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Judge by the skewness/kurtosis and a QQ plot instead.","Group 'UMAP 2' rejects normality (p = 0.0000); prefer a rank-based test.","Group 'UMAP 2' has n = 2000; at this size a normality test flags departures far too small to affect a t-test. Judge by the skewness/kurtosis and a QQ plot instead."],"results":[{"excess_kurtosis":-1.2529133011965379,"group":"UMAP 1","interpretation":"Data significantly deviates from normality (W = 0.9422, p = 0.0000)","n":2000,"normality_rejected":true,"p_value":2.849213094206145e-27,"skewness":-0.17071134288823964,"statistic":0.9422077027887164,"test":"Shapiro-Wilk"},{"excess_kurtosis":-1.6118769050391721,"group":"UMAP 2","interpretation":"Data significantly deviates from normality (W = 0.8752, p = 0.0000)","n":2000,"normality_rejected":true,"p_value":2.529057447851563e-37,"skewness":-0.1749210942964271,"statistic":0.8751870537690664,"test":"Shapiro-Wilk"}],"source":{"kind":"arrays"}},"error":null},{"label":"stats.normality","method":"stats.normality","params":{"method":"anderson_darling"},"result":{"all_normal":false,"alpha":0.05,"method":"anderson_darling","notes":["Group 'UMAP 1' rejects normality (p = 0.0000); prefer a rank-based test.","Group 'UMAP 1' has n = 2000; at this size a normality test flags departures far too small to affect a t-test. Judge by the skewness/kurtosis and a QQ plot instead.","Group 'UMAP 2' rejects normality (p = 0.0000); prefer a rank-based test.","Group 'UMAP 2' has n = 2000; at this size a normality test flags departures far too small to affect a t-test. Judge by the skewness/kurtosis and a QQ plot instead."],"results":[{"excess_kurtosis":-1.2529133011965379,"group":"UMAP 1","interpretation":"Data significantly deviates from normality (A² = 38.9129, p = 0.0000)","n":2000,"normality_rejected":true,"p_value":3.7e-24,"skewness":-0.17071134288823964,"statistic":38.91285063963005,"test":"Anderson-Darling"},{"excess_kurtosis":-1.6118769050391721,"group":"UMAP 2","interpretation":"Data significantly deviates from normality (A² = 111.8738, p = 0.0000)","n":2000,"normality_rejected":true,"p_value":3.7e-24,"skewness":-0.1749210942964271,"statistic":111.87377379816417,"test":"Anderson-Darling"}],"source":{"kind":"arrays"}},"error":null},{"label":"stats.gmm","method":"stats.gmm","params":{"k_max":5},"result":{"n_init":10,"notes":["'UMAP 1': BIC prefers 3 components over 1 — the column looks like a mixture, not a single population.","'UMAP 2': BIC prefers 2 components over 1 — the column looks like a mixture, not a single 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A scatter plot (plot.create kind='scatter') is worth a look before reporting it; use method='spearman' if the relationship is monotonic but curved."],"p_value":1.2604634880938796e-30,"r_squared":0.06410585088607275,"significant":true,"source":{"kind":"arrays"},"t_statistic":-11.698581644123815,"test":"Pearson","variables":["a","b"]},"error":null},{"label":"stats.correlation","method":"stats.correlation","params":{"method":"spearman"},"result":{"alpha":0.05,"coefficient":-0.12176167171373642,"interpretation":"weak negative monotonic correlation (ρ = -0.122, p = 0.0000)","method":"spearman","n":2000,"n_dropped":0,"notes":[],"p_value":4.700629742968337e-08,"r_squared":null,"significant":true,"source":{"kind":"arrays"},"t_statistic":-5.483424297888862,"test":"Spearman","variables":["a","b"]},"error":null},{"label":"stats.correlation","method":"stats.correlation","params":{"method":"kendall"},"result":{"alpha":0.05,"coefficient":-0.08860630315157579,"interpretation":"negligible negative rank correlation (τ = -0.089, p = 0.0000)","method":"kendall","n":2000,"n_dropped":0,"notes":[],"p_value":2.8730008675607828e-09,"r_squared":null,"significant":true,"source":{"kind":"arrays"},"t_statistic":-5.938694828694172,"test":"Kendall","variables":["a","b"]},"error":null}]}