{"example":"2D Histogram: Flow Cytometry FSC vs SSC","labtools_version":"0.14.3","generated":"2026-09-23","calls":[{"label":"stats.describe","method":"stats.describe","params":{},"result":{"columns":[{"excess_kurtosis":0.15263115611470734,"iqr":215.52499999999998,"max":899.2,"mean":471.4367,"median":451.05,"min":20.2,"n":20000,"n_missing":0,"name":"FSC-A","q1":390.775,"q3":606.3,"range":879.0,"sd":155.75172895722108,"sem":1.1013310372718017,"skewness":-0.41972589496176266,"sum":9428734.000000022,"variance":24258.601073163656},{"excess_kurtosis":-1.0967855574257785,"iqr":313.0,"max":795.8,"mean":294.45169500000003,"median":202.2,"min":10.2,"n":20000,"n_missing":0,"name":"SSC-A","q1":168.0,"q3":481.0,"range":785.5999999999999,"sd":174.3627778255483,"sem":1.2329310258696857,"skewness":0.6693647164084416,"sum":5889033.89999998,"variance":30402.378291041525}],"n_columns":2,"notes":[],"source":{"kind":"arrays"}},"error":null},{"label":"stats.normality","method":"stats.normality","params":{"method":"shapiro_wilk"},"result":null,"error":"stats.normality: Invalid argument: Shapiro-Wilk not recommended for n > 5000 (use Anderson-Darling instead)"},{"label":"stats.normality","method":"stats.normality","params":{"method":"anderson_darling"},"result":{"all_normal":false,"alpha":0.05,"method":"anderson_darling","notes":["Group 'FSC-A' rejects normality (p = 0.0000); prefer a rank-based test.","Group 'FSC-A' has n = 20000; 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 'SSC-A' rejects normality (p = 0.0000); prefer a rank-based test.","Group 'SSC-A' has n = 20000; 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":0.15263115611470734,"group":"FSC-A","interpretation":"Data significantly deviates from normality (A² = 236.3117, p = 0.0000)","n":20000,"normality_rejected":true,"p_value":3.7e-24,"skewness":-0.41972589496176266,"statistic":236.31167734459814,"test":"Anderson-Darling"},{"excess_kurtosis":-1.0967855574257794,"group":"SSC-A","interpretation":"Data significantly deviates from normality (A² = 1572.3959, p = 0.0000)","n":20000,"normality_rejected":true,"p_value":3.7e-24,"skewness":0.6693647164084414,"statistic":1572.3959239021242,"test":"Anderson-Darling"}],"source":{"kind":"arrays"}},"error":null},{"label":"stats.normality","method":"stats.normality","params":{"method":"kolmogorov_smirnov"},"result":{"all_normal":false,"alpha":0.05,"method":"kolmogorov_smirnov","notes":["Group 'FSC-A' rejects normality (p = 0.0000); prefer a rank-based test.","Group 'FSC-A' has n = 20000; 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 'SSC-A' rejects normality (p = 0.0000); prefer a rank-based test.","Group 'SSC-A' has n = 20000; 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":0.15263115611470734,"group":"FSC-A","interpretation":"Data significantly deviates from normality (D = 0.0768, p = 0.0000)","n":20000,"normality_rejected":true,"p_value":5.69944e-319,"skewness":-0.41972589496176266,"statistic":0.07676486979021147,"test":"Kolmogorov-Smirnov (Lilliefors)"},{"excess_kurtosis":-1.0967855574257794,"group":"SSC-A","interpretation":"Data significantly deviates from normality (D = 0.2592, p = 0.0000)","n":20000,"normality_rejected":true,"p_value":0.0,"skewness":0.6693647164084414,"statistic":0.2592141787527209,"test":"Kolmogorov-Smirnov (Lilliefors)"}],"source":{"kind":"arrays"}},"error":null},{"label":"stats.gmm","method":"stats.gmm","params":{"k_max":3},"result":{"n_init":10,"notes":["'FSC-A': BIC prefers 3 components over 1 — the column looks like a mixture, not a single population.","'SSC-A': BIC prefers 3 components over 1 — the column looks like a mixture, not a single population.","'SSC-A': the selected k=3 fit did not converge; raise n_init or lower k_max before trusting its