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I am being tortured with the following problem...

I have a set of crude mortality rates for ages 0 to 60. Let's call them Observed Rates. I use a smoothing technique (cubic spline regression) on the crude mortality rates and so smoothed mortality rates are produced for ages 0 to 60. Let's call them Estimated Rates.

I want to know whether the Estimated Rates are a good representation of the Observed Rates. I have calculated the R-square, however I am also looking to confirm this with a statistical test.

Could wilcoxon signed rank test work for my case?

Panos
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  • Welcome to CV. You're asking whether your model fits your data well without including your data *or* a summary of your model. Also, why would you want to do a significance test? If you find no significant deviation between the fitted and actual rates, that doesn't mean your model fits the data well. – Frans Rodenburg Jul 10 '19 at 09:11

2 Answers2

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Take a look at this answer.

You cannot use a statistical test like the Wilcoxon to confirm that two samples are similar, or come from the same population.

All you can do is show how similar the two samples are, perhaps using something like the RMSE.

Vincent B. Lortie
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  • Vincent i attached you the following paragraph from "1.3.5.16. Kolmogorov-Smirnov Goodness-of-Fit Test". The paragraph "Importance" said the following: There are many non-parametric and robust techniques that are not based on strong distributional assumptions. By non-parametric, we mean a technique, such as the sign test, that is not based on a specific distributional assumption. https://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm Can you tell your opinion?? – Panos Sep 28 '18 at 13:51
  • As far as I know that's correct. The point here is not whether you should use a parametric or non-parametric test, it is whether or not a test can confirm equivalence or similarity between two samples. – Vincent B. Lortie Sep 29 '18 at 01:10
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As Vincent (and the link he supplied) say, you cannot use a significance test for this.

I would graph the expected vs. observed in various ways:

  1. A scatterplot of one vs. the other
  2. A Tukey mean density plot of one vs. the other
  3. A box plot of the differences between them
  4. A QQ plot of one vs. the other
Peter Flom
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