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{"sheet":"Normality tests","index":3,"n_rows":72,"n_cols":9,"rows_kept":72,"cut":false,"hidden":false,"merged":[[22,1,23,9],[35,1,36,9],[49,1,50,9],[64,1,65,9]]}
[null,"XLSTAT 2023.1.1.1405 - Normality tests - Start time: 10/03/2023 at 14:29:38 / End time: 10/03/2023 at 14:29:39 / Microsoft Excel 16.016130"]
[null,"Data: Workbook = DemoTransformation_fr.xlsm / Sheet = Data / Range = 'Data'!$B:$B / 47 rows and 1 column"]
[null,"Significance level (%): 5"]
[]
[]
[]
[]
[null,"Summary statistics:"]
[]
[null,"Variable","Observations","Obs. with missing data","Obs. without missing data","Minimum","Maximum","Mean","Std. deviation"]
[null,"Level of waste",47,0,47,2.7155197406246303E-2,4.8807557526188319,0.98837028054489728,1.258440008993104]
[]
[]
[null,"Shapiro-Wilk test (Level of waste):"]
[]
[null,"W",0.73738369363897638]
[null,"p-value (Two-tailed)",8.1155338560456869E-8]
[null,"alpha",0.05]
[]
[null,"Test interpretation:"]
[null,"H0: The variable from which the sample was extracted follows a Normal distribution."]
[null,"Ha: The variable from which the sample was extracted does not follow a Normal distribution."]
[null,"As the computed p-value is lower than the significance level alpha=0,05, one should reject the null hypothesis H0, and accept the alternative hypothesis Ha."]
[]
[]
[]
[null,"Anderson-Darling test (Level of waste):"]
[]
[null,"A²",4.4552213556442624]
[null,"p-value (Two-tailed)",3.1184232123860897E-11]
[null,"alpha",0.05]
[]
[null,"Test interpretation:"]
[null,"H0: The variable from which the sample was extracted follows a Normal distribution."]
[null,"Ha: The variable from which the sample was extracted does not follow a Normal distribution."]
[null,"As the computed p-value is lower than the significance level alpha=0,05, one should reject the null hypothesis H0, and accept the alternative hypothesis Ha."]
[]
[]
[]
[null,"Lilliefors test (Level of waste):"]
[]
[null,"D",0.24913457060472549]
[null,"D (standardized)",1.7079805650852249]
[null,"p-value (Two-tailed)",7.9677447373650889E-8]
[null,"alpha",0.05]
[]
[null,"Test interpretation:"]
[null,"H0: The variable from which the sample was extracted follows a Normal distribution."]
[null,"Ha: The variable from which the sample was extracted does not follow a Normal distribution."]
[null,"As the computed p-value is lower than the significance level alpha=0,05, one should reject the null hypothesis H0, and accept the alternative hypothesis Ha."]
[]
[]
[]
[null,"Jarque-Bera test (Level of waste):"]
[]
[null,"JB (Observed value)",32.0517323785866]
[null,"JB (Critical value)",5.9914645471101275]
[null,"DF",2]
[null,"p-value (Two-tailed)",1.0966164243342291E-7]
[null,"alpha",0.05]
[]
[null,"Test interpretation:"]
[null,"H0: The variable from which the sample was extracted follows a Normal distribution."]
[null,"Ha: The variable from which the sample was extracted does not follow a Normal distribution."]
[null,"As the computed p-value is lower than the significance level alpha=0,05, one should reject the null hypothesis H0, and accept the alternative hypothesis Ha."]
