Well,

You can use the Cumulative residual standard

It means you might not have sufficient evidence to conclude that MV moderates the relationship between IV1 and DV.

Keep in mind that p-values are just one kind of evidence. They should be considered in the context of other evidence as well (you should not make a decision based only on the p-value). P-values are also continuous, and should be interpreted as such (a lot of evidence against the null hypothesis, some evidence against the null hypothesis, not much evidence against the null hypothesis, etc.), not just split into two categories "significant" and "not significant".

For more information, see the below paper. Article The ASA's Statement on p-Values: Context, Process, and Purpose

Stephen Politzer-Ahles and Dounia Mrad Thank you so much for your answers

Hi Fatemeh,

Here is a similar debate:

https://www.researchgate.net/post/Is_it_ok_if_some_variables_moderate_insignificant_relationships_in_the_technology_adoption_model

https://www.researchgate.net/post/How_can_we_decide_a_moderation_effect_significant_or_not

https://www.researchgate.net/post/interpreting_moderation_effect

Also, I suggest to you to read Dawson's (2014) article:

Dawson, J. F. (2014). Moderation in management research: What, why, when, and how. Journal of Business and Psychology, 29(1), 1-19.

Saeed Awadh Bin-Nashwan thank u very much.

You could calculate your achieved power to see if your sample size was sufficient to detect a significant interaction (i.e., moderation). If your sample size was not significant, you could talk about how you are approaching significance. I have to report on non-signifiant moderation as well, and I just stated that the interaction was not significant and reported the stats in the text (e.g., (b = -.007, t(46) = -1.43, p = .16)). Maybe you could say that for the different levels of the moderator, there is no relationship between IV 1 and DV. Here is a video I found helpful about moderation: https://www.youtube.com/watch?v=0vcUtzPDGrw

Dana Goetz -- Thank you very much for your suggestion, but I would actually not recommend calculating this kind of achieved power (also sometimes called "post-hoc power", "observed power", etc.). Long story short, if the test was not significant, we already know that the sample did not have significant power to detect an effect of the size the study observed (or smaller); the conversion between the observed p-value and the smallest possible effect size that could be detected is fairly straightforward (the easiest way is to look at the confidence interval around the effect; that tells you that the study had did not have enough power to detect effect sizes anywhere within that confidence interval). Some relevant references:

• https://www.vims.edu/people/hoenig_jm/pubs/hoenig2.pdf
• http://www.dokeefe.net/pub/okeefe07cmm-posthoc.pdf
• https://dirnagl.com/2014/07/14/why-post-hoc-power-calculation-does-not-help/

Also, I wouldn't say that there is "no relationship between IV1 and DV". Technically, there is always a relationship; it's just that sometimes the relationship is not significantly different than zero.

What you have done in your example (reporting the result and stating that it's not significant) is I think the perfect approach.

Stephen Politzer-Ahles, Thank you for the feedback! I wish I had your stats brain! If calculating achieved power does not make sense, then hopefully Fatemeh Maleki calculated a priori power, and can speak to the power of the sample in that way as it pertains to the findings?

While having an a priori power analysis is certainly helpful, what I like to do to help interpret non-significant results is to look at the range of hypotheses that cannot be statistically ruled out by the data (i.e., the confidence interval). Consider the attached graph, where each bar represents an effect (maybe a difference between two conditions, maybe an interaction term) and the error bar represents the confidence interval of that effect, and the red line represents what we consider to be the smallest meaningful effect size (this will depend on your field of study). Both effects are non-significant (i.e., their confidence intervals include zero). The first effect, however, is non-significant in an informative way: we can safely conclude that it's not significantly different than zero, and that it is significantly smaller than any effect we might care about, so this is the sort of situation where we typically would conclude there is practically no effect. On the other hand, the second effect is not very informative: it's not significantly different from zero, but also not significantly different from potentially interesting effects --- i.e., it's potentially consistent with the presence of an effect. The latter situation corresponds to not having enough power (because of small sample size, too much variation in the measurement, etc.) to rule out potentially important effects.

This is a common and often recommended way to think about results; for example, Lakens (https://daniellakens.blogspot.com/2016/12/tost-equivalence-testing-r-package.html, among others) and Simonsohn (http://datacolada.org/wp-content/uploads/2015/05/Small-Telescopes-Published.pdf, among others) often stress the importance of distinguishing between informative null results and inconclusive null results like this.