{"metadata":{"kernelspec":{"language":"python","display_name":"Python 3","name":"python3"},"language_info":{"pygments_lexer":"ipython3","nbconvert_exporter":"python","version":"3.6.4","file_extension":".py","codemirror_mode":{"name":"ipython","version":3},"name":"python","mimetype":"text/x-python"}},"nbformat_minor":4,"nbformat":4,"cells":[{"cell_type":"code","source":"# Hypothesis testing\nimport pandas as pd\nfrom scipy import stats\nimport numpy as np\nimport matplotlib.pyplot as plt \nfrom statsmodels.stats.proportion import proportions_ztest # used in proportion test\nfrom statsmodels.stats.multicomp import pairwise_tukeyhsd # used in posthoc ANOVA\nimport math # used in confidence interval range computation in proportion test","metadata":{"id":"tqTTs89ZI0V8","execution":{"iopub.status.busy":"2023-05-02T08:59:06.338965Z","iopub.execute_input":"2023-05-02T08:59:06.339923Z","iopub.status.idle":"2023-05-02T08:59:06.346027Z","shell.execute_reply.started":"2023-05-02T08:59:06.339882Z","shell.execute_reply":"2023-05-02T08:59:06.344598Z"},"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"# New Section","metadata":{"id":"6UuV-NkFscbd"}},{"cell_type":"markdown","source":"Dataset needed:\ncranksh.csv, Exh_Stat.csv, Furnace.csv, diet_indep.csv, Diet_B_A.csv, Paired_Diff_1T.csv, carpet.csv, FilterNoise_data.csv, QC_2.csv,Biscuits_Chi.csv,Car.csv","metadata":{"id":"uQZKDpPIARrd"}},{"cell_type":"code","source":"# connecting google drive\nfrom google.colab import drive\ndrive.mount('/content/drive')","metadata":{"id":"oOehndzjVzii","outputId":"9a35d261-7cad-4259-d2ac-da13b2f0373f"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":" # Loading Data\n import pandas as pd\ncrank= pd.read_csv(\"/content/drive/MyDrive/DBA DATA SET/cranksh (2).csv\")\ncrank.tail(10)","metadata":{"id":"oKnwYwgWV-WF","outputId":"cfaf637d-2878-4e0e-d90b-33a591b4543d"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"crank.tail()","metadata":{"id":"jnRPTbawl-Z3","outputId":"4786dcc8-ae4d-4903-f737-6520e38c3c3b"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"crank.shape","metadata":{"id":"j0zIZ7Cal-om","outputId":"6b6083b7-6a79-4f40-9df4-0289afb6e88f"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"crank.isnull().sum()","metadata":{"id":"60zhbazymStx","outputId":"095034cf-7886-46ef-c3ec-fc0594788730"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"","metadata":{"id":"QL86HJNomSyS"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"","metadata":{"id":"3cGf8L-3mS2n"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"crank.AtoBDist","metadata":{"id":"at2lPt9noHno","outputId":"73802113-1034-43d1-9741-541dbb7082af"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# find number of columns and rows\ncrank.shape","metadata":{"id":"emZo0X3WWPU0","outputId":"01bb5453-3db8-4725-f266-54717d3d7f6a"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"#testing for normality,Ho= Data is normally distributed\nfrom statistics import as stat\nstats.shapiro(crank.AtoBDist)  # testing for normality","metadata":{"id":"HKi2D3PrWKBg","outputId":"8a9d142d-1105-41cb-833a-abe6bef6b3ad"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# Loading Data\ndf=pd.read_csv(\"/content/drive/MyDrive/DBA DATA SET/Exh_Stat (2).csv\")","metadata":{"id":"aP0dHc0OCuEt"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"df.head()","metadata":{"id":"ozeyc08CJQ0V","outputId":"a45480cb-ead7-40ce-c18e-473fec17e32e"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# One-sample t-test\nimport statistics\nstats.ttest_1samp(df.Values,5, nan_policy='omit')# One-sample t-test\n","metadata":{"id":"y-XlaDQBWVV4","outputId":"cae5bcd8-a5b9-4085-aad0-1502a325bf61"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# Two-sample t-test\nFurnace=pd.read_csv(\"/content/drive/MyDrive/DBA DATA SET/Furnace (3).csv\")\nFurnace.tail()","metadata":{"id":"7oCXpy2UaoRD","outputId":"0a5a10c3-9ebc-4fff-abcd-39946e99afd3"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"Furnace.tail()","metadata":{"id":"e_x91N0jazF2","outputId":"7b78a3be-8543-4fee-b02e-c459001bff68"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"Furnace[Furnace.Damper==1].BTU_In","metadata":{"id":"qvTFAufUwg-B","outputId":"e37992e6-2f54-4aad-a5cf-b7c767fc00c9"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"BTU_Damper_1=Furnace[Furnace.Damper==1].BTU_In\nBTU_Damper_2=Furnace[Furnace.Damper==2].BTU_In\nstats.shapiro(BTU_Damper_1) # normality