No significance in ANOVA between groups but means are different?

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Sld011
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Hi, i conducted a 2 x 2 anova with group and omission in two conditions, the numbers in my ANOVA output are not significant however when looking at the means for the two groups in these conditions the means are very different? and looks as if one group produced way more omissions than the other (which is what I expecte to find) Is there anyway to report this? or do I have to just say no significance main effect for group therefore groups did not differ statistically in the number of omissions??

thank you!!!
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monkyvirus
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You could say "despite the large mean difference an ANOVA did not return a statistically significant result". Make sure to report the relevant values. If you believe the difference is practically significant you should mention that.

You coud present the difference graphically to show your point (I suggest using a boxplot). I would guess the "box" parts of the boxplots overlap quite a bit. If they don't then you may have made a mistake so double check the ANOVA.

Statistical significance means "this difference cannot plausibly be explained by random variation between samples"*. So if your samples had high variances that's probably why you didn't get statistical significance. It doesn't mean there isn't a difference just that at the moment you can't be sure it wasn't due to random variation.

*This is a practical definition, not a formal one!
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iammichealjackson
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(Original post by Sld011)
Hi, i conducted a 2 x 2 anova with group and omission in two conditions, the numbers in my ANOVA output are not significant however when looking at the means for the two groups in these conditions the means are very different? and looks as if one group produced way more omissions than the other (which is what I expecte to find) Is there anyway to report this? or do I have to just say no significance main effect for group therefore groups did not differ statistically in the number of omissions??

thank you!!!
If you had a very small sample or if the SDs for each group are high you would not get a significant result. You may not have sampled enough people to detect any effect, or there may be too much "noise" in the measurements. If your p is less than .20 you can report the effect as being "marginally" significant.
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