I need to conduct K-means cluster analysis. That's why I test the Sphericity of clustering variables. But Mauchly's Test of Sphericity p-value is not greater than 0.05. So I am violating Sphericity. But my Huynh-Feldt value is .861 and its p-value is 0.000. In this circumstances can I run the k-means cluster analysis? By the way N= 11521. And variances of variables are same.
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If Mauchly's Test of Sphericity p-value is less than 0.05, it indicates that there is a violation of the assumption of sphericity. This assumption is important for conducting K-means cluster analysis accurately.
However, the Huynh-Feldt correction can be used to adjust for the violation of sphericity assumption. In your case, the Huynh-Feldt value is .861 with a p-value of 0.000, which indicates that there is a significant violation of sphericity. The Huynh-Feldt correction adjusts for the violation of sphericity assumption and can be used to conduct K-means cluster analysis.
Given that your N value is large (N=11521) and the variances of the variables are the same, it is reasonable to proceed with K-means cluster analysis using the Huynh-Feldt correction.
However, it is important to keep in mind that the Huynh-Feldt correction may affect the results of the analysis, and it may be necessary to interpret the results with caution. It is also advisable to explore other clustering techniques and compare the results to ensure the validity of the analysis.
Elif Ceyhan When conducting k-means cluster analysis, assumptions such as sphericity may need to be considered. Sphericity assumes that the variances of the clustering variables are equal, and the variances-covariances between variables are the same. If Mauchly's Test of Sphericity is significant (p < 0.05), indicating a violation of sphericity, alternative methods, such as the Huynh-Feldt correction, can be applied.
In your case, the Huynh-Feldt correction factor is 0.861, and its associated p-value is 0.000. This suggests that the assumption of sphericity is violated, and the variances-covariances between variables are not the same. Therefore, using traditional k-means clustering analysis may not be appropriate.
However, k-means clustering is a non-parametric method that does not rely on assumptions of sphericity or equal variances. It is based on the mean values of variables within clusters. Therefore, you can still proceed with k-means clustering analysis despite the violation of sphericity.
Keep in mind that k-means clustering is sensitive to the scale and range of variables. Make sure to standardize or normalize your variables if they have different measurement units or ranges. Additionally, consider the interpretability and meaningfulness of the results obtained from k-means clustering, as it is primarily a partitioning method rather than a formal statistical test.
Given that your sample size is relatively large (N = 11521), k-means clustering can still provide useful insights into the patterns and structure within your data. Just be cautious when interpreting the results and consider the potential limitations associated with violating the assumption of sphericity.
If you have any further questions or concerns, feel free to ask. Good luck with your analysis!
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