Automatically select the right number of bins (or combine the bins) for the expected frequencies in crosstab, in order to guarantee at least 5 elements per bin

4 次查看（过去 30 天）

Sim 2024-8-23

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2147474-automatically-select-the-right-number-of-bins-or-combine-the-bins-for-the-expected-frequencies-in

评论： Star Strider 2024-8-23

I have two observed datasets, "x" and "y", representing "future stock prices", and I want to compare the observed frequencies in bins of "x" and "y" against the other, through crosstab. To do so, I first need to place the elements of "x" and "y" into bins, by using the histcounts function. The resulting binned arrays, "cx" and "cy", are then compared to each other with a chi-square test, perfomed by crosstab. The chi-square test of independence is performed to determine if there is a significant association between the frequencies of "x" and "y" across the bins.

However, the chi-square test "is not valid for small samples, and if some of the counts (in the expected frequency) are less than five, you may need to combine some bins in the tails.". In the following example, several bins of the observed frequencies "cx" and "cy" have zero elements, and I do not know if they affect the expected frequencies calculated within/by crosstab.

Therefore, is there a way in crosstab to automatically select the right number of bins for the expected frequencies, or to combine them if some are empty, in order to guarantee at least 5 elements per bin?

rng default;  % for reproducibility
a = 0;
b = 100;
nb = 50;
% Create two log-normal distributed random datasets, "x" and "y' 
% (but we can use any randomly distributed data)
x = (b-a).*round(lognrnd(1,1,1000,1)) + a;
y = (b-a).*round(lognrnd(0.88,1.1,1000,1)) + a;
% Counts/frequency of "x" and "y"
cx = histcounts(x,'NumBins',nb);
cy = histcounts(y,'NumBins',nb);
[~,chi2,p] = crosstab(cx,cy)
chi2 = 476.6926
p = 2.9412e-28

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

回答（1 个）

Star Strider 2024-8-23

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2147474-automatically-select-the-right-number-of-bins-or-combine-the-bins-for-the-expected-frequencies-in#answer_1504139

One option for small samples is to use the fishertest function.

6 个评论
显示 4更早的评论隐藏 4更早的评论

Sim 2024-8-23

Thanks @Star Strider :-)

Star Strider 2024-8-23

My pleasure!

Since your data are not normally distributed, friedman may be the most appropriate, since like other nonparametric distributions (explore them, such as ranksum as well), it only requires that the values to be compared share the same distribution, regardless of what that particular distribution is. I usually use it or other nonparametric analysis functions to compare lognormally-distributed data, since most of what I deal with (physiological data) are lognormally distributed.

请先登录，再进行评论。

请先登录，再回答此问题。