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I'm reading a paper and I found this real data, I generated the graph in EXCEL (see below), there's a cross of the two lines, in this situation, is it possible that the interaction is not significant?

Okay maybe I'm asking a obvious question, but it's really against my intuition. I never thought about it before.

Thanks everyone!

enter image description here

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  • $\begingroup$ Do you know what the standard errors are? $\endgroup$ Mar 16 '16 at 12:47
  • $\begingroup$ Sorry, I don't have that... $\endgroup$ Mar 16 '16 at 13:03
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You could also be looking at a situation where a line graph is not an appropriate method of visualizing the data. Human brains are really good at picking out and understanding certain types of patterns, and good visualizations take advantage of that, while bad visualizations use it to mislead.

Are A and B categorical values, or are they different points in time? I suspect that they're nominal categorical, in which case connecting the "white" and "black" values with a line is thoroughly deceptive. Lines imply a temporal or spatial order, which by definition doesn't exist in nominal variables. So what you see as a cross in the line on the graph isn't significant because the lines themselves are effectively meaningless.

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  • $\begingroup$ Thank you! Yes! A and B refer to categorical values! I see, so in this situation, a more appropriate way is to present the data with bar chart? $\endgroup$ Mar 17 '16 at 2:30
  • $\begingroup$ Yes, a bar chart would be more appropriate here. Put one dimension on the x-axis, and color the bars based on the other dimension. $\endgroup$ Mar 18 '16 at 23:00
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As was stated earlier, it depends on the standard errors. If you have a small dataset with a lot of variability the regression lines might cross on a graph but the interaction term might not meet your level of statistical significant. Consider the following plot, where the different colors represent theoretical data from participants of different genders: enter image description here

Each dataset only has 10 observations, and fitting a regression model to the table results in the following stats:

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   8.4922     1.6514   5.143 9.83e-05 ***
time          0.6303     0.2661   2.368   0.0308 *  
gender        2.1139     2.3354   0.905   0.3788    
time:gender  -0.5282     0.3764  -1.403   0.1796  

Hopefully that helps!

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  • $\begingroup$ I see. If A and B referred to continuous value, then the variability of a small sample size should result in such way! Thank you! $\endgroup$ Mar 17 '16 at 2:34

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