{"example":"Q–Q Plot: Model Residuals","labtools_version":"0.14.3","generated":"2026-09-23","calls":[{"label":"stats.describe","method":"stats.describe","params":{},"result":{"columns":[{"excess_kurtosis":2.785674815227419,"iqr":1.61625,"max":5.465,"mean":-0.04086500000000005,"median":0.0275,"min":-5.627,"n":200,"n_missing":0,"name":"Residuals","q1":-0.85475,"q3":0.7615000000000001,"range":11.091999999999999,"sd":1.4707402152244264,"sem":0.10399703795489543,"skewness":0.08758568455151301,"sum":-8.173000000000009,"variance":2.163076780678392}],"n_columns":1,"notes":[],"source":{"kind":"arrays"}},"error":null},{"label":"stats.normality","method":"stats.normality","params":{"method":"shapiro_wilk"},"result":{"all_normal":false,"alpha":0.05,"method":"shapiro_wilk","notes":["Group 'Residuals' rejects normality (p = 0.0000); prefer a rank-based test."],"results":[{"excess_kurtosis":2.785674815227419,"group":"Residuals","interpretation":"Data significantly deviates from normality (W = 0.9607, p = 0.0000)","n":200,"normality_rejected":true,"p_value":2.3290287999892373e-05,"skewness":0.08758568455151301,"statistic":0.9606534120966674,"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 'Residuals' rejects normality (p = 0.0014); prefer a rank-based test."],"results":[{"excess_kurtosis":2.785674815227419,"group":"Residuals","interpretation":"Data significantly deviates from normality (A² = 1.3776, p = 0.0014)","n":200,"normality_rejected":true,"p_value":0.0014080901623528823,"skewness":0.08758568455151301,"statistic":1.377623853623021,"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 'Residuals' rejects normality (p = 0.0167); prefer a rank-based test."],"results":[{"excess_kurtosis":2.785674815227419,"group":"Residuals","interpretation":"Data significantly deviates from normality (D = 0.0706, p = 0.0167)","n":200,"normality_rejected":true,"p_value":0.016748755927846637,"skewness":0.08758568455151301,"statistic":0.07064452417931844,"test":"Kolmogorov-Smirnov (Lilliefors)"}],"source":{"kind":"arrays"}},"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":3.6055252993213185,"group":"Residuals","interpretation":"Detected 1 outlier (G = 3.798, critical = 3.606)","n":200,"outlier_count":1,"outliers":[{"index":139,"test_statistic":3.7981792720256773,"value":-5.627}],"test":"Grubbs"}],"source":{"kind":"arrays"},"total_outliers":1},"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":3.6009809335493643,"group":"Residuals","interpretation":"Detected 4 outlier(s) out of maximum 5","n":200,"outlier_count":4,"outliers":[{"index":139,"test_statistic":3.7981792720256773,"value":-5.627},{"index":99,"test_statistic":3.8583583208303875,"value":5.465},{"index":31,"test_statistic":3.8637870462144965,"value":-5.328},{"index":143,"test_statistic":3.9839689815335237,"value":5.24}],"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":"Residuals","interpretation":"Detected 4 outlier(s) using modified Z-score (threshold = 3.50)","n":200,"outlier_count":4,"outliers":[{"index":31,"test_statistic":4.344299158147925,"value":-5.328},{"index":99,"test_statistic":4.410816295850871,"value":5.465},{"index":139,"test_statistic":4.5868433553818395,"value":-5.627},{"index":143,"test_statistic":4.228299759470836,"value":5.24}],"test":"Modified Z-Score"}],"source":{"kind":"arrays"},"total_outliers":4},"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":"Residuals","interpretation":"Detected 7 outlier(s) outside [-3.279, 3.186] (k = 1.5)","n":200,"outlier_count":7,"outliers":[{"index":31,"test_statistic":2.7676720804331016,"value":-5.328},{"index":90,"test_statistic":1.7436968290796597,"value":-3.673},{"index":99,"test_statistic":2.9101314771848417,"value":5.465},{"index":116,"test_statistic":2.0878576952822896,"value":4.136},{"index":139,"test_statistic":2.9526682134570765,"value":-5.627},{"index":143,"test_statistic":2.7709203402938907,"value":5.24},{"index":182,"test_statistic":2.1670533642691416,"value":4.264}],"test":"IQR Method"}],"source":{"kind":"arrays"},"total_outliers":7},"error":null},{"label":"stats.ttest","method":"stats.ttest","params":{"test":"one_sample","mu":0},"result":{"alpha":0.05,"alternative":"two_sided","assumptions":{"alpha":0.05,"homogeneity_of_variance":null,"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":"data","normality_rejected":true,"p_value":2.3290287999892373e-05,"statistic":0.9606534120966674,"test":"Shapiro-Wilk"}]},"ci_of_difference":{"conf_level":0.95,"lower":-0.24594263957796628,"method":"t","upper":0.1642126395779662},"df":199.0,"effect_size":{"cohens_d":-0.027785328487644763,"estimate":-0.027785328487644763,"interpretation":"Mean minus mu, in sample standard deviations.","magnitude":"negligible","name":"cohens_d"},"groups":[{"excess_kurtosis":2.785674815227419,"iqr":1.61625,"max":5.465,"mean":-0.04086500000000005,"median":0.0275,"min":-5.627,"n":200,"n_missing":0,"name":"data","q1":-0.85475,"q3":0.7615000000000001,"range":11.091999999999999,"sd":1.4707402152244264,"sem":0.10399703795489543,"skewness":0.08758568455151301,"sum":-8.173000000000009,"variance":2.163076780678392}],"mean_difference":-0.04086500000000005,"notes":["Group 'data' departs from normality (Shapiro–Wilk W = 0.9607, p = 0.0000 < 0.05). Consider stats.mannwhitney."],"p_two_sided":0.6947815351320096,"p_value":0.6947815351320096,"significant":false,"source":{"kind":"arrays"},"statistic":-0.3929438838221874,"test":"one_sample"},"error":null},{"label":"stats.ci","method":"stats.ci","params":{},"result":{"conf_level":0.95,"estimate":-0.04086500000000005,"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":-0.2459426395779663,"margin_of_error":0.20507763957796626,"method":"t","n":200,"name":"data","notes":[],"sd":1.4707402152244264,"source":{"kind":"arrays_or_dataset"},"upper":0.16421263957796622},"error":null}]}