question actually revolves again around the null/alternative hypothesis. My regression analysis indicates that there is actually a negative relationship between board size and firm performance. Since this means neither my null or alternative hypothesis are correct, does this mean, in my conclusions, I have to produce a second alternative hypothesis? (and call it 'H2', for example?)

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    $\begingroup$ Maybe you can explain why a t test addresses the hypothesis test you pose. I don't see it. It sounds to me more like you are interested in correlation or simple regression. Maybe you want to test for significance of a regression slope parameter or a correlation coefficient.. You need to explain what you did in Stata to get those results? $\endgroup$ Commented Nov 29, 2016 at 16:16
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    $\begingroup$ I am only speculating. Maybe you are applying a two sample t test. But these are different variables and probably are not even in the same units. $\endgroup$ Commented Nov 29, 2016 at 16:19
  • $\begingroup$ I agree with @MichaelChernick. What you have done exactly is not at all clear. Questions here should be independent of software, but you do need to show results and not just allude to them. It is hard to see that board size could be a binary variable and, if it is, that is a very poor way to use information on board size. Perhaps you are referring to the t statistic associated with a regression coefficient, but we should not have to speculate. $\endgroup$
    – Nick Cox
    Commented Nov 29, 2016 at 16:50
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    $\begingroup$ Are you controlling for other things that influence the performance? Are you accounting for endogeneity? Poor performance may cause downsizing of the boards, for instance. This is a typical corp fin study, you should use the "standard" control variables for this field. $\endgroup$
    – Aksakal
    Commented Nov 29, 2016 at 16:58
  • $\begingroup$ Thank you for your comments thus far. I have been told to carry out a T-test in order to 'test' the hypotheses by my supervisor. I took their word as the bible. To be frank, I don't know how it is supposed to figure with my work. Perhaps anyone can shed light on its use? I must be thick as I've been researching this for months now. @Aksakal Regarding endogeneity/heterogeneity, I am also running Panel Data and GMM regressions to account for these. I am also using other explanatory variables including Independence and Risk. $\endgroup$
    – user140454
    Commented Nov 29, 2016 at 17:33

1 Answer 1


Ignoring a very useful comment regarding the inclusion of control variables and the possible issue of endogeneity, the OP seems to run a simple regression (hopefully using also a constant term) of "Return on Assets" on "Board Size".

Then the t-test tests for the null hypothesis that Board Size does not have a statistically significant effect on Return on Assets. Apply this by specifying the complementary alternative "Board Size has a statistically significant effect on Return on Assets".

If the null is rejected, just look at the sign of the coefficient estimate : if it is positive, you have statistical evidence that Board Size affects positively Return on Assets, because you have a statistically significant and positive coefficient estimate (which gives the direction of influence). Analogously for the case where the estimate is a negative value.

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    $\begingroup$ If this is right (noting comments on the question), then yet another dimension is the applicability of plain regression to a response or outcome variable that is typically positive and likely to be highly skewed. $\endgroup$
    – Nick Cox
    Commented Nov 29, 2016 at 18:01
  • $\begingroup$ @NickCox That's very interesting and I guess there exists a whole separate discussion on the matter (of which I am unfamiliar). Is there some pointer you can provide (CV threads or literature)? $\endgroup$ Commented Nov 29, 2016 at 18:49
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    $\begingroup$ I guess that you really are familiar with the idea, but just not recognising my allusion! It's what motivates use of a logarithmic link in generalized linear models to ensure positive predictions. With a suitably generous definition, it's Poisson regression. blog.stata.com/2011/08/22/… is a favourite way in; non-Stata users can hum their way through the Stata parts while translating freely to their own customary software. $\endgroup$
    – Nick Cox
    Commented Nov 29, 2016 at 18:59
  • $\begingroup$ @NickCox Ah yes, now I recognize the face of the beast. Jensen's inequality making our life harder (and perhaps more interesting?) $\endgroup$ Commented Nov 29, 2016 at 22:26

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