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Essentially, I have a statistical standardization method that I am running on data to show that the data is more significantly similar to the linear model Y=X AFTER standardization.

I have a p value of .1 before standardization, and a p-value of .6 after standardization. Although the p-value before standardization is > .05 (and thus does not reject the null hypothesis of Y=X), since it is closer to .05 than .6, can I draw any statistical conclusions from this?

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You can directly answer this question by performing hypothesis testing comparing your two models (standardized and non-standardized). Your current p-values tell you that neither model is significantly different from the null linear model. You should now run a test to see whether one model is significantly different from the other.

I suspect you won't have enough evidence to conclude that the models are significantly different from one another. It is possible (but unlikely) that the models are such that neither is different from the null model, but they are different from one another.

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