{"example":"Ridgeline Plot: Cell Size over Time","labtools_version":"0.14.3","generated":"2026-09-23","calls":[{"label":"stats.describe","method":"stats.describe","params":{},"result":{"columns":[{"excess_kurtosis":1.673983209081967,"iqr":44.474999999999994,"max":257.5,"mean":108.69633333333334,"median":102.9,"min":38.2,"n":300,"n_missing":0,"name":"0 h","q1":83.5,"q3":127.975,"range":219.3,"sd":37.18804272380637,"sem":2.1470526477224907,"skewness":1.0632063132830867,"sum":32608.9,"variance":1382.9505216276477},{"excess_kurtosis":0.11918790819524006,"iqr":62.94999999999999,"max":295.4,"mean":146.15433333333345,"median":141.3,"min":57.2,"n":300,"n_missing":0,"name":"12 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prefer a rank-based test.","Group '36 h' rejects normality (p = 0.0002); prefer a rank-based test.","Group '4 h' rejects normality (p = 0.0000); prefer a rank-based test.","Group '48 h' rejects normality (p = 0.0078); prefer a rank-based test.","Group '8 h' rejects normality (p = 0.0001); prefer a rank-based test."],"results":[{"excess_kurtosis":1.673983209081967,"group":"0 h","interpretation":"Data significantly deviates from normality (W = 0.9412, p = 0.0000)","n":300,"normality_rejected":true,"p_value":1.4928637428323473e-09,"skewness":1.0632063132830867,"statistic":0.9412370086416394,"test":"Shapiro-Wilk"},{"excess_kurtosis":0.11918790819524006,"group":"12 h","interpretation":"Data significantly deviates from normality (W = 0.9721, p = 0.0000)","n":300,"normality_rejected":true,"p_value":1.4506145992874282e-05,"skewness":0.6149457371779425,"statistic":0.9721332052715042,"test":"Shapiro-Wilk"},{"excess_kurtosis":0.5051206241459072,"group":"2 h","interpretation":"Data significantly 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prefer a rank-based test.","Group '12 h' rejects normality (p = 0.0000); prefer a rank-based test.","Group '2 h' rejects normality (p = 0.0001); prefer a rank-based test.","Group '24 h' rejects normality (p = 0.0000); prefer a rank-based test.","Group '36 h' rejects normality (p = 0.0004); prefer a rank-based test.","Group '4 h' rejects normality (p = 0.0010); prefer a rank-based test.","Group '48 h' rejects normality (p = 0.0232); prefer a rank-based test.","Group '8 h' rejects normality (p = 0.0006); prefer a rank-based test."],"results":[{"excess_kurtosis":1.673983209081967,"group":"0 h","interpretation":"Data significantly deviates from normality (A² = 3.9998, p = 0.0000)","n":300,"normality_rejected":true,"p_value":5.618135637468892e-10,"skewness":1.0632063132830867,"statistic":3.9998196827122,"test":"Anderson-Darling"},{"excess_kurtosis":0.11918790819524006,"group":"12 h","interpretation":"Data significantly deviates from normality (A² = 2.0031, p = 0.0000)","n":300,"normality_rejected":true,"p_value":4.124835618219855e-05,"skewness":0.6149457371779425,"statistic":2.0031060970110843,"test":"Anderson-Darling"},{"excess_kurtosis":0.5051206241459072,"group":"2 h","interpretation":"Data significantly deviates from normality (A² = 1.8586, p = 0.0001)","n":300,"normality_rejected":true,"p_value":9.332768536092938e-05,"skewness":0.6543686258722284,"statistic":1.8586231397866868,"test":"Anderson-Darling"},{"excess_kurtosis":0.9031279901090774,"group":"24 h","interpretation":"Data significantly deviates from normality (A² = 2.5445, p = 0.0000)","n":300,"normality_rejected":true,"p_value":1.9481772554306477e-06,"skewness":0.8025513827355766,"statistic":2.5445214224723713,"test":"Anderson-Darling"},{"excess_kurtosis":0.04846697424961022,"group":"36 h","interpretation":"Data significantly deviates from normality (A² = 1.5981, p = 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method='levene'."],"p_value":5.56804408145351e-21,"significant":true,"source":{"kind":"arrays"},"statistic":111.04700175290655,"test":"Bartlett's Test","variance_ratio":2.1631603339953447},"error":null},{"label":"stats.outliers","method":"stats.outliers","params":{"method":"grubbs"},"result":{"alpha":0.05,"method":"grubbs","notes":["Flagged points are candidates, not verdicts, and nothing has been removed. Look for a physical cause before excluding anything; if there is none, keep the point and use a robust test instead. Any exclusion must be reported.","Grubbs tests only the single most extreme point, so