基于加速度实验数据集的两种分布比较统计检验问询

Hey there, let's work through the statistical tests that fit your scenario. First, let's recap your setup to make sure I'm on the same page: you've got 50 objects $O_i$, each measured at 100Hz for 2 seconds (so 200 data points per object) across 50 experiments, resulting in each dataset $D_i$ and each object being represented by its acceleration mean ($M_i$) and standard deviation ($SD_i$). You're looking to compare two distributions—here are the best approaches based on what exactly you're targeting:

Comparing Distributions of Acceleration Means ($M_i$) #

This is the most straightforward comparison if you care about central tendency between two groups of objects:

• If your $M_i$ values follow a normal distribution (verify this with a Shapiro-Wilk test, or visually with Q-Q plots):
  • If the variances of the two groups are equal (check with Levene's test): Use the independent samples t-test to compare group means.
  • If variances are unequal: Opt for Welch's t-test, which adjusts for unequal variances without assuming normality of variances.
• If normality isn't met (common with small sample sizes, though your 50 samples are decent):
  • Go with the Mann-Whitney U test, a non-parametric alternative that compares median ranks instead of means, and doesn't rely on normality assumptions.

Comparing Distributions of Acceleration Standard Deviations ($SD_i$) #

Standard deviations are inherently right-skewed, so direct normality-based tests aren't ideal. Instead, focus on variances ($SD_i^2$) or use robust methods:

• For normal data: Use an F-test to compare the variances of the two groups (this is the standard test for equal variances).
• For non-normal data or when you want a more robust test:
  • Levene's test (or the even more robust Brown-Forsythe test) checks for equal variances without strict normality assumptions.
  • The Ansari-Bradley test is a non-parametric option that compares the scale (spread) of two distributions, which aligns with comparing SDs.

Comparing Raw Acceleration Data Distributions (If You're Targeting Full Distributions) #

If you want to compare the entire acceleration distribution of two objects (or two groups of objects' raw data) instead of just summary stats:

• Use the Kolmogorov-Smirnov (KS) test, which checks if two continuous distributions are identical, no normality assumptions required.
• For comparing more than two groups, the Kruskal-Wallis H test (non-parametric ANOVA) works to see if there are differences in distributions across groups.

Quick Notes #

• Since each $D_i$ has 200 data points, your $M_i$ and $SD_i$ are very precise estimates—so tests based on these summary stats will be reliable.
• Always visualize first! Boxplots for group comparisons, histograms/QQ plots for normality checks will help you confirm which test is the right fit.

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