MATLAB: How shall I confirm the significance of week days’ Up-Downs for some stock

significance

I survey on the ups and downs of one stock in the past 3000 trading days and sort them by week day: Monday (ups53%, 0.53-0.5=0.03), Tuesday(ups55%, 0.55-0.5=0.05),… like this; Then I get below picture:
Then how shall I confirm the difference between week days is significant or just random?

Best Answer

Typically one would perform an Analysis of Variance ( anova1) on the actual dataset, not on your summary statistics. This will test the null hypothesis of equal mean returns vs. the alternative that at least one day's mean return is different. If you want a pairwise comparisson you can then pass the stats output to the multcompare function.
[p,tbl,stats] = anova1(data);
c = multcompar(stats);
If your data (returns) are non-normal then use the kruskal-wallis test, similar concept but uses the medians.
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