a second outlier can mask the first. On larger samples use method='generalized_esd'."],"results":[{"critical_value":3.7235545937169086,"group":"0 h","interpretation":"Detected 1 outlier (G = 4.001, critical = 3.724)","n":300,"outlier_count":1,"outliers":[{"index":23,"test_statistic":4.001384740031188,"value":257.5}],"test":"Grubbs"},{"critical_value":3.7235545937169086,"group":"12 h","interpretation":"No outliers detected (G = 3.165, critical = 3.724)","n":300,"outlier_count":0,"outliers":[],"test":"Grubbs"},{"critical_value":3.7235545937169086,"group":"2 h","interpretation":"No outliers detected (G = 3.667, critical = 3.724)","n":300,"outlier_count":0,"outliers":[],"test":"Grubbs"},{"critical_value":3.7235545937169086,"group":"24 h","interpretation":"No outliers detected (G = 3.613, critical = 3.724)","n":300,"outlier_count":0,"outliers":[],"test":"Grubbs"},{"critical_value":3.7235545937169086,"group":"36 h","interpretation":"No outliers detected (G = 3.323, critical = 3.724)","n":300,"outlier_count":0,"outliers":[],"test":"Grubbs"},{"critical_value":3.7235545937169086,"group":"4 h","interpretation":"Detected 1 outlier (G = 4.004, critical = 3.724)","n":300,"outlier_count":1,"outliers":[{"index":21,"test_statistic":4.003635881424147,"value":282.5}],"test":"Grubbs"},{"critical_value":3.7235545937169086,"group":"48 h","interpretation":"Detected 1 outlier (G = 4.026, critical = 3.724)","n":300,"outlier_count":1,"outliers":[{"index":192,"test_statistic":4.025967785710584,"value":404.4}],"test":"Grubbs"},{"critical_value":3.7235545937169086,"group":"8 h","interpretation":"No outliers detected (G = 3.490, critical = 3.724)","n":300,"outlier_count":0,"outliers":[],"test":"Grubbs"}],"source":{"kind":"arrays"},"total_outliers":3},"error":null},{"label":"stats.outliers","method":"stats.outliers","params":{"method":"generalized_esd","max_outliers":5},"result":{"alpha":0.05,"method":"generalized_esd","notes":["Flagged points are candidates, not verdicts, and nothing has been removed. Look for a physical cause before excluding anything; if there is none, keep the point and use a robust test instead. Any exclusion must be reported."],"results":[{"critical_value":3.722611119332026,"group":"0 h","interpretation":"Detected 2 outlier(s) out of maximum 5","n":300,"outlier_count":2,"outliers":[{"index":23,"test_statistic":4.001384740031188,"value":257.5},{"index":247,"test_statistic":3.869130216057145,"value":248.4}],"test":"Generalized ESD"},{"critical_value":3.7235545937169086,"group":"12 h","interpretation":"No outliers detected (tested up to 5 outliers)","n":300,"outlier_count":0,"outliers":[],"test":"Generalized ESD"},{"critical_value":3.7235545937169086,"group":"2 h","interpretation":"No outliers detected (tested up to 5 outliers)","n":300,"outlier_count":0,"outliers":[],"test":"Generalized ESD"},{"critical_value":3.7235545937169086,"group":"24 h","interpretation":"No outliers detected (tested up to 5 outliers)","n":300,"outlier_count":0,"outliers":[],"test":"Generalized ESD"},{"critical_value":3.7235545937169086,"group":"36 h","interpretation":"No outliers detected (tested up to 5 outliers)","n":300,"outlier_count":0,"outliers":[],"test":"Generalized ESD"},{"critical_value":3.7235545937169086,"group":"4 h","interpretation":"Detected 1 outlier(s) out of maximum 5","n":300,"outlier_count":1,"outliers":[{"index":21,"test_statistic":4.003635881424147,"value":282.5}],"test":"Generalized ESD"},{"critical_value":3.7235545937169086,"group":"48 h","interpretation":"Detected 1 outlier(s) out of maximum 5","n":300,"outlier_count":1,"outliers":[{"index":192,"test_statistic":4.025967785710584,"value":404.4}],"test":"Generalized ESD"},{"critical_value":3.7235545937169086,"group":"8 h","interpretation":"No outliers detected (tested up to 5 outliers)","n":300,"outlier_count":0,"outliers":[],"test":"Generalized ESD"}],"source":{"kind":"arrays"},"total_outliers":4},"error":null},{"label":"stats.outliers","method":"stats.outliers","params":{"method":"modified_z"},"result":{"alpha":0.05,"method":"modified_z","notes":["Flagged points are candidates, not verdicts, and nothing has been removed. Look for a physical cause before excluding anything; if there is none, keep the point and use a robust test instead. Any exclusion must be