[]
[]
[]
[null,"Summary:"]
[]
[null,"Variable\\Test","Shapiro-Wilk","Anderson-Darling","Lilliefors","Jarque-Bera"]
[null,"Level of waste",8.1155338560456869E-8,3.1184232123860897E-11,7.9677447373650889E-8,1.0966164243342291E-7]

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[2.3736296473189764,0]
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[2.3763191516469639,0]

{"sheet":"Histogram","index":5,"n_rows":45,"n_cols":9,"rows_kept":45,"cut":false,"hidden":false,"merged":[]}
[null,"XLSTAT 2023.1.1.1405 - Histograms - Start time: 10/03/2023 at 14:29:50 / End time: 10/03/2023 at 14:29:51 / Microsoft Excel 16.016130"]
[null,"Data: Workbook = DemoTransformation_fr.xlsm / Sheet = Data / Range = 'Data'!$B:$B / 47 rows and 1 column"]
[null,"Intervals: Number = 10"]
[]
[]
[]
[]
[null,"Summary statistics:"]
[]
[null,"Variable","Observations","Obs. with missing data","Obs. without missing data","Minimum","Maximum","Mean","Std. deviation"]
[null,"Level of waste",47,0,47,2.7155197406246303E-2,4.8807557526188319,0.98837028054489728,1.258440008993104]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null," "]
[]
[]
[null,"Descriptive statistics for the intervals (Level of waste):"]
[]
[null,"Lower bound","Upper bound","Frequency","Relative frequency","Density (Data)","Density (Distribution)"]
[null,0,0.49807557526188317,25,0.53191489361702127,1.0679401280364846,0.13230275216925491]
[null,0.49807557526188317,0.99615115052376635,6,0.1276595744680851,0.25630563072875628,0.15405235131199652]
[null,0.99615115052376635,1.4942267257856496,5,0.10638297872340426,0.21358802560729689,0.15368070809021905]
[null,1.4942267257856496,1.9923023010475327,5,0.10638297872340426,0.21358802560729698,0.1313475297885689]
[null,1.9923023010475327,2.4903778763094158,1,2.1276595744680851E-2,4.2717605121459397E-2,9.6177576270108589E-2]
[null,2.4903778763094158,2.9884534515712993,0,0,0,6.033520907152512E-2]
[null,2.9884534515712993,3.4865290268331823,0,0,0,3.2426982512444469E-2]
[null,3.4865290268331823,3.9846046020950654,2,4.2553191489361701E-2,8.5435210242918794E-2,1.4930440735136608E-2]
[null,3.9846046020950654,4.4826801773569489,2,4.2553191489361701E-2,8.543521024291871E-2,5.889234482742145E-3]
[null,4.4826801773569489,4.9807557526188315,1,2.1276595744680851E-2,4.2717605121459432E-2,1.9900003629182983E-3]

{"sheet":"Variables transformation","index":6,"n_rows":73,"n_cols":3,"rows_kept":73,"cut":false,"hidden":false,"merged":[[19,1,20,9]]}
[null,"XLSTAT 2023.1.1.1405 - Variables transformation - Start time: 10/03/2023 at 15:11:16 / End time: 10/03/2023 at 15:11:17 / Microsoft Excel 16.016130"]
[null,"Data: Workbook = demo-variable-transformation.xlsm / Sheet = Data / Range = 'Data'!$B:$B / 47 rows and 1 column"]
[null,"Transformation: Johnson transformation"]
[null,"Test: Shapiro-Wilk"]
[]
[]
[]
[]
[null,"Formula (Level of waste): Obs (New) = 1.259 + 0.527 * ln( (Obs - 0.020) / (5.564 + 0.020 - Obs) )"]
[]
[null,"Normality test (Level of waste):"]
[]
[null,"W",0.98448607920081677]
[null,"p-value (Two-tailed)",0.7802566610325693]
[null,"alpha",0.05]
[]
[null,"Test interpretation:"]
[null,"H0: The variable from which the sample was extracted follows a Normal distribution."]
[null,"Ha: The variable from which the sample was extracted does not follow a Normal distribution."]
[null,"As the computed p-value is greater than the significance level alpha=0,05, one cannot reject the null hypothesis H0."]
