I am researching jobs scheduling using a heuristic algorithm. I want to prove that the solutions, obtained by the heuristic algorithm are close to the optimal solution.
I have experimental data sets with 100 values for each, obtained by the heuristic and the exact algorithm. My idea is to show that the two experimental data groups belong to the same general totality. For this I am doing the following:
1. Proving the normal distribution of the two data sets using the Pearson's chi-squared test.
2. Performing Student's t-test to show, that the data sets with normal distribution belong to the same general totality.
I am not an expert in statistical analysis. Is my thinking correct?
Perhaps you should be looking at using tests of equivalence. Typical statistical hypothesis testing tests for differences. Tests of equivalence show the results obtained are similar to a desired degree. For continuous data, two one sided t-tests may be appropriate. Equivalence testing is used in pharmacological research where it is not enough to demonstrate a non-significant result indicating lack of significant difference, but you need to demonstrate equivalence. Another approach would be to plot the 95% confidence intervals of the two distributions and visually compare the degree to which the two overlap.
Hi, following Macintosh, you can use a concordance test, for example, if you have continuous data, you could use the Lin concordance correlation.
Jorge Camacho
If you are interested in using an approach where differences in two Normally distributed data sets can be visualized, I have developed a spreadsheet that will do so. It is on Google Docs at https://docs.google.com/spreadsheet/ccc?key=0AixHzIqC4EIYdFBaWEU0M294c3RSczgtdFc2ZFZVamc#gid=0.
Mr Osborn, great thanks!
Excuse me for the question, but why do we need to sort the values? Couldn't we build histograms for the distribution of the two data sets? I think this will visualize the differences too.
I've found by sorting the data it allows for a point-to-point comparison in a way that the brain can comprehend more readily. Mathematically, there is no need to sort the data. For example, if the data are truly Normally distributed, sorting the data produces a symmetrical distribution around the mean which will also be the median (or close). Our brains are hard wired to see symmetry. Bell shaped curves are also nice but more difficult to generate from the original data. The sorted data when plotted against the probability represents the area under the bell curve.
use Student t-test for the equality of means and F-test of equality of variance..
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