reported."],"results":[{"critical_value":3.5,"group":"0 h","interpretation":"Detected 5 outlier(s) using modified Z-score (threshold = 3.50)","n":300,"outlier_count":5,"outliers":[{"index":23,"test_statistic":4.7291473922902485,"value":257.5},{"index":29,"test_statistic":3.832873015873014,"value":228.2},{"index":90,"test_statistic":3.5300362811791377,"value":218.3},{"index":209,"test_statistic":4.151004535147391,"value":238.6},{"index":247,"test_statistic":4.450782312925169,"value":248.4}],"test":"Modified Z-Score"},{"critical_value":3.5,"group":"12 h","interpretation":"No outliers detected (threshold = 3.50)","n":300,"outlier_count":0,"outliers":[],"test":"Modified Z-Score"},{"critical_value":3.5,"group":"2 h","interpretation":"Detected 2 outlier(s) using modified Z-score (threshold = 3.50)","n":300,"outlier_count":2,"outliers":[{"index":124,"test_statistic":3.7097500000000014,"value":254.8},{"index":269,"test_statistic":3.8165241312741323,"value":258.9}],"test":"Modified Z-Score"},{"critical_value":3.5,"group":"24 h","interpretation":"Detected 3 outlier(s) using modified Z-score (threshold = 3.50)","n":300,"outlier_count":3,"outliers":[{"index":81,"test_statistic":3.574953292496171,"value":322.8},{"index":188,"test_statistic":4.143062021439509,"value":350.3},{"index":264,"test_statistic":3.9963866768759564,"value":343.2}],"test":"Modified Z-Score"},{"critical_value":3.5,"group":"36 h","interpretation":"No outliers detected (threshold = 3.50)","n":300,"outlier_count":0,"outliers":[],"test":"Modified Z-Score"},{"critical_value":3.5,"group":"4 h","interpretation":"Detected 1 outlier(s) using modified Z-score (threshold = 3.50)","n":300,"outlier_count":1,"outliers":[{"index":21,"test_statistic":4.290133720930231,"value":282.5}],"test":"Modified Z-Score"},{"critical_value":3.5,"group":"48 h","interpretation":"Detected 1 outlier(s) using modified Z-score (threshold = 3.50)","n":300,"outlier_count":1,"outliers":[{"index":192,"test_statistic":3.9037124352331607,"value":404.4}],"test":"Modified Z-Score"},{"critical_value":3.5,"group":"8 h","interpretation":"Detected 1 outlier(s) using modified Z-score (threshold = 3.50)","n":300,"outlier_count":1,"outliers":[{"index":65,"test_statistic":3.655506993006992,"value":288.7}],"test":"Modified Z-Score"}],"source":{"kind":"arrays"},"total_outliers":13},"error":null},{"label":"stats.outliers","method":"stats.outliers","params":{"method":"iqr"},"result":{"alpha":0.05,"method":"iqr","notes":["Flagged points are candidates, not verdicts, and nothing has been removed. Look for a physical cause before excluding anything; if there is none, keep the point and use a robust test instead. Any exclusion must be reported.","The IQR rule is descriptive — it has no p-value and flags roughly 0.7% of a perfectly normal sample by construction."],"results":[{"critical_value":1.5,"group":"0 h","interpretation":"Detected 11 outlier(s) outside [16.788, 194.688] (k = 1.5)","n":300,"outlier_count":11,"outliers":[{"index":23,"test_statistic":2.9123102866779096,"value":257.5},{"index":29,"test_statistic":2.2535132096683532,"value":228.2},{"index":86,"test_statistic":1.7768409218662173,"value":207.0},{"index":89,"test_statistic":1.5227655986509276,"value":195.7},{"index":90,"test_statistic":2.030916245081507,"value":218.3},{"index":96,"test_statistic":1.5205171444631818,"value":195.6},{"index":136,"test_statistic":1.7768409218662173,"value":207.0},{"index":152,"test_statistic":1.7003934794828557,"value":203.6},{"index":179,"test_statistic":1.549747048903879,"value":196.9},{"index":209,"test_statistic":2.4873524451939293,"value":238.6},{"index":247,"test_statistic":2.7077009555930305,"value":248.4}],"test":"IQR Method"},{"critical_value":1.5,"group":"12 h","interpretation":"Detected 4 outlier(s) outside [18.350, 270.150] (k = 1.5)","n":300,"outlier_count":4,"outliers":[{"index":14,"test_statistic":1.6945988880063543,"value":282.4},{"index":155,"test_statistic":1.6675933280381257,"value":280.7},{"index":266,"test_statistic":1.888403494837173,"value":294.6},{"index":284,"test_statistic":1.9011119936457506,"value":295.4}],"test":"IQR Method"},{"critical_value":1.5,"group":"2 h","interpretation":"Detected 5 outlier(s) outside [17.825, 215.825] (k = 