{"example":"Dose–Response Curve: IC50","labtools_version":"0.14.3","generated":"2026-09-23","calls":[{"label":"stats.anova","method":"stats.anova","params":{"design":"two_way","factor_a_name":"Compound","factor_b_name":"Concentration"},"result":{"alpha":0.05,"assumptions":{"note":"Residuals are assumed normal with equal variance across cells, and observations independent. Check the per-cell SDs in `cells`: a spread of more than about 2x between the largest and smallest is a problem."},"cells":[[{"factor_a":"A1","factor_b":"B1","mean":97.99333333333334,"n":3,"sd":4.119008780438969,"sem":2.378110828180871},{"factor_a":"A1","factor_b":"B2","mean":95.81333333333333,"n":3,"sd":1.2706428819040152,"sem":0.7336060099111651},{"factor_a":"A1","factor_b":"B3","mean":79.79,"n":3,"sd":2.135860482334929,"sem":1.2331396244275552},{"factor_a":"A1","factor_b":"B4","mean":53.1,"n":3,"sd":2.9496440463215228,"sem":1.7029777841573082},{"factor_a":"A1","factor_b":"B5","mean":27.253333333333334,"n":3,"sd":3.5865907674745015,"sem":2.07071914507443},{"factor_a":"A1","factor_b":"B6","mean":11.606666666666667,"n":3,"sd":3.8821686379307807,"sem":2.241371108148859},{"factor_a":"A1","factor_b":"B7","mean":1.8499999999999996,"n":3,"sd":4.6285958994062115,"sem":2.672321088492174},{"factor_a":"A1","factor_b":"B8","mean":6.803333333333332,"n":3,"sd":1.2553220038433692,"sem":0.7247604968386296}],[{"factor_a":"A2","factor_b":"B1","mean":101.78000000000002,"n":3,"sd":2.528873266891799,"sem":1.4600456613864286},{"factor_a":"A2","factor_b":"B2","mean":100.58,"n":3,"sd":1.8930398833622124,"sem":1.0929470862458712},{"factor_a":"A2","factor_b":"B3","mean":96.29666666666667,"n":3,"sd":4.355689765505959,"sem":2.5147586586213633},{"factor_a":"A2","factor_b":"B4","mean":88.89,"n":3,"sd":4.286128789478914,"sem":2.4745976103870557},{"factor_a":"A2","factor_b":"B5","mean":83.09,"n":3,"sd":1.7050219939930458,"sem":0.9843949072061176},{"factor_a":"A2","factor_b":"B6","mean":57.4,"n":3,"sd":3.4803879094146932,"sem":2.0094028963848922},{"factor_a":"A2","factor_b":"B7","mean":33.48666666666667,"n":3,"sd":3.8351053875132726,"sem":2.214199127851372},{"factor_a":"A2","factor_b":"B8","mean":14.99,"n":3,"sd":1.0137060717979356,"sem":0.5852634734316963}]],"design":"two_way","factor_a":{"df":1,"f":763.2945070484695,"ms":7673.744752083326,"name":"Compound","p_value":6.734549915617139e-24,"partial_eta_squared":0.9597633333106251,"significant":true,"ss":7673.744752083326},"factor_a_levels":["A1","A2"],"factor_b":{"df":7,"f":752.9235512535244,"ms":7569.480844940476,"name":"Concentration","p_value":1.2168460018099354e-33,"partial_eta_squared":0.9939650708015452,"significant":true,"ss":52986.36591458334},"factor_b_levels":["B1","B2","B3","B4","B5","B6","B7","B8"],"grand_mean":59.42020833333334,"groups":[],"interaction":{"df":7,"f":58.77058419195562,"ms":590.8472520833333,"name":"Compound × Concentration","p_value":1.8116250606119476e-16,"partial_eta_squared":0.9278294393879578,"significant":true,"ss":4135.930764583333},"n_total":48,"notes":["The interaction is significant, so the main effects are not interpretable on their own — the effect of one factor depends on the level of the other. Report simple effects at each level instead."],"post_hoc":"Follow a significant main effect with pairwise stats.ttest comparisons across that factor's levels, corrected via stats.adjust. If the interaction is significant, test simple effects within each level instead.","residual":{"df":32,"ms":10.053452083333333,"ss":321.71046666666666},"source":{"kind":"arrays"}},"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":-12.202064006572764,"method":"t (Welch)","upper":4.628730673239412},"df":3.3201753146836417,"effect_size":{"ci":{"conf_level":0.95,"lower":-2.254310209735787,"upper":0.5673270140851949},"cohens_d":-1.1079555360956446,"estimate":-0.8863644288765157,"interpretation":"Standardised mean