# Statistical test for comparing the performance of two methods using absolute differences

I am doing a study where I have to compare tumor sizes measured using two different methods with the real tumor size.

What I want to prove is that the absolute difference between method 1 and real tumor size is no bigger than 10 milimeters, and the same for method 2.

Considering this is an absolute difference, what statistical test should I use and how do I do this one-tailed test in SPSS or Python?

I thought about using the Wilcoxon test, but I don't think this would work since I want to evaluate absolute differences.

• Welcome to CV. I don't see how you could possibly "prove" such a statement, but you could establish a high degree of credibility by collecting many independent measurements and finding that all are within 10 mm of the size as established by a procedure known to be highly accurate and reasonably precise. If you have no such "ground truth" procedure, then all bets are off: you would have no way to determine the errors in the first place. Do you have such a procedure? What do you know about its accuracy and precision? – whuber Sep 6 '18 at 21:17
• I think Wilcoxon signed-rank test should work in this scenario. en.wikipedia.org/wiki/Wilcoxon_signed-rank_test – Maxtron Sep 7 '18 at 2:11
• @whuber I know that the mean difference between Method 1 and Ground Truth/Real tumor size was 4,6 +- 5,5 mm, between Method 2 and Ground Truth was 4,37 +- 3,77 mm. I have to consider the ground truth to be measurement error free, or I cannot do this. Not all measurements are within 10mm of the real size since I have some outliers. What I wanted was to prove that, even with those outliers, the difference is smaller than 10mm, with statistical significance. – Paulo Maia Sep 7 '18 at 15:20
• You need to be more precise in your statement. It sounds like you want to demonstrate something about an average difference rather than all the observed differences. – whuber Sep 7 '18 at 15:43
• @whuber I do, sorry if that was not clear. For all observed differences I used a bland-altmann plot, but I also wanted to do the statistical testing on the average of the absolute value of the differences – Paulo Maia Sep 7 '18 at 15:54