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I have N objects and the mean of one attribute A1 is namely, M1 and the standard deviation of the attribute A1 is namely, S1.

This N objects is divided into K-clusters. If for cluster Ki, i have a mean of attribute A1 of N1, what technique should i use to check if N1(cluster mean) is significantly different from M1?

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Depending on the sample size you could consider a permutation test. First calculate the difference in the means of the two clusters. Then estimate the distribution of the differences in the means of the two clusters by randomly assigning observed objects to each cluster (I.e. Assuming the cluster assignment is independent of the attribute). If the observed difference is improbably large then it indicates the difference is significant.

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  • $\begingroup$ Hi. The clusters are created based on the attributes (k means clustering) and Im just wondering what technique to use to tell if a certain attribute in Cluster 1 is significant by trying to find a way to know if there is a significant difference from the whole N population mean and the cluster mean of an attribute. $\endgroup$ Apr 7, 2017 at 19:17
  • $\begingroup$ So are you wanting to determine whether an attribute is effectively irrelevant when trying to learn to which clusters objects belong? $\endgroup$ Apr 7, 2017 at 19:30
  • $\begingroup$ I already know which cluster are some objects belong. Yes. Im trying to know if an attribute in that cluster is significant by comparing the means of the cluster and population. $\endgroup$ Apr 8, 2017 at 6:20
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    $\begingroup$ Variable selection has a broad literature. The tool you use will depend on the purpose of your analysis. For instance, you may want to perform cross validation to assess which attributes improve the predictive performance of the model. You could take a look at this document to help think about the problem: jmlr.org/papers/volume3/guyon03a/guyon03a.pdf. $\endgroup$ Apr 8, 2017 at 7:52

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