difference (group 1 minus group 2), small-sample-bias corrected.","magnitude":"large","name":"hedges_g"},"groups":[{"excess_kurtosis":null,"iqr":3.9849999999999994,"max":102.58,"mean":97.99333333333334,"median":96.79,"min":94.61,"n":3,"n_missing":0,"name":"a","q1":95.7,"q3":99.685,"range":7.969999999999999,"sd":4.119008780438969,"sem":2.378110828180871,"skewness":1.202436842367779,"sum":293.98,"variance":16.96623333333332},{"excess_kurtosis":null,"iqr":2.5,"max":104.06,"mean":101.78000000000002,"median":102.22,"min":99.06,"n":3,"n_missing":0,"name":"b","q1":100.64,"q3":103.14,"range":5.0,"sd":2.528873266891799,"sem":1.4600456613864286,"skewness":-0.7592551474095071,"sum":305.34000000000003,"variance":6.395199999999998}],"mean_difference":-3.786666666666676,"notes":["Group 'a' has n = 3; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.","Group 'b' has n = 3; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality."],"p_two_sided":0.25968834295602505,"p_value":0.25968834295602505,"significant":false,"source":{"kind":"arrays"},"statistic":-1.3569628605630593,"test":"welch"},"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":-8.63777856256559,"method":"t (Welch)","upper":-0.8955547707677427},"df":3.4980585258468215,"effect_size":{"ci":{"conf_level":0.95,"lower":-4.3498071897877555,"upper":-0.28879843116550846},"cohens_d":-2.956691910302142,"estimate":-2.3653535282417137,"interpretation":"Standardised mean difference (group 1 minus group 2), small-sample-bias corrected.","magnitude":"very large","name":"hedges_g"},"groups":[{"excess_kurtosis":null,"iqr":1.2700000000000102,"max":97.06,"mean":95.81333333333333,"median":95.86,"min":94.52,"n":3,"n_missing":0,"name":"a","q1":95.19,"q3":96.46000000000001,"range":2.5400000000000063,"sd":1.2706428819040152,"sem":0.7336060099111651,"skewness":-0.1650477428409392,"sum":287.44,"variance":1.6145333333333414},{"excess_kurtosis":null,"iqr":1.8700000000000045,"max":102.62,"mean":100.58,"median":100.24,"min":98.88,"n":3,"n_missing":0,"name":"b","q1":99.56,"q3":101.43,"range":3.740000000000009,"sd":1.8930398833622124,"sem":1.0929470862458712,"skewness":0.7821521217295085,"sum":301.74,"variance":3.5836000000000188}],"mean_difference":-4.766666666666666,"notes":["Group 'a' has n = 3; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.","Group 'b' has n = 3; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality."],"p_two_sided":0.028044911554529067,"p_value":0.028044911554529067,"significant":true,"source":{"kind":"arrays"},"statistic":-3.6211932534275486,"test":"welch"},"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":-25.579543186766017,"method":"t (Welch)","upper":-7.433790146567302},"df":2.9092449179497,"effect_size":{"ci":{"conf_level":0.95,"lower":-6.685931834188917,"upper":-0.9702525561137332},"cohens_d":-4.812016631491127,"estimate":-3.849613305192902,"interpretation":"Standardised mean difference (group 1 minus group 2), small-sample-bias corrected.","magnitude":"very large","name":"hedges_g"},"groups":[{"excess_kurtosis":null,"iqr":2.0649999999999977,"max":82.17,"mean":79.79,"median":79.16,"min":78.04,"n":3,"n_missing":0,"name":"a","q1":78.6,"q3":80.66499999999999,"range":4.1299999999999955,"sd":2.135860482334929,"sem":1.2331396244275552,"skewness":1.2118515633717986,"sum":239.37,"variance":4.561899999999996},{"excess_kurtosis":null,"iqr":4.295000000000002,"max":101.01,"mean":96.29666666666667,"median":95.46,"min":92.42,"n":3,"n_missing":0,"name":"b","q1":93.94,"q3":98.235,"range":8.590000000000003,"sd":4.355689765505959,"sem":2.5147586586213633,"skewness":0.8324933571416273,"sum":288.89,"variance":18.972033333333357}],"mean_difference":-16.50666666666666,"notes":["Group 'a' has n = 3; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.","Group 'b' has n = 3; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality."],"p_two_sided":0.010622996788519013,"p_value":0.010622996788519013,"significant":true,"source":{"kind":"arrays"},"statistic":-5.893492690469787,"test":"welch"},"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":-44.5673071969518,"method":"t (Welch)","upper":-27.012692803048196},"df":3.5473304495096487,"effect_size":{"ci":{"conf_level":0.95,"lower":-13.121895568826439,"upper":-2.51361321475381},"cohens_d":-9.72796815813231,"estimate":-7.782374526505848,"interpretation":"Standardised mean difference (group 1 minus group 2), small-sample-bias corrected.","magnitude":"very large","name":"hedges_g"},"groups":[{"excess_kurtosis":null,"iqr":2.8400000000000034,"max":55.48,"mean":53.1,"median":54.02,"min":49.8,"n":3,"n_missing":0,"name":"a","q1":51.91,"q3":54.75,"range":5.68,"sd":2.9496440463215228,"sem":1.7029777841573082,"skewness":-1.2670169021858788,"sum":159.3,"variance":8.700400000000005},{"excess_kurtosis":null,"iqr":4.090000000000003,"max":92.24,"mean":88.89,"median":90.37,"min":84.06,"n":3,"n_missing":0,"name":"b","q1":87.215,"q3":91.305,"range":8.179999999999993,"sd":4.286128789478914,"sem":2.4745976103870557,"skewness":-1.3685810341988658,"sum":266.67,"variance":18.370899999999978}],"mean_difference":-35.79,"notes":["Group 'a' has n = 3; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.","Group 'b' has n = 3; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality."],"p_two_sided":0.0005486990573759188,"p_value":0.0005486990573759188,"significant":true,"source":{"kind":"arrays"},"statistic":-11.91427911073323,"test":"welch"},"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":-63.33957357669972,"method":"t (Welch)","upper":-48.333759756633626},"df":2.8600493428546807,"effect_size":{"ci":{"conf_level":0.95,"lower":-26.615935736613405,"upper":-5.439219296491035},"cohens_d":-19.88421899383511,"estimate":-15.907375195068088,"interpretation":"Standardised mean difference (group 1 minus group 2), small-sample-bias corrected.","magnitude":"very large","name":"hedges_g"},"groups":[{"excess_kurtosis":null,"iqr":3.259999999999998,"max":29.65,"mean":27.253333333333334,"median":28.98,"min":23.13,"n":3,"n_missing":0,"name":"a","q1":26.055,"q3":29.314999999999998,"range":6.52,"sd":3.5865907674745015,"sem":2.07071914507443,"skewness":-1.6643000291247456,"sum":81.76,"variance":12.863633333333334},{"excess_kurtosis":null,"iqr":1.5799999999999983,"max":85.04,"mean":83.09,"median":82.35,"min":81.88,"n":3,"n_missing":0,"name":"b","q1":82.115,"q3":83.695,"range":3.160000000000011,"sd":1.7050219939930458,"sem":0.9843949072061176,"skewness":1.585164210991179,"sum":249.27,"variance":2.907100000000022}],"mean_difference":-55.83666666666667,"notes":["Group 'a' has n = 3; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.","Group 'b' has n = 3; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality."],"p_two_sided":0.0002094675258366073,"p_value":0.0002094675258366073,"significant":true,"source":{"kind":"arrays"},"statistic":-24.353095234326776,"test":"welch"},"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":-54.190228408208064,"method":"t (Welch)","upper":-37.396438258458595},"df":3.9531892368895005,"effect_size":{"ci":{"conf_level":0.95,"lower":-16.68949355570742,"upper":-3.304460164560745},"cohens_d":-12.421038608886024,"estimate":-9.936830887108819,"interpretation":"Standardised mean difference (group 1 minus group 2), small-sample-bias corrected.","magnitude":"very large","name":"hedges_g"},"groups":[{"excess_kurtosis":null,"iqr":3.834999999999999,"max":15.79,"mean":11.606666666666667,"median":10.91,"min":8.12,"n":3,"n_missing":0,"name":"a","q1":9.515,"q3":13.35,"range":7.67,"sd":3.8821686379307807,"sem":2.241371108148859,"skewness":0.7815328828498472,"sum":34.82,"variance":15.071233333333332},{"excess_kurtosis":null,"iqr":3.479999999999997,"max":60.91,"mean":57.4,"median":57.34,"min":53.95,"n":3,"n_missing":0,"name":"b","q1":55.645,"q3":59.125,"range":6.959999999999994,"sd":3.4803879094146932,"sem":2.0094028963848922,"skewness":0.07755450349852056,"sum":172.2,"variance":12.113099999999978}],"mean_difference":-45.79333333333333,"notes":["Group 