[]
[]
[]
[null,"Transformed data:"]
[]
[null,"Observation","Level of waste"]
[null,"Obs1",-0.43211015563345123]
[null,"Obs2",-2.1921510964200523]
[null,"Obs3",-1.0186241241351988]
[null,"Obs4",-0.58857944963548259]
[null,"Obs5",1.0199389560279366]
[null,"Obs6",0.48605252624201634]
[null,"Obs7",-1.5347811896099215]
[null,"Obs8",-0.58818413912920042]
[null,"Obs9",-0.12792555713229659]
[null,"Obs10",1.8606261086809595]
[null,"Obs11",-1.7480604439457379]
[null,"Obs12",0.14214812557442058]
[null,"Obs13",-0.31555260773680271]
[null,"Obs14",-0.96262342004831392]
[null,"Obs15",1.6445990052375106]
[null,"Obs16",-6.7945662526157191E-2]
[null,"Obs17",1.5300239133770752]
[null,"Obs18",0.75859387063191519]
[null,"Obs19",0.93370767019652123]
[null,"Obs20",0.23100821575167174]
[null,"Obs21",-1.0903904783198402]
[null,"Obs22",0.69396817197840077]
[null,"Obs23",1.8878790025055032]
[null,"Obs24",-0.81716284344944357]
[null,"Obs25",2.2790086559749501]
[null,"Obs26",7.6466222521238691E-2]
[null,"Obs27",-2.2239451053174246]
[null,"Obs28",-1.1335156614886877]
[null,"Obs29",0.11809056366318438]
[null,"Obs30",-0.38106357341867558]
[null,"Obs31",-0.2368989492589948]
[null,"Obs32",0.77902870076959196]
[null,"Obs33",0.158969253177633]
[null,"Obs34",0.88189486911149018]
[null,"Obs35",-0.51139941091192687]
[null,"Obs36",-0.13458986300082953]
[null,"Obs37",0.83901156856233983]
[null,"Obs38",0.6475609481715715]
[null,"Obs39",-1.2855675796742323]
[null,"Obs40",-2.1178364285480091]
[null,"Obs41",-0.5612264906314115]
[null,"Obs42",-0.58922257351082497]
[null,"Obs43",7.8332442910564959E-2]
[null,"Obs44",0.59137092330552776]
[null,"Obs45",-7.3704062470224763E-2]
[null,"Obs46",0.63616500522844532]
[null,"Obs47",-0.21572345307298924]

{"sheet":"Normality tests_afterTransf","index":7,"n_rows":72,"n_cols":9,"rows_kept":72,"cut":false,"hidden":false,"merged":[[22,1,23,9],[35,1,36,9],[49,1,50,9],[64,1,65,9]]}
[null,"XLSTAT 2023.1.1.1405 - Normality tests - Start time: 10/03/2023 at 15:26:53 / End time: 10/03/2023 at 15:26:54 / Microsoft Excel 16.016130"]
[null,"Data: Workbook = demo-variable-transformation.xlsm / Sheet = Variables transformation / Range = 'Variables transformation'!$C$26:$C$73 / 47 rows and 1 column"]
[null,"Significance level (%): 5"]
[]
[]
[]
[]
[null,"Summary statistics:"]
[]
[null,"Variable","Observations","Obs. with missing data","Obs. without missing data","Minimum","Maximum","Mean","Std. deviation"]
[null,"Level of waste",47,0,47,-2.2239451053174246,2.2790086559749501,-5.6900842540971511E-2,1.0663539704558118]
[]
[]
[null,"Shapiro-Wilk test (Level of waste):"]
[]
[null,"W",0.98448607920081677]
[null,"p-value (Two-tailed)",0.7802566610325693]
[null,"alpha",0.05]
[]
[null,"Test interpretation:"]
[null,"H0: The variable from which the sample was extracted follows a Normal distribution."]
[null,"Ha: The variable from which the sample was extracted does not follow a Normal distribution."]
[null,"As the computed p-value is greater than the significance level alpha=0,05, one cannot reject the null hypothesis H0."]
