Comparing datasets of varying independent variable

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Arun S 2022-9-23

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回答： Aditya 2023-11-16

Hi,

I have two datasets with the following information - time, count. I wish to quantify how well they match using some measure like the chi square statistic or something similar.

However the time information in both data sets is not exactly the same. For instance dataset 1 would have a point like time=1.9, count=.9 and dataset2 would have a point like time=1.85, count=0.8. The difference between the sampled times of both datasets is also not uniform. How do I accomplish this? Here is a picture showing both plots.

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Torsten 2022-9-23

https://stats.stackexchange.com/questions/19103/how-to-statistically-compare-two-time-series

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Answer 1

Aditya 2023-11-16

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Hi Arun,

I understand that you want to compare two different time series dataset statistically.

To quantify how well two datasets with different time points match, you can use interpolation to align the data points and then calculate a measure of similarity, such as the chi-square statistic. Here's a step-by-step approach:

Import the datasets: Load both datasets into MATLAB, ensuring that each dataset has two columns representing time and count.
Interpolate the data: Use interpolation techniques, such as linear interpolation or spline interpolation, to align the data points from both datasets onto a common time grid. This will allow you to compare the counts at corresponding time points accurately.
Calculate the chi-square statistic: Once the data points are aligned, you can calculate the chi-square statistic to measure the similarity between the datasets. The chi-square statistic compares the observed counts in each dataset to the expected counts based on a reference distribution (e.g., uniform distribution or another dataset).

Here's an example code snippet to illustrate the process:

% Load the datasets (assuming dataset1 and dataset2 are already loaded)
% Interpolate the data onto a common time grid
commonTime = min(dataset1(:, 1)):0.01:max(dataset1(:, 1)); % Define a common time grid
interpolatedCount1 = interp1(dataset1(:, 1), dataset1(:, 2), commonTime);
interpolatedCount2 = interp1(dataset2(:, 1), dataset2(:, 2), commonTime);
% Calculate the chi-square statistic
chiSquareStat = sum((interpolatedCount1 - interpolatedCount2).^2 ./ interpolatedCount1);
% Display the plots
plot(dataset1(:, 1), dataset1(:, 2), 'b', 'LineWidth', 1.5);
hold on;
plot(dataset2(:, 1), dataset2(:, 2), 'r', 'LineWidth', 1.5);
xlabel('Time');
ylabel('Count');
title('Comparison of Datasets');
legend('Dataset 1', 'Dataset 2');
% Output the chi-square statistic
disp(['Chi-Square Statistic: ', num2str(chiSquareStat)]);

In this code, the datasets are interpolated onto a common time grid using 'interp1'. Then, the chi-square statistic is calculated by taking the squared differences between the interpolated counts and dividing them by the expected counts (interpolatedCount1). Finally, the plots of both datasets are displayed, and the chi-square statistic is outputted.

Make sure to adjust the code according to your specific dataset format and interpolation requirements.

Hope this helps.

Thanks and Regards,

Aditya Kaloji