'a' has n = 3; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.","Group 'b' has n = 3; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality."],"p_two_sided":0.00011765827625676924,"p_value":0.00011765827625676924,"significant":true,"source":{"kind":"arrays"},"statistic":-15.212603333590073,"test":"welch"},"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":-41.40487672669197,"method":"t (Welch)","upper":-21.868456606641374},"df":3.866423175330875,"effect_size":{"ci":{"conf_level":0.95,"lower":-10.110699070588355,"upper":-1.8213485992236322},"cohens_d":-7.443207329712898,"estimate":-5.954565863770319,"interpretation":"Standardised mean difference (group 1 minus group 2), small-sample-bias corrected.","magnitude":"very large","name":"hedges_g"},"groups":[{"excess_kurtosis":null,"iqr":4.455,"max":5.58,"mean":1.8499999999999996,"median":3.3,"min":-3.33,"n":3,"n_missing":0,"name":"a","q1":-0.015000000000000124,"q3":4.4399999999999995,"range":8.91,"sd":4.6285958994062115,"sem":2.672321088492174,"skewness":-1.2713680955104312,"sum":5.549999999999999,"variance":21.4239},{"excess_kurtosis":null,"iqr":3.6799999999999997,"max":37.79,"mean":33.48666666666667,"median":32.24,"min":30.43,"n":3,"n_missing":0,"name":"b","q1":31.335,"q3":35.015,"range":7.359999999999999,"sd":3.8351053875132726,"sem":2.214199127851372,"skewness":1.3082297515733696,"sum":100.46000000000001,"variance":14.70803333333333}],"mean_difference":-31.63666666666667,"notes":["Group 'a' has n = 3; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.","Group 'b' has n = 3; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality."],"p_two_sided":0.000940091474880954,"p_value":0.000940091474880954,"significant":true,"source":{"kind":"arrays"},"statistic":-9.116030003770156,"test":"welch"},"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":-10.818969377151728,"method":"t (Welch)","upper":-5.554363956181607},"df":3.8301544246656687,"effect_size":{"ci":{"conf_level":0.95,"lower":-9.759378414440151,"upper":-1.7381349316020858},"cohens_d":-7.175445580447392,"estimate":-5.740356464357914,"interpretation":"Standardised mean difference (group 1 minus group 2), small-sample-bias corrected.","magnitude":"very large","name":"hedges_g"},"groups":[{"excess_kurtosis":null,"iqr":1.25,"max":8.12,"mean":6.803333333333332,"median":6.67,"min":5.62,"n":3,"n_missing":0,"name":"a","q1":6.145,"q3":7.395,"range":2.499999999999999,"sd":1.2553220038433692,"sem":0.7247604968386296,"skewness":0.47257284811598027,"sum":20.409999999999997,"variance":1.575833333333332},{"excess_kurtosis":null,"iqr":1.0099999999999998,"max":16.05,"mean":14.99,"median":14.89,"min":14.03,"n":3,"n_missing":0,"name":"b","q1":14.46,"q3":15.47,"range":2.0200000000000014,"sd":1.0137060717979356,"sem":0.5852634734316963,"skewness":0.4395957334645414,"sum":44.97,"variance":1.0276000000000012}],"mean_difference":-8.186666666666667,"notes":["Group 'a' has n = 3; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.","Group 'b' has n = 3; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality."],"p_two_sided":0.0011234129180025026,"p_value":0.0011234129180025026,"significant":true,"source":{"kind":"arrays"},"statistic":-8.788090174602388,"test":"welch"},"error":null},{"label":"stats.adjust","method":"stats.adjust","params":{"method":"bonferroni","alpha":0.05},"result":{"alpha":0.05,"controls":"familywise_error_rate","method":"bonferroni","n_significant_adjusted":5,"n_significant_raw":7,"n_tests":8,"notes":["2 comparison(s) were significant on the raw p-values but are not after correction. Report the adjusted values.","Holm controls the same familywise error rate as Bonferroni and rejects at least as