[]
[]
[]
[null,"Anderson-Darling test (Level of waste):"]
[]
[null,"A²",0.20062043103461491]
[null,"p-value (Two-tailed)",0.87525903232767599]
[null,"alpha",0.05]
[]
[null,"Test interpretation:"]
[null,"H0: The variable from which the sample was extracted follows a Normal distribution."]
[null,"Ha: The variable from which the sample was extracted does not follow a Normal distribution."]
[null,"As the computed p-value is greater than the significance level alpha=0,05, one cannot reject the null hypothesis H0."]
[]
[]
[]
[null,"Lilliefors test (Level of waste):"]
[]
[null,"D",7.4777411190787429E-2]
[null,"D (standardized)",0.51264810303620234]
[null,"p-value (Two-tailed)",0.73457295356725716]
[null,"alpha",0.05]
[]
[null,"Test interpretation:"]
[null,"H0: The variable from which the sample was extracted follows a Normal distribution."]
[null,"Ha: The variable from which the sample was extracted does not follow a Normal distribution."]
[null,"As the computed p-value is greater than the significance level alpha=0,05, one cannot reject the null hypothesis H0."]
[]
[]
[]
[null,"Jarque-Bera test (Level of waste):"]
[]
[null,"JB (Observed value)",0.14725928811372266]
[null,"JB (Critical value)",5.9914645471101275]
[null,"DF",2]
[null,"p-value (Two-tailed)",0.92901569662013062]
[null,"alpha",0.05]
[]
[null,"Test interpretation:"]
[null,"H0: The variable from which the sample was extracted follows a Normal distribution."]
[null,"Ha: The variable from which the sample was extracted does not follow a Normal distribution."]
[null,"As the computed p-value is greater than the significance level alpha=0,05, one cannot reject the null hypothesis H0."]
[]
[]
[]
[null,"Summary:"]
[]
[null,"Variable\\Test","Shapiro-Wilk","Anderson-Darling","Lilliefors","Jarque-Bera"]
[null,"Level of waste",0.7802566610325693,0.87525903232767599,0.73457295356725716,0.92901569662013062]

{"sheet":"Histogram_afterTransf","index":8,"n_rows":45,"n_cols":9,"rows_kept":45,"cut":false,"hidden":false,"merged":[]}
[null,"XLSTAT 2023.1.1.1405 - Histograms - Start time: 10/03/2023 at 15:28:55 / End time: 10/03/2023 at 15:28:56 / Microsoft Excel 16.016130"]
[null,"Data: Workbook = demo-variable-transformation.xlsm / Sheet = Variables transformation / Range = 'Variables transformation'!$C$26:$C$73 / 47 rows and 1 column"]
[null,"Intervals: Number = 10"]
[]
[]
[]
[]
[null,"Summary statistics:"]
[]
[null,"Variable","Observations","Obs. with missing data","Obs. without missing data","Minimum","Maximum","Mean","Std. deviation"]
[null,"Level of waste",47,0,47,-2.2239451053174246,2.2790086559749501,-5.6900842540971511E-2,1.0663539704558118]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null," "]
[]
[]
[null,"Descriptive statistics for the intervals (Level of waste):"]
[]
[null,"Lower bound","Upper bound","Frequency","Relative frequency","Density (Data)","Density (Distribution)"]
[null,-3,-2.4620991344025049,0,0,0,9.1595143651986462E-3]
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[null,0.22740519358496947,0.76530605918246453,7,0.14893617021276595,0.27688405008854022,0.17454264824838139]
[null,0.76530605918246453,1.3032069247799596,5,0.10638297872340426,0.19777432149181443,0.11926953411953933]
[null,1.3032069247799596,1.8411077903774542,2,4.2553191489361701E-2,7.910972859672584E-2,6.3524829464962629E-2]
[null,1.8411077903774542,2.3790086559749497,3,6.3829787234042548E-2,0.11866459289508856,2.636983400094417E-2]

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