1.5)","n":300,"outlier_count":5,"outliers":[{"index":70,"test_statistic":1.5641414141414147,"value":219.0},{"index":124,"test_statistic":2.2873737373737386,"value":254.8},{"index":159,"test_statistic":1.6550505050505058,"value":223.5},{"index":237,"test_statistic":1.550000000000001,"value":218.3},{"index":269,"test_statistic":2.370202020202021,"value":258.9}],"test":"IQR Method"},{"critical_value":1.5,"group":"24 h","interpretation":"Detected 11 outlier(s) outside [14.788, 278.487] (k = 1.5)","n":300,"outlier_count":11,"outliers":[{"index":2,"test_statistic":1.610921501706485,"value":285.8},{"index":13,"test_statistic":1.893060295790671,"value":304.4},{"index":19,"test_statistic":1.5760333712552144,"value":283.5},{"index":61,"test_statistic":1.5199089874857796,"value":279.8},{"index":81,"test_statistic":2.1721653394008347,"value":322.8},{"index":83,"test_statistic":1.542662116040956,"value":281.3},{"index":125,"test_statistic":1.5411452408039439,"value":281.2},{"index":188,"test_statistic":2.5893060295790673,"value":350.3},{"index":206,"test_statistic":1.7550246492226018,"value":295.3},{"index":264,"test_statistic":2.4816078877512324,"value":343.2},{"index":287,"test_statistic":1.7929465301478957,"value":297.8}],"test":"IQR Method"},{"critical_value":1.5,"group":"36 h","interpretation":"Detected 3 outlier(s) outside [20.050, 314.250] (k = 1.5)","n":300,"outlier_count":3,"outliers":[{"index":15,"test_statistic":2.0010197144799453,"value":351.1},{"index":82,"test_statistic":1.515635622025832,"value":315.4},{"index":109,"test_statistic":1.8650577838205302,"value":341.1}],"test":"IQR Method"},{"critical_value":1.5,"group":"4 h","interpretation":"Detected 5 outlier(s) outside [16.075, 229.675] (k = 1.5)","n":300,"outlier_count":5,"outliers":[{"index":21,"test_statistic":2.4892322097378266,"value":282.5},{"index":124,"test_statistic":1.5922284644194746,"value":234.6},{"index":165,"test_statistic":1.6147003745318345,"value":235.8},{"index":191,"test_statistic":1.7382958801498118,"value":242.4},{"index":291,"test_statistic":1.8150749063670402,"value":246.5}],"test":"IQR Method"},{"critical_value":1.5,"group":"48 h","interpretation":"Detected 1 outlier(s) outside [30.300, 335.500] (k = 1.5)","n":300,"outlier_count":1,"outliers":[{"index":192,"test_statistic":2.403014416775884,"value":404.4}],"test":"IQR Method"},{"critical_value":1.5,"group":"8 h","interpretation":"Detected 5 outlier(s) outside [19.388, 244.687] (k = 1.5)","n":300,"outlier_count":5,"outliers":[{"index":15,"test_statistic":1.7416777629826905,"value":258.3},{"index":65,"test_statistic":2.281402574345318,"value":288.7},{"index":185,"test_statistic":1.6458055925432762,"value":252.9},{"index":242,"test_statistic":1.933422103861519,"value":269.1},{"index":264,"test_statistic":1.9458499778073688,"value":269.8}],"test":"IQR Method"}],"source":{"kind":"arrays"},"total_outliers":45},"error":null},{"label":"stats.ci","method":"stats.ci","params":{"conf_level":0.95},"result":{"conf_level":0.95,"estimate":108.69633333333334,"interpretation":"Over repeated sampling, intervals built this way contain the true mean at the stated rate. It is not the probability that this particular interval contains it.","kind":"mean","lower":104.47108472683419,"margin_of_error":4.22524860649915,"method":"t","n":300,"name":"data","notes":[],"sd":37.18804272380637,"source":{"kind":"arrays_or_dataset"},"upper":112.92158193983249},"error":null},{"label":"stats.ci","method":"stats.ci","params":{"conf_level":0.95},"result":{"conf_level":0.95,"estimate":118.60133333333336,"interpretation":"Over repeated sampling, intervals built this way contain the true mean at the stated rate. It is not the probability that this particular interval contains it.","kind":"mean","lower":114.25436602669645,"margin_of_error":4.3469673066369126,"method":"t","n":300,"name":"data","notes":[],"sd":38.259335952338944,"source":{"kind":"arrays_or_dataset"},"upper":122.94830063997027},"error":null},{"label":"stats.ci","method":"stats.ci","params":{"conf_level":0.95},"result":{"conf_level":0.95,"estimate":124.24666666666671,"interpretation":"Over repeated sampling, intervals built this way contain the true mean at the stated rate. It is not the probability that this particular interval contains