test","metadata":{"id":"5g6ZCCmCa3Uf","outputId":"d027af42-0353-427c-ab14-b20e6af0e442"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"stats.shapiro(BTU_Damper_2)","metadata":{"id":"MddeQmx1yb-A","outputId":"6665d2ac-99c8-4164-a9a9-67e95ff7a670"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"stats.levene(BTU_Damper_1,BTU_Damper_2) # HOV test","metadata":{"id":"8IKi0ACVyfo9","outputId":"d1903325-f78f-47ae-f266-cfb133a07326"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"stats.ttest_ind(BTU_Damper_1,BTU_Damper_2,equal_var=True)","metadata":{"id":"_rAgJX9EykNz","outputId":"5aec2233-972b-495c-c1b5-42f00992cc9a"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# Paired t-test\n\n# first run the independent samples t test on the following file\nDiet1=pd.read_csv(\"/content/drive/MyDrive/Data/DBA_lecture/Industry-data/python_data/Hypothesis_Test/diet_indep.csv\")\nDiet1.head()","metadata":{"id":"ygH_MlGD24eo","outputId":"904d1463-0952-4302-cc7d-4580bd075eed"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"# New Section","metadata":{"id":"F3oZw6R_as-B"}},{"cell_type":"code","source":"Diet1_S_A=Diet1[Diet1.stage=='A'].weight\nDiet1_S_B=Diet1[Diet1.stage=='B'].weight","metadata":{"id":"SAJIeUnZ8TVf","outputId":"cf0c7260-7879-432a-a3da-a04c84c0355d"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"stats.levene(Diet1_S_A,Diet1_S_B) # HOV test","metadata":{"id":"fDRrnVsP9aG8","outputId":"2f472a89-8340-4e87-f73b-c1a281cf032a"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"stats.ttest_ind(Diet1_S_A,Diet1_S_B,equal_var=True)","metadata":{"id":"ZRqpRVpy3yAx","outputId":"4979f4ef-841e-4268-d841-2f590a7c0800"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# Now run a paired t test on teh following file\nDiet2=pd.read_csv(\"/content/drive/MyDrive/Data/DBA_lecture/Industry-data/python_data/Hypothesis_Test/Diet_B_A.csv\")\nDiet2.head()","metadata":{"id":"pPs5xWzx-zkb","outputId":"ead46a3d-0eca-4ad0-e67a-faf704a9fa7a"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"Diet2['Diff']=Diet2['After']-Diet2['Before']\nDiet2","metadata":{"id":"ORcECQUWzIPd","outputId":"ee8a8fe5-21a8-4854-c5bb-c01dc3a37e53"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"stats.ttest_rel(Diet2.Before,Diet2.After) # paired t test","metadata":{"id":"zxV87E5Y_TPq","outputId":"8dc78575-7ebe-4c22-ffe6-6e6883019318"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# Now we will run 1-t test for the follwing file to explain paired t test \nDiet3=pd.read_csv(\"/content/drive/MyDrive/Data/DBA_lecture/Industry-data/python_data/Hypothesis_Test/Paired_Diff_1T.csv\")\nDiet3.head()","metadata":{"id":"ZUoBNQ2nU0bp","outputId":"64137eba-95c1-43fc-fb77-dd4bad4574ff"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"stats.ttest_1samp(Diet3.Diff,0, nan_policy='omit',)# One-sample t-test","metadata":{"id":"KG3ihAArVr3f","outputId":"29df6967-106f-46b9-89ba-740a75f46b90"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# (HoV)\n#Furnace=pd.read_csv(\"/content/drive/My Drive/python_data/Hypothesis_Test/Furnace.csv\")\n#Furnace.head()\n#BTU_Damper_1=Furnace[Furnace.Damper==1].BTU_In\n#BTU_Damper_2=Furnace[Furnace.Damper==2].BTU_In\n#stats.levene(BTU_Damper_1,BTU_Damper_2) # HOV test","metadata":{"id":"tE2L2t6szCFN"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# ANOVA\ncarpet=pd.read_csv(\"/content/drive/My Drive/Learning Modules/python_data/Hypothesis_Test/carpet.csv\")\ncarpet","metadata":{"id":"kVHpKNMA0Q8h","outputId":"21739591-f3a2-4f45-a683-42f38fdc17c5"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"Dur_1=carpet[carpet.Carpet==1].Durability\nDur_2=carpet[carpet.Carpet==2].Durability\nDur_3=carpet[carpet.Carpet==3].Durability\nDur_4=carpet[carpet.Carpet==4].Durability\nstats.levene(Dur_1,Dur_2,Dur_3,Dur_4) # HOV