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I have a significant result for linear regression: enter image description here

When I control for age and sex, the main coefficient of interest is no longer significant:

enter image description here

What is the appropriate way to write in APA format the non-significant results?

So far I wrote:

MEAN_FA was a significant predictor for RMSSD (F(1, 248) = 5.79, p = 0.016, R2adj = 0.018) but did not remain significant when controlled for age and sex.

Is it appropriate to leave it at that or should any values be reported?

What if the multiple regression was significant or trending?

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  • $\begingroup$ Is it even meaningful to report the results of the first model? (In light of the second model, wouldn't that be misleading?) Your answer to that might help you determine what else you need to report. $\endgroup$
    – whuber
    Oct 12, 2020 at 22:36
  • $\begingroup$ Yes, its meaningful to report non-significant results, Im just unsure how detailed to get $\endgroup$
    – CanyonView
    Oct 12, 2020 at 23:29
  • $\begingroup$ What are the conventions you notice in your field and in that journal? $\endgroup$
    – Dave
    Oct 12, 2020 at 23:33
  • $\begingroup$ My question wasn't concerned about reporting non-significant results: it was concerned with the conflict between the two models. In light of the second model's results, the first isn't merely non-significant: it gives misleading information, regardless of any apparent level of significance. $\endgroup$
    – whuber
    Oct 13, 2020 at 12:33

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APA's standard write-up for all results is to describe the result in words first (e.g., "there was a significant effect for X" or "scores on Y were significantly greater than for Z") and then write the decision statement (i.e., the statistic you used to make that conclusion). Here's a link to a short page with examples of APA 7th edition result write-up. What you wrote would likely be sufficient for most cases, though it does depend on what else you're reporting. For example, if these two models constitute the entirety of your analyses, then you'd probably want to discuss the details and thus talk about each predictor and the change in $R^2$. If this is just part of the statistical analyses you'll be reporting, then it's fine to hit the high points and move on.

Now, to your other question about the model's significance. Generally speaking, there are few cases where we actually are about whether a regression model is significant or not. Primarily, we tend to be interested in what predictors are significant or what predictors improve our prediction accuracies. By and large, it's not hard to get a significant regression model.

Now, to speak to reporting on trends. I assume this means whether a result trends toward significant or not. It's important to remember that a result either is or is not significant as null hypothesis testing only has two outcomes: reject the null or fail to reject the null. If there's a question about how "meaningful" or "real" a result is, then you want to look at the effect size. The only time that I think it's useful to comment on a close to significant result is when you have legitimate concern for your ability to detect a true effect due to sample size. In other words, if you think that your power is too low, then it's worth just commenting on that as a possible explanation for the result but highlight that the result should not be treated as significant and that follow-up with a larger sample would be warranted. You can formally test what your power to detect an effect would be with software like G*Power (see details for multiple regression here), and it's good practice to compute that as part of your routine analyses.

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