it.","kind":"mean","lower":119.75562339476582,"margin_of_error":4.491043271900892,"method":"t","n":300,"name":"data","notes":[],"sd":39.527404094760094,"source":{"kind":"arrays_or_dataset"},"upper":128.7377099385676},"error":null},{"label":"stats.ci","method":"stats.ci","params":{"conf_level":0.95},"result":{"conf_level":0.95,"estimate":135.58166666666656,"interpretation":"Over repeated sampling, intervals built this way contain the true mean at the stated rate. It is not the probability that this particular interval contains it.","kind":"mean","lower":130.59673414932877,"margin_of_error":4.984932517337796,"method":"t","n":300,"name":"data","notes":[],"sd":43.87431384390112,"source":{"kind":"arrays_or_dataset"},"upper":140.56659918400436},"error":null},{"label":"stats.ci","method":"stats.ci","params":{"conf_level":0.95},"result":{"conf_level":0.95,"estimate":146.15433333333345,"interpretation":"Over repeated sampling, intervals built this way contain the true mean at the stated rate. It is not the probability that this particular interval contains it.","kind":"mean","lower":140.79629708521313,"margin_of_error":5.358036248120328,"method":"t","n":300,"name":"data","notes":[],"sd":47.15814368989175,"source":{"kind":"arrays_or_dataset"},"upper":151.51236958145378},"error":null},{"label":"stats.ci","method":"stats.ci","params":{"conf_level":0.95},"result":{"conf_level":0.95,"estimate":153.77066666666667,"interpretation":"Over repeated sampling, intervals built this way contain the true mean at the stated rate. It is not the probability that this particular interval contains it.","kind":"mean","lower":147.59070531187322,"margin_of_error":6.179961354793448,"method":"t","n":300,"name":"data","notes":[],"sd":54.39222358183332,"source":{"kind":"arrays_or_dataset"},"upper":159.95062802146012},"error":null},{"label":"stats.ci","method":"stats.ci","params":{"conf_level":0.95},"result":{"conf_level":0.95,"estimate":171.42666666666662,"interpretation":"Over repeated sampling, intervals built this way contain the true mean at the stated rate. It is not the probability that this particular interval contains it.","kind":"mean","lower":165.28310038795436,"margin_of_error":6.143566278712257,"method":"t","n":300,"name":"data","notes":[],"sd":54.0718964791483,"source":{"kind":"arrays_or_dataset"},"upper":177.57023294537888},"error":null},{"label":"stats.ci","method":"stats.ci","params":{"conf_level":0.95},"result":{"conf_level":0.95,"estimate":184.19966666666676,"interpretation":"Over repeated sampling, intervals built this way contain the true mean at the stated rate. It is not the probability that this particular interval contains it.","kind":"mean","lower":177.98530360392775,"margin_of_error":6.214363062739011,"method":"t","n":300,"name":"data","notes":[],"sd":54.69500628268634,"source":{"kind":"arrays_or_dataset"},"upper":190.41402972940577},"error":null},{"label":"stats.anova","method":"stats.anova","params":{},"result":{"alpha":0.05,"assumptions":{"alpha":0.05,"homogeneity_of_variance":{"equal_variance_rejected":true,"p_value":2.9549292581955017e-18,"statistic":14.257702420201264,"test":"Levene's Test"},"independence":"Assumed, not tested — observations must come from independent sampling units. Repeated measures on the same unit require a paired or mixed-model analysis instead.","normality":[{"group":"0 h","normality_rejected":true,"p_value":1.4928637428323473e-09,"statistic":0.9412370086416394,"test":"Shapiro-Wilk"},{"group":"12 h","normality_rejected":true,"p_value":1.4506145992874282e-05,"statistic":0.9721332052715042,"test":"Shapiro-Wilk"},{"group":"2 h","normality_rejected":true,"p_value":2.7693331715134135e-05,"statistic":0.973851941633308,"test":"Shapiro-Wilk"},{"group":"24 h","normality_rejected":true,"p_value":2.1024336387115034e-07,"statistic":0.9594867912590244,"test":"Shapiro-Wilk"},{"group":"36 h","normality_rejected":true,"p_value":0.0001517497654450404,"statistic":0.9781298240119727,"test":"Shapiro-Wilk"},{"group":"4 h","normality_rejected":true,"p_value":1.9818461412545906e-05,"statistic":0.9729692053139652,"test":"Shapiro-Wilk"},{"group":"48 h","normality_rejected":true,"p_value":0.007813461732835746,"statistic":0.9868538201556254,"test":"Shapiro-Wilk"},{"group":"8 h","normality_rejected":true,"p_value":7.414444969400142e-05,"statistic":0.9763704566065435,"test":"Shapiro-Wilk"}]},"design":"one_way","df_between":7.0,"df_within":2392.0,"effect_size":{"cohens_f":0.5261692132692686,"estimate":0.21446301013844227,"eta_squared":0.2168251280915582,"interpretation":"eta-squared