Segment your sample into naturally occurring groups based on multivariate similarity — without predefined labels.
K-Means Cluster Analysis is an unsupervised machine learning technique that partitions observations into k groups (clusters) such that each observation belongs to the cluster with the nearest centroid (mean). Unlike classification methods, clustering requires no predefined outcome labels — it discovers structure in your data purely from the pattern of similarities and differences across multiple variables. This makes it ideal for exploratory research where you suspect your sample contains meaningful subgroups.
Cluster analysis is widely used in market research (customer segmentation by purchase behaviour), psychology (identifying client profiles or coping style subtypes), health sciences (classifying patient phenotypes), and educational research (grouping learners by performance profiles). The resulting clusters are described by their means on each clustering variable, allowing you to give each cluster a substantive label (e.g., 'high engagement, low anxiety' vs. 'low engagement, high anxiety').
StatRyx automates the cluster analysis process: it standardises variables to remove the influence of different measurement scales, uses the elbow method and silhouette scores to help determine the optimal number of clusters k, runs K-Means with multiple random starts to find the global solution, profiles each cluster on all clustering variables, and performs one-way ANOVAs to confirm that clusters differ significantly on each variable.
| Variable | Cluster 1 (n=84) | Cluster 2 (n=112) | Cluster 3 (n=76) | F | p |
|---|---|---|---|---|---|
| Conscientiousness | 0.82 | 0.11 | −0.74 | 94.3 | < .001 |
| Neuroticism | −0.69 | 0.05 | 0.91 | 87.6 | < .001 |
| Agreeableness | 0.23 | 0.76 | −0.41 | 56.2 | < .001 |
| Extraversion | 0.14 | 0.68 | −0.55 | 48.9 | < .001 |
K-means cluster analysis was conducted on standardised scores of five personality variables. The elbow criterion and silhouette analysis both suggested a three-cluster solution (silhouette coefficient = .42). Cluster 1 (n = 84, 31%) was characterised by high conscientiousness and low neuroticism, designated 'Organised-Stable.' Cluster 2 (n = 112, 41%) showed high agreeableness and extraversion, designated 'Social-Agreeable.' Cluster 3 (n = 76, 28%) displayed high neuroticism and low conscientiousness, designated 'Anxious-Disorganised.'
Yes. You can run it without an account (3 free analyses), and a free account adds 10 more — a one-time allowance, no payment needed. Every result includes the APA 7 write-up. Paid plans (Student from $9/month) add more analyses and Word, PDF and Excel export.
No coding required. Specify the variables to cluster in plain English and StatRyx handles standardisation, the search for optimal k, multiple random starts, and all output tables and plots.
StatRyx uses both the elbow method (plotting within-cluster sum of squares against k and identifying the 'elbow' where improvement diminishes) and the silhouette coefficient (which measures how similar each observation is to its own cluster vs. neighbouring clusters). The solution with the highest silhouette score is recommended.
There is no strict minimum, but cluster solutions become more stable and replicable with larger samples. A rough guideline is at least 5 times the number of variables, with a practical minimum of around 50–100 observations to detect meaningful clusters.
Validation strategies include: running the analysis on a random split-half of your sample and checking whether the same clusters emerge; using discriminant analysis to verify that the clusters are well-separated; and checking whether cluster membership predicts theoretically meaningful external variables (criterion validity).
Run a K-Means Cluster Analysis on your data →