much, so there is no statistical reason to prefer bonferroni."],"results":[{"adjusted":1.0,"index":0,"label":"0.01 µM","p_value":0.25968834295602505,"significant":false},{"adjusted":0.22435929243623254,"index":1,"label":"0.03 µM","p_value":0.028044911554529067,"significant":false},{"adjusted":0.08498397430815209,"index":2,"label":"0.1 µM","p_value":0.010622996788519011,"significant":false},{"adjusted":0.004389592459007351,"index":3,"label":"0.3 µM","p_value":0.0005486990573759188,"significant":true},{"adjusted":0.0016757402066928584,"index":4,"label":"1 µM","p_value":0.0002094675258366073,"significant":true},{"adjusted":0.0009412662100541539,"index":5,"label":"3 µM","p_value":0.00011765827625676924,"significant":true},{"adjusted":0.007520731799047632,"index":6,"label":"10 µM","p_value":0.000940091474880954,"significant":true},{"adjusted":0.008987303344020021,"index":7,"label":"30 µM","p_value":0.0011234129180025026,"significant":true}],"source":{"kind":"p_values"}},"error":null},{"label":"stats.adjust","method":"stats.adjust","params":{"method":"holm","alpha":0.05},"result":{"alpha":0.05,"controls":"familywise_error_rate","method":"holm","n_significant_adjusted":6,"n_significant_raw":7,"n_tests":8,"notes":["1 comparison(s) were significant on the raw p-values but are not after correction. Report the adjusted values."],"results":[{"adjusted":0.25968834295602505,"index":0,"label":"0.01 µM","p_value":0.25968834295602505,"significant":false},{"adjusted":0.056089823109058135,"index":1,"label":"0.03 µM","p_value":0.028044911554529067,"significant":false},{"adjusted":0.031868990365557036,"index":2,"label":"0.1 µM","p_value":0.010622996788519011,"significant":true},{"adjusted":0.003292194344255513,"index":3,"label":"0.3 µM","p_value":0.0005486990573759188,"significant":true},{"adjusted":0.001466272680856251,"index":4,"label":"1 µM","p_value":0.0002094675258366073,"significant":true},{"adjusted":0.0009412662100541539,"index":5,"label":"3 µM","p_value":0.00011765827625676924,"significant":true},{"adjusted":0.00470045737440477,"index":6,"label":"10 µM","p_value":0.000940091474880954,"significant":true},{"adjusted":0.00470045737440477,"index":7,"label":"30 µM","p_value":0.0011234129180025026,"significant":true}],"source":{"kind":"p_values"}},"error":null},{"label":"stats.adjust","method":"stats.adjust","params":{"method":"benjamini_hochberg","alpha":0.05},"result":{"alpha":0.05,"controls":"false_discovery_rate","method":"benjamini_hochberg","n_significant_adjusted":7,"n_significant_raw":7,"n_tests":8,"notes":[],"results":[{"adjusted":0.25968834295602505,"index":0,"label":"0.01 µM","p_value":0.25968834295602505,"significant":false},{"adjusted":0.03205132749089036,"index":1,"label":"0.03 µM","p_value":0.028044911554529067,"significant":true},{"adjusted":0.014163995718025348,"index":2,"label":"0.1 µM","p_value":0.010622996788519011,"significant":true},{"adjusted":0.0014631974863357836,"index":3,"label":"0.3 µM","p_value":0.0005486990573759188,"significant":true},{"adjusted":0.0008378701033464292,"index":4,"label":"1 µM","p_value":0.0002094675258366073,"significant":true},{"adjusted":0.0008378701033464292,"index":5,"label":"3 µM","p_value":0.00011765827625676924,"significant":true},{"adjusted":0.0017974606688040042,"index":6,"label":"10 µM","p_value":0.000940091474880954,"significant":true},{"adjusted":0.0017974606688040042,"index":7,"label":"30 µM","p_value":0.0011234129180025026,"significant":true}],"source":{"kind":"p_values"}},"error":null},{"label":"stats.adjust","method":"stats.adjust","params":{"method":"benjamini_yekutieli","alpha":0.05},"result":{"alpha":0.05,"controls":"false_discovery_rate","method":"benjamini_yekutieli","n_significant_adjusted":6,"n_significant_raw":7,"n_tests":8,"notes":["1 comparison(s) were significant on the raw p-values but are not after correction. 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