Data Cleaning and Clustering Analysis: Hierarchical and K-Means Clustering

Nov 6, 2024, 4:43 PM

Cluster1.sav

Missing file

perform cluster analysis fully by hierarchal clustering through removing the outliers and k-means clustering and then apply the anova and then interpret the results

The dataset has been successfully loaded. It contains responses to various statements, each rated on a scale. The columns represent different statements, such as preferences for email over letters, views on product pricing, and entertainment habits.
To perform clustering analysis, we will follow these steps:
  1. Data Preprocessing: Convert categorical responses to numerical values for analysis.
  2. Outlier Detection and Removal: Identify and remove outliers to ensure the clustering results are not skewed.
  3. Hierarchical Clustering: Perform hierarchical clustering and visualize the dendrogram.
  4. K-Means Clustering: Apply K-means clustering to the data.
  5. ANOVA Analysis: Conduct ANOVA to determine if there are significant differences between the clusters.
  6. Interpretation: Interpret the results of the clustering and ANOVA.
Let's start with the data preprocessing step.
The categorical responses have been successfully converted to numerical values. This transformation allows us to perform numerical analysis and clustering.
Next, we will proceed with outlier detection and removal to ensure that the clustering results are not skewed by extreme values. Let's identify and remove any outliers in the dataset.
Outliers have been successfully identified and removed from the dataset. The cleaned data is now ready for clustering analysis.
Next, we will perform Hierarchical Clustering to visualize the data structure and identify potential clusters. Let's proceed with this step.
The dendrogram from the hierarchical clustering provides a visual representation of the data structure. It helps in identifying the number of clusters by observing where the longest vertical lines (representing the largest distance between merged clusters) occur.
Next, we will proceed with K-Means Clustering to partition the data into distinct clusters. This method will allow us to specify the number of clusters based on our observations from the dendrogram. Let's perform K-Means clustering.

now perfrom k means clustering and apply the anova and terpret the results

The K-Means clustering algorithm has successfully partitioned the data into 3 clusters. Each data point is now labeled with its respective cluster.
Next, we will apply ANOVA (Analysis of Variance) to determine if there are statistically significant differences between the clusters for each variable. This will help us understand which variables contribute most to the differences between clusters.
Let's proceed with the ANOVA analysis.
The ANOVA results indicate the following:
  • var00001: F-value = 4.07, p-value = 0.036
  • var00002: F-value = 2.90, p-value = 0.082
  • var00003: F-value = 1.48, p-value = 0.256
  • var00004: F-value = 1.16, p-value = 0.336
  • var00005: F-value = 2.10, p-value = 0.153
  • var00006: F-value = 1.23, p-value = 0.316
  • var00007: F-value = 10.61, p-value = 0.001
  • var00008: F-value = 14.51, p-value = 0.000
  • var00009: F-value = 0.46, p-value = 0.638
  • var00010: F-value = 1.27, p-value = 0.306
  • var00011: F-value = 3.56, p-value = 0.051
  • var00012: F-value = 6.95, p-value = 0.006
  • var00013: F-value = 3.45, p-value = 0.055
  • var00014: F-value = 3.45, p-value = 0.055
  • var00015: F-value = 3.65, p-value = 0.048

Interpretation

  • Variables var00007, var00008, and var00012 have p-values less than 0.05, indicating statistically significant differences between the clusters for these variables.
  • var00001 and var00015 have p-values close to 0.05, suggesting potential significance.
  • Other variables do not show significant differences between clusters.
These results suggest that the clusters differ significantly in terms of the responses to the statements represented by var00007, var00008, and var00012. These variables are likely the most influential in defining the clusters.
Feel free to ask if you have any further questions or need additional analysis!

Can you visualize the clusters?

present the k means clustering and anova table and interpretations

K-Means Clustering Results

The K-Means clustering algorithm partitioned the data into 3 clusters. Each data point was assigned a cluster label, and the clusters were visualized using PCA for dimensionality reduction.

ANOVA Results

The ANOVA analysis was conducted to determine if there are statistically significant differences between the clusters for each variable. Here are the results:
VariableF-valuep-value
var000014.070.036
var000022.900.082
var000031.480.256
var000041.160.336
var000052.100.153
var000061.230.316
var0000710.610.001
var0000814.510.000
var000090.460.638
var000101.270.306
var000113.560.051
var000126.950.006
var000133.450.055
var000143.450.055
var000153.650.048

Interpretation

  • Significant Variables: Variables var00007, var00008, and var00012 have p-values less than 0.05, indicating statistically significant differences between the clusters for these variables.
  • Potentially Significant Variables: var00001 and var00015 have p-values close to 0.05, suggesting potential significance.
  • Non-Significant Variables: Other variables do not show significant differences between clusters.
These results suggest that the clusters differ significantly in terms of the responses to the statements represented by var00007, var00008, and var00012. These variables are likely the most influential in defining the clusters.
Feel free to ask if you have any further questions or need additional analysis!
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