is the variance explained in THIS sample and is upward-biased; omega-squared estimates the population value and is the one to report.","magnitude":"large","name":"omega_squared","omega_squared":0.21446301013844227},"groups":[{"excess_kurtosis":1.673983209081967,"iqr":44.474999999999994,"max":257.5,"mean":108.69633333333334,"median":102.9,"min":38.2,"n":300,"n_missing":0,"name":"0 h","q1":83.5,"q3":127.975,"range":219.3,"sd":37.18804272380637,"sem":2.1470526477224907,"skewness":1.0632063132830867,"sum":32608.9,"variance":1382.9505216276477},{"excess_kurtosis":0.11918790819524006,"iqr":62.94999999999999,"max":295.4,"mean":146.15433333333345,"median":141.3,"min":57.2,"n":300,"n_missing":0,"name":"12 h","q1":112.775,"q3":175.725,"range":238.2,"sd":47.15814368989175,"sem":2.722676695384205,"skewness":0.6149457371779425,"sum":43846.30000000004,"variance":2223.8905162764772},{"excess_kurtosis":0.5051206241459072,"iqr":49.499999999999986,"max":258.9,"mean":118.60133333333336,"median":112.35,"min":38.0,"n":300,"n_missing":0,"name":"2 h","q1":92.075,"q3":141.575,"range":220.89999999999998,"sd":38.259335952338944,"sem":2.2089037911099214,"skewness":0.6543686258722284,"sum":35580.40000000001,"variance":1463.776787513935},{"excess_kurtosis":0.9031279901090774,"iqr":65.925,"max":350.3,"mean":153.77066666666667,"median":149.75,"min":56.0,"n":300,"n_missing":0,"name":"24 h","q1":113.675,"q3":179.6,"range":294.3,"sd":54.39222358183332,"sem":3.1403364926793773,"skewness":0.8025513827355766,"sum":46131.2,"variance":2958.513986176145},{"excess_kurtosis":0.04846697424961022,"iqr":73.55000000000001,"max":351.1,"mean":171.42666666666662,"median":166.45,"min":64.8,"n":300,"n_missing":0,"name":"36 h","q1":130.375,"q3":203.925,"range":286.3,"sd":54.0718964791483,"sem":3.1218423987829844,"skewness":0.5386666964796152,"sum":51427.999999999985,"variance":2923.76998885173},{"excess_kurtosis":0.7163187456610647,"iqr":53.40000000000002,"max":282.5,"mean":124.24666666666671,"median":118.4,"min":40.3,"n":300,"n_missing":0,"name":"4 h","q1":96.175,"q3":149.57500000000002,"range":242.2,"sd":39.527404094760094,"sem":2.2821157394476854,"skewness":0.6754236179338664,"sum":37274.000000000015,"variance":1562.4156744704571},{"excess_kurtosis":0.09869705021265185,"iqr":76.30000000000001,"max":404.4,"mean":184.19966666666676,"median":181.0,"min":46.5,"n":300,"n_missing":0,"name":"48 h","q1":144.75,"q3":221.05,"range":357.9,"sd":54.69500628268634,"sem":3.157817660063723,"skewness":0.36513863616917797,"sum":55259.90000000002,"variance":2991.5437122630988},{"excess_kurtosis":0.3897281828204546,"iqr":56.32499999999999,"max":288.7,"mean":135.58166666666656,"median":133.7,"min":34.6,"n":300,"n_missing":0,"name":"8 h","q1":103.875,"q3":160.2,"range":254.1,"sd":43.87431384390112,"sem":2.5330846908286433,"skewness":0.5750815091713081,"sum":40674.49999999997,"variance":1924.9554152731334}],"k_groups":8,"ms_between":206142.0845142859,"ms_within":2178.977075306581,"n_total":2400,"notes":["Group '0 h' departs from normality (Shapiro–Wilk W = 0.9412, p = 0.0000 < 0.05). Consider stats.kruskal.","Group '12 h' departs from normality (Shapiro–Wilk W = 0.9721, p = 0.0000 < 0.05). Consider stats.kruskal.","Group '2 h' departs from normality (Shapiro–Wilk W = 0.9739, p = 0.0000 < 0.05). Consider stats.kruskal.","Group '24 h' departs from normality (Shapiro–Wilk W = 0.9595, p = 0.0000 < 0.05). Consider stats.kruskal.","Group '36 h' departs from normality (Shapiro–Wilk W = 0.9781, p = 0.0002 < 0.05). Consider stats.kruskal.","Group '4 h' departs from normality (Shapiro–Wilk W = 0.9730, p = 0.0000 < 0.05). Consider stats.kruskal.","Group '48 h' departs from normality (Shapiro–Wilk W = 0.9869, p = 0.0078 < 0.05). Consider stats.kruskal.","Group '8 h' departs from normality (Shapiro–Wilk W = 0.9764, p = 0.0001 < 0.05). Consider stats.kruskal.","Group variances are unequal (Levene W = 14.2577, p = 0.0000 < 0.05); the equal-variance assumption of this test is violated. Use the Welch variant instead."],"p_value":3.7406794143542214e-122,"post_hoc":"A significant F is an omnibus result. Run pairwise stats.ttest comparisons and pass their p-values through stats.adjust before reporting any specific pair.","significant":true,"source":{"kind":"arrays"},"statistic":94.60498086483165},"error":null},{"label":"stats.kruskal","method":"stats.kruskal","params":{},"result":{"alpha":0.05,"assumptions":{"note":"Distribution-free. Groups must be independent; similar group shapes are needed to read the result as a difference in medians rather than in distribution."