两种分布比较的统计检验：基于加速度实验数据的技术问询

Got it, let's walk through the best statistical tests for your acceleration data setup, based on what you've described:

First, let's recap your data structure to make sure we're aligned #

• You ran 50 experiments on object Oi, each collecting 2 seconds of acceleration data at 100Hz (so 200 data points per dataset Di)
• Each Di gives you a mean Mi and standard deviation SDi, so each experiment's result is summarized as Oi(Mi, SDi)
• You also have a merged dataset combining all 50 experiments, and you need to compare distributions here

Now, let's break down the test options based on what exactly you want to compare: #

1. Comparing a single experiment's dataset vs the merged dataset

If you want to check if one individual Di comes from the same underlying distribution as the full merged dataset:

• Kolmogorov-Smirnov (K-S) Test: The go-to nonparametric test for comparing two sample distributions. It doesn't require assuming your data follows a specific distribution (like normal), which is great for physical sensor data that might have noise or outliers.
• Anderson-Darling Test: Similar to K-S, but it weights the tails of the distribution more heavily. This is useful if you care about detecting differences in extreme acceleration values (like sudden jolts).

2. Comparing the distribution of 50 experiment means (Mi) vs the merged dataset's overall mean

If you're looking to see if the 50 individual experiment means are consistent with the overall merged mean:

• One-Sample t-Test: First, check if your 50 Mi values are approximately normally distributed (use the Shapiro-Wilk test for this). If they are, this test will tell you if the average of the Mis is significantly different from the merged dataset's mean.
• Wilcoxon Signed-Rank Test: If the Mis aren't normally distributed (common with smallish sample sizes), this nonparametric alternative compares medians instead of means, avoiding the normality assumption.

3. Comparing the distribution of 50 experiment standard deviations (SDi) vs the merged dataset's standard deviation

If you want to check if the spread of acceleration data is consistent across experiments vs the merged data:

• Chi-Squared Test: Use this to test if the sample standard deviation of a single Di matches the merged dataset's standard deviation. You can run this for each Di, or aggregate the SDis to test the overall distribution.
• Levene's Test: This checks if the variances (squared standard deviations) of multiple groups are equal. Here, you can treat each Di as a group and compare their variances to the merged dataset's variance to see if spread differs significantly.

Quick practical tip #

Before jumping into statistical tests, visualize your data first! Plot histograms or boxplots of individual Dis alongside the merged dataset, or plot the distribution of all Mis and SDis. This will give you a gut check on where differences might lie, helping you pick the right test for your goal.

If you're coding this up, most of these tests are available in Python's scipy.stats library (e.g., ks_2samp() for K-S, ttest_1samp() for t-tests) or R's base stats package.

内容的提问来源于stack exchange，提问作者Carlo Allocca