components."],"results":[{"best_fit":{"aic":251921.5743407983,"bic":251984.8022412186,"components":[{"mean":174.52376092539313,"sigma":91.47382884396195,"weight":0.10832158112040145},{"mean":421.6982623703235,"sigma":49.077147402354704,"weight":0.5399161723892383},{"mean":639.2110034396906,"sigma":59.94598209004737,"weight":0.3517622464903604}],"converged":true,"k":3,"k_fitted":3,"log_likelihood":-125952.78717039916,"n_iter":97,"n_parameters":8},"best_k_aic":3,"best_k_bic":3,"error":null,"fits":[{"aic":258691.07164138206,"bic":258706.87861648714,"components":[{"mean":471.4367000000011,"sigma":155.7478351185335,"weight":1.0}],"converged":true,"k":1,"k_fitted":1,"log_likelihood":-129343.53582069103,"n_iter":3,"n_parameters":2},{"aic":257944.64103478912,"bic":257984.1584725518,"components":[{"mean":228.69397360337717,"sigma":144.2215941148883,"weight":0.10976233292086927},{"mean":501.36579526765075,"sigma":128.54129297779318,"weight":0.8902376670791308}],"converged":false,"k":2,"k_fitted":2,"log_likelihood":-128967.32051739456,"n_iter":100,"n_parameters":5},{"aic":251921.5743407983,"bic":251984.8022412186,"components":[{"mean":174.52376092539313,"sigma":91.47382884396195,"weight":0.10832158112040145},{"mean":421.6982623703235,"sigma":49.077147402354704,"weight":0.5399161723892383},{"mean":639.2110034396906,"sigma":59.94598209004737,"weight":0.3517622464903604}],"converged":true,"k":3,"k_fitted":3,"log_likelihood":-125952.78717039916,"n_iter":97,"n_parameters":8}],"group":"FSC-A","n":20000},{"best_fit":{"aic":237021.87832705156,"bic":237085.10622747184,"components":[{"mean":57.07677291177899,"sigma":29.4712557002911,"weight":0.037739997864528106},{"mean":179.91073652357014,"sigma":31.82912424565437,"weight":0.6122381858470531},{"mean":520.3944048404842,"sigma":70.10597051075474,"weight":0.3500218162884189}],"converged":false,"k":3,"k_fitted":3,"log_likelihood":-118502.93916352578,"n_iter":100,"n_parameters":8},"best_k_aic":3,"best_k_bic":3,"error":null,"fits":[{"aic":263206.063655033,"bic":263221.8706301381,"components":[{"mean":294.451694999999,"sigma":174.35841870448027,"weight":1.0}],"converged":true,"k":1,"k_fitted":1,"log_likelihood":-131601.0318275165,"n_iter":3,"n_parameters":2},{"aic":239762.05957284156,"bic":239801.57701060423,"components":[{"mean":172.90814892569657,"sigma":42.96944537532732,"weight":0.6505906905007395},{"mean":520.7624927280513,"sigma":69.60850034676129,"weight":0.3494093094992605}],"converged":true,"k":2,"k_fitted":2,"log_likelihood":-119876.02978642078,"n_iter":14,"n_parameters":5},{"aic":237021.87832705156,"bic":237085.10622747184,"components":[{"mean":57.07677291177899,"sigma":29.4712557002911,"weight":0.037739997864528106},{"mean":179.91073652357014,"sigma":31.82912424565437,"weight":0.6122381858470531},{"mean":520.3944048404842,"sigma":70.10597051075474,"weight":0.3500218162884189}],"converged":false,"k":3,"k_fitted":3,"log_likelihood":-118502.93916352578,"n_iter":100,"n_parameters":8}],"group":"SSC-A","n":20000}],"seed":42,"source":{"kind":"arrays"}},"error":null},{"label":"stats.correlation","method":"stats.correlation","params":{"method":"pearson"},"result":{"alpha":0.05,"coefficient":0.8325667916237133,"interpretation":"very strong positive correlation (r = 0.833, p = 0.0000)","method":"pearson","n":20000,"n_dropped":0,"notes":["Pearson's r measures LINEAR association only, and is sensitive to outliers. 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":0.0,"r_squared":0.6931674625146036,"significant":true,"source":{"kind":"arrays"},"t_statistic":212.55026976002304,"test":"Pearson","variables":["a","b"]},"error":null},{"label":"stats.correlation","method":"stats.correlation","params":{"method":"spearman"},"result":{"alpha":0.05,"coefficient":0.8459518772702279,"interpretation":"very strong positive monotonic correlation (ρ = 0.846, p = 0.0000)","method":"spearman","n":20000,"n_dropped":0,"notes":[],"p_value":0.0,"r_squared":null,"significant":true,"source":{"kind":"arrays"},"t_statistic":224.33681403895275,"test":"Spearman","variables":["a","b"]},"error":null},{"label":"stats.correlation","method":"stats.correlation","params":{"method":"kendall"},"result":{"alpha":0.05,"coefficient":0.6530641932096605,"interpretation":"very strong positive rank correlation (τ = 0.653, p = 0.0000)","method":"kendall","n":20000,"n_dropped":0,"notes":[],"p_value":0.0,"r_squared":null,"significant":true,"source":{"kind":"arrays"},"t_statistic":138.52371496976306,"test":"Kendall","variables":["a","b"]},"error":null}]}