},"df":7,"effect_size":{"estimate":0.21734031160506798,"interpretation":"Proportion of rank variance explained by group; 0..1.","name":"epsilon_squared"},"groups":[{"excess_kurtosis":1.673983209081967,"iqr":44.474999999999994,"max":257.5,"mean":108.69633333333334,"median":102.9,"min":38.2,"n":300,"n_missing":0,"name":"0 h","q1":83.5,"q3":127.975,"range":219.3,"sd":37.18804272380637,"sem":2.1470526477224907,"skewness":1.0632063132830867,"sum":32608.9,"variance":1382.9505216276477},{"excess_kurtosis":0.11918790819524006,"iqr":62.94999999999999,"max":295.4,"mean":146.15433333333345,"median":141.3,"min":57.2,"n":300,"n_missing":0,"name":"12 h","q1":112.775,"q3":175.725,"range":238.2,"sd":47.15814368989175,"sem":2.722676695384205,"skewness":0.6149457371779425,"sum":43846.30000000004,"variance":2223.8905162764772},{"excess_kurtosis":0.5051206241459072,"iqr":49.499999999999986,"max":258.9,"mean":118.60133333333336,"median":112.35,"min":38.0,"n":300,"n_missing":0,"name":"2 h","q1":92.075,"q3":141.575,"range":220.89999999999998,"sd":38.259335952338944,"sem":2.2089037911099214,"skewness":0.6543686258722284,"sum":35580.40000000001,"variance":1463.776787513935},{"excess_kurtosis":0.9031279901090774,"iqr":65.925,"max":350.3,"mean":153.77066666666667,"median":149.75,"min":56.0,"n":300,"n_missing":0,"name":"24 h","q1":113.675,"q3":179.6,"range":294.3,"sd":54.39222358183332,"sem":3.1403364926793773,"skewness":0.8025513827355766,"sum":46131.2,"variance":2958.513986176145},{"excess_kurtosis":0.04846697424961022,"iqr":73.55000000000001,"max":351.1,"mean":171.42666666666662,"median":166.45,"min":64.8,"n":300,"n_missing":0,"name":"36 h","q1":130.375,"q3":203.925,"range":286.3,"sd":54.0718964791483,"sem":3.1218423987829844,"skewness":0.5386666964796152,"sum":51427.999999999985,"variance":2923.76998885173},{"excess_kurtosis":0.7163187456610647,"iqr":53.40000000000002,"max":282.5,"mean":124.24666666666671,"median":118.4,"min":40.3,"n":300,"n_missing":0,"name":"4 h","q1":96.175,"q3":149.57500000000002,"range":242.2,"sd":39.527404094760094,"sem":2.2821157394476854,"skewness":0.6754236179338664,"sum":37274.000000000015,"variance":1562.4156744704571},{"excess_kurtosis":0.09869705021265185,"iqr":76.30000000000001,"max":404.4,"mean":184.19966666666676,"median":181.0,"min":46.5,"n":300,"n_missing":0,"name":"48 h","q1":144.75,"q3":221.05,"range":357.9,"sd":54.69500628268634,"sem":3.157817660063723,"skewness":0.36513863616917797,"sum":55259.90000000002,"variance":2991.5437122630988},{"excess_kurtosis":0.3897281828204546,"iqr":56.32499999999999,"max":288.7,"mean":135.58166666666656,"median":133.7,"min":34.6,"n":300,"n_missing":0,"name":"8 h","q1":103.875,"q3":160.2,"range":254.1,"sd":43.87431384390112,"sem":2.5330846908286433,"skewness":0.5750815091713081,"sum":40674.49999999997,"variance":1924.9554152731334}],"interpretation":"At least one group significantly differs (H = 521.399, df = 7, p = 0.0000)","n_total":2400,"notes":[],"p_value":2.006785677654809e-108,"post_hoc":"A significant H is an omnibus result. Run pairwise stats.mannwhitney comparisons and pass their p-values through stats.adjust (benjamini_hochberg or holm) before reporting any specific pair.","sample_sizes":[300,300,300,300,300,300,300,300],"significant":true,"source":{"kind":"arrays"},"statistic":521.3994075405581,"test":"Kruskal-Wallis"},"error":null},{"label":"stats.ttest","method":"stats.ttest","params":{"test":"welch","check_assumptions":false},"result":{"alpha":0.05,"alternative":"two_sided","assumptions":{"checked":false},"ci_of_difference":{"conf_level":0.95,"lower":-15.954799593369353,"method":"t (Welch)","upper":-3.8552004066306775},"df":597.5183134545647,"effect_size":{"ci":{"conf_level":0.95,"lower":-0.42262119305485824,"upper":-0.10158385619507543},"cohens_d":-0.2625406425950019,"estimate":-0.2622112315001525,"interpretation":"Standardised mean difference (group 1 minus group 