网页色彩偏好调研数据的差异检验与聚类分析技术咨询

Hey there! Let's break down how to tackle your two tasks with that Likert-scale color preference data—super common scenario, so I’ve got you covered.

Since you’re working with ordinal Likert data and comparing 10 color groups per webpage, here’s a step-by-step approach:

• Pick the right statistical test: Skip parametric ANOVA (it assumes normality, which Likert data rarely meets) and go with the Kruskal-Wallis H test—the non-parametric equivalent for comparing multiple ordinal groups. If it returns a p-value ≤ 0.05, that means at least one color has a statistically different preference rating than others.
• Follow up with post-hoc tests: To pinpoint exactly which color pairs differ, use Dunn’s test with a Bonferroni correction (this adjusts for the multiple comparisons that would otherwise inflate your Type I error rate). Tools like R’s dunn.test package or Python’s scikit-posthocs library make this straightforward.
• Quick code example (R):

  # Load dependencies
  library(dunn.test)
  library(tidyverse)
  
  # Filter data for a single webpage (repeat this for each of your 10 webpages)
  target_webpage <- your_data %>% filter(webpage == "ecommerce")
  
  # Run Kruskal-Wallis test
  kruskal_result <- kruskal.test(likert_score ~ color, data = target_webpage)
  print(kruskal_result)
  
  # If significant, run Dunn's post-hoc test
  if (kruskal_result$p.value <= 0.05) {
    dunn_posthoc <- dunn.test(target_webpage$likert_score, target_webpage$color, method = "bonferroni")
    print(dunn_posthoc)
  }
  

• Interpretation: Focus on the adjusted p-values from Dunn’s test—any pair with an adjusted p-value ≤ 0.05 has a statistically significant difference in preference.

Once you’ve confirmed differences, you can cluster similar colors using a mix of stats and practical color logic:

• Hierarchical clustering on mean scores: This method groups colors based on how close their average Likert ratings are. Here’s how to implement it:
  1. Calculate the mean Likert score for each color in your target webpage.
  2. Compute a distance matrix (Euclidean distance works well for ordinal means here).
  3. Use Ward’s method for hierarchical clustering—it minimizes within-group variance, leading to tight, meaningful clusters.
  4. Cut the resulting dendrogram at a height that balances statistical rigor and practical sense (the elbow method can help you find the optimal number of clusters).
• Quick code example (Python):

  import pandas as pd
  import scipy.cluster.hierarchy as sch
  import matplotlib.pyplot as plt
  
  # Filter data for one webpage
  blog_webpage = your_data[your_data['webpage'] == "blog"]
  color_avg_scores = blog_webpage.groupby("color")["likert_score"].mean().reset_index()
  
  # Generate linkage matrix for clustering
  distance_matrix = sch.distance.pdist(color_avg_scores[["likert_score"]])
  linkage_matrix = sch.linkage(distance_matrix, method="ward")
  
  # Plot dendrogram to visualize clusters
  plt.figure(figsize=(10, 6))
  sch.dendrogram(linkage_matrix, labels=color_avg_scores["color"].values)
  plt.title("Hierarchical Clustering of Color Preferences for Blog Webpages")
  plt.xlabel("Color")
  plt.ylabel("Distance Between Groups")
  plt.show()
  

• Validate with color theory: Don’t rely only on stats—cross-check your clusters with established color principles (e.g., warm vs cool tones, analogous vs complementary colors) to ensure the groups make intuitive sense for your design use case.

内容的提问来源于stack exchange，提问作者Iden