# Omnibus F-stat insignificant, anything left to say about reg. coefficients?

##### New Member
Hi there.

I am calculating a multivariate regression by hand, and just calculated the F-stat for the model.

Calculated F-stat = 4.899
Critical F*-score from table= 19.25
Since my F-stat is not larger than my F* score, my overall model is insignificant.
Note: N=8.

In Tacq (1997): "One should always start with the test of the global model, for if this does not show a significant result, then the regression function is unfit for use. The analysis should then be terminated. Only in the second instance, when R2 is significant, does it become legitimate to investigate whether this is also the case for each of the predictors separately."
---Therefore, I will not calculate the signifiance of my predictors and their significance will not be discussed in my results.

My question is: What can I say, if anything, about the regression coefficients? Is it dangerous to interpret the regression coefficients like normal but to mention that our overal assumed linear model is insignificant and that further research is needed to better understand if the relationship takes a different form? Or is it irresponsible to say anything at all about the coefficients?

#### hlsmith

##### Omega Contributor
How many independent variables did you have in the model? An n-value of eight would not typically power more than a single variable at most.

##### New Member
Thanks for your message. I knew someone would ask about that. I have slightly altered the F, f* and N that I reported because it is for an exam, and I don't want to create problems for myself if this post was ever found.

But I can guarantee with 100% that my calculations are correct and that the conclusion drawn about the insignificance of the model is correct. So I'm just trying to figure out how to report (or not report) the coefficients.

#### hlsmith

##### Omega Contributor
Typically you may opt not to report coefficients. Though you may look to see if any has a big effect but my have been underpowered.

#### Dragan

##### Super Moderator
Hi there.

Calculated F-stat = 4.899
Critical F*-score from table= 19.25
Since my F-stat is not larger than my F* score, my overall model is insignificant.
Note: N=8.
Your critical F-value that you're stating above cannot be correct - even with a p-value of 0.01 with n=8 on 1 degree of freedom in the numerator - it's 11.26.

##### New Member
Thanks, hlsmith! I calculated the Cohen's D-stat of the test, which came out to be 0.53641011, which under Cohen's suggestion should be considered "medium". So I just saidd:

"We did not find any significant results that X1 and X2 affect Y. However, this does not necessarily mean that there is not relationship between these variables. Indeed, we did find a moderately large effect size in our study which implies that X1 and X2 together do have some sort of relationship with Y. One of the limitations of our study was our small sample size of 8 respondents, which may not have provided enough statistical power to find statistically significant results. Our results, however, also imply that the relationship might not take the shape of a straight line like we assumed, and that it might possibly have a U-shaped or plateau-shaped relationship. Further research is necessary with a larger sample size to investiage whether the relationship takes on a different form than we assumed in this analysis.”

(Note: Avoidance of statistical jargon was intentional).

Last edited:

#### hlsmith

##### Omega Contributor
If the relationship does not seem linear you can try transforming the IV or DV, or both.