2), small-sample-bias corrected.","magnitude":"small","name":"hedges_g"},"groups":[{"excess_kurtosis":1.673983209081967,"iqr":44.474999999999994,"max":257.5,"mean":108.69633333333334,"median":102.9,"min":38.2,"n":300,"n_missing":0,"name":"a","q1":83.5,"q3":127.975,"range":219.3,"sd":37.18804272380637,"sem":2.1470526477224907,"skewness":1.0632063132830867,"sum":32608.9,"variance":1382.9505216276477},{"excess_kurtosis":0.5051206241459072,"iqr":49.499999999999986,"max":258.9,"mean":118.60133333333336,"median":112.35,"min":38.0,"n":300,"n_missing":0,"name":"b","q1":92.075,"q3":141.575,"range":220.89999999999998,"sd":38.259335952338944,"sem":2.2089037911099214,"skewness":0.6543686258722284,"sum":35580.40000000001,"variance":1463.776787513935}],"mean_difference":-9.905000000000015,"notes":[],"p_two_sided":0.0013726797170967313,"p_value":0.0013726797170967313,"significant":true,"source":{"kind":"arrays"},"statistic":-3.215453055500807,"test":"welch"},"error":null},{"label":"stats.mannwhitney","method":"stats.mannwhitney","params":{},"result":{"alpha":0.05,"alternative":"two_sided","assumptions":{"note":"Distribution-free: no normality assumption. Observations must be independent both within and between groups, and the two distributions are assumed to have similar shape if the result is to be read as a median shift."},"effect_size":{"estimate":-0.16725555555555555,"interpretation":"P(x > y) - P(x < y) for a random pair, one value from each group. 0 means complete overlap.","magnitude":"small","name":"cliffs_delta","rank_biserial_r":-0.1672555555555556},"groups":[{"excess_kurtosis":1.673983209081967,"iqr":44.474999999999994,"max":257.5,"mean":108.69633333333334,"median":102.9,"min":38.2,"n":300,"n_missing":0,"name":"a","q1":83.5,"q3":127.975,"range":219.3,"sd":37.18804272380637,"sem":2.1470526477224907,"skewness":1.0632063132830867,"sum":32608.9,"variance":1382.9505216276477},{"excess_kurtosis":0.5051206241459072,"iqr":49.499999999999986,"max":258.9,"mean":118.60133333333336,"median":112.35,"min":38.0,"n":300,"n_missing":0,"name":"b","q1":92.075,"q3":141.575,"range":220.89999999999998,"sd":38.259335952338944,"sem":2.2089037911099214,"skewness":0.6543686258722284,"sum":35580.40000000001,"variance":1463.776787513935}],"interpretation":"Distributions significantly differ (U = 37473.5, Z = -3.545, p = 0.0004)","notes":[],"p_two_sided":0.00039284313356561476,"p_value":0.00039284313356561476,"sample_sizes":[300,300],"significant":true,"source":{"kind":"arrays"},"statistic":37473.5,"test":"Mann-Whitney U"},"error":null},{"label":"stats.ttest","method":"stats.ttest","params":{"test":"welch","check_assumptions":false},"result":{"alpha":0.05,"alternative":"two_sided","assumptions":{"checked":false},"ci_of_difference":{"conf_level":0.95,"lower":-21.704089209673594,"method":"t (Welch)","upper":-9.396577456993146},"df":595.7880593751901,"effect_size":{"ci":{"conf_level":0.95,"lower":-0.5660064785586946,"upper":-0.24307396778832055},"cohens_d":-0.40521456915503634,"estimate":-0.40470614435057584,"interpretation":"Standardised mean difference (group 1 minus group 2), small-sample-bias corrected.","magnitude":"small","name":"hedges_g"},"groups":[{"excess_kurtosis":1.673983209081967,"iqr":44.474999999999994,"max":257.5,"mean":108.69633333333334,"median":102.9,"min":38.2,"n":300,"n_missing":0,"name":"a","q1":83.5,"q3":127.975,"range":219.3,"sd":37.18804272380637,"sem":2.1470526477224907,"skewness":1.0632063132830867,"sum":32608.9,"variance":1382.9505216276477},{"excess_kurtosis":0.7163187456610647,"iqr":53.40000000000002,"max":282.5,"mean":124.24666666666671,"median":118.4,"min":40.3,"n":300,"n_missing":0,"name":"b","q1":96.175,"q3":149.57500000000002,"range":242.2,"sd":39.527404094760094,"sem":2.2821157394476854,"skewness":0.6754236179338664,"sum":37274.000000000015,"variance":1562.4156744704571}],"mean_difference":-15.55033333333337,"notes":[],"p_two_sided":9.079014242777721e-07,"p_value":9.079014242777721e-07,"significant":true,"source":{"kind":"arrays"},"statistic":-4.962844653857832,"test":"welch"},"error":null},{"label":"stats.mannwhitney","method":"stats.mannwhitney","params":{},"result":{"alpha":0.05,"alternative":"two_sided","assumptions":{"note":"Distribution-free: no normality assumption. 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