test","metadata":{"id":"pwFcDZno0slM","outputId":"75959f7a-b4b3-4f8d-a3c6-c5d9d1d8a0ab"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"stats.shapiro(Dur_1)","metadata":{"id":"5YH4sjlc0Qwq","outputId":"520f0a7b-5334-447e-d4c6-7d9ff39be29c"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"stats.shapiro(Dur_2)","metadata":{"id":"EqNombPG02XN","outputId":"e6b5ee54-99d6-4212-d3c5-eca05cf2d3e8"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"stats.shapiro(Dur_3)","metadata":{"id":"cpYrcGC-04yI","outputId":"f496746f-9aa1-45b4-bbb0-5bf071931133"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"stats.shapiro(Dur_4)","metadata":{"id":"7EmNK5pk07Yj","outputId":"585ff229-a55b-4c90-cafa-3a400ca9bd3a"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"stats.f_oneway(Dur_1,Dur_2,Dur_3,Dur_4) # ANOVA - One-way","metadata":{"id":"fHON4FoF09ZV","outputId":"9602e042-ca88-4cc6-e64f-7b3c9c4df55d"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# posthoc anova\nprint(pairwise_tukeyhsd(carpet.Durability, carpet.Carpet,alpha=0.05))","metadata":{"id":"oR71lmiJ1tec","outputId":"5377d87f-8eef-44b2-c082-4f2fcea376cf"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# one way ANOVA with filter_noise data with Filter Type as X and Noise as Y\nFilter_Noise=pd.read_csv(\"/content/drive/MyDrive/Data/DBA_lecture/Industry-data/python_data/Hypothesis_Test/FilterNoise_data.csv\")\nFilter_Noise","metadata":{"id":"gxb-euAGM7B9","outputId":"067929fb-8abe-4b5b-c61c-0bc2c6bdbbd3"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"Noise_1=Filter_Noise[Filter_Noise.TYPE==1].NOISE\nNoise_2=Filter_Noise[Filter_Noise.TYPE==2].NOISE","metadata":{"id":"iV0eJ8xrN1xE"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"stats.f_oneway(Noise_1,Noise_2) # ANOVA - One-way","metadata":{"id":"44mg4rKUOnD3","outputId":"2422e3b5-895f-49b8-e435-1abb337421cb"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"!pip install pingouin # This installation of library is for 2-way ANOVA","metadata":{"id":"22DKkZsz5KPV","outputId":"f6ef8881-5d60-4bdf-aac1-bffca7de95ad"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"import pingouin as pg # loading the library to use a method to run 2-way ANOVA","metadata":{"id":"oPYDDn285Qtr"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"df=pd.read_csv(\"/content/drive/MyDrive/Data/DBA_lecture/Industry-data/python_data/Hypothesis_Test/FilterNoise_data.csv\")\ndf.head()","metadata":{"id":"Ajd8fYFN55ew","outputId":"df5c0267-cf1a-42ab-d3fb-0ad3fe987ed8"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# Before running 2-way ANOVA, run one way ANOVA with Noise as outcome and Filter Type as X factor. \n# You will observe a P-value which suggest that Filter Type is insignifacnt\n# Now run 2-way ANOVA to see the different outcome. Filter Type becomes significant along the interaction effect\npg.anova(data=df,dv=\"NOISE\", between=[\"SIZE\", \"TYPE\"]).round(3)\n# data=dataframe, dv=Name of column in data containing the dependent variable.\n# between=If 'between' is a list with two or more elements, a N-way ANOVA is performed.\n# in the output np2=partial eta-square(effect size) ","metadata":{"id":"VPoYz-bV6lkx","outputId":"7980a6e7-74c8-4758-8789-0c93fa304043"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# proportion test\ndf=pd.read_csv(\"/content/drive/My Drive/python_data/Hypothesis_Test/QC_2.csv\")\ndf.head()","metadata":{"id":"vk2_LxUoYhcp","outputId":"9bc11b09-904f-4f9e-9ec5-adc00bc86685"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"df['Run1'].value_counts()","metadata":{"id":"yOyoqNLggbMN","outputId":"937e6d3f-8ef8-47a0-da59-a9a315573233"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"df['Run2'].value_counts()","metadata":{"id":"WrTlC5RGg3Rs","outputId":"beb2179d-015e-4040-b085-626328238cbf"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"m=df['Run1'].value_counts()\nm","metadata":{"id":"wnkm7bldhHFU","outputId":"fc64efbc-7131-4d7b-a9b6-2a9e3580c8d4"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"m[1]","metadata":{"id":"qAXXvQNVhbUv","outputId":"19b03110-f1d6-4824-c6f0-d96fe7057a1e"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# Ho:proportion=value ( One sample test)\nproportions_ztest(count=23, nobs=1000,value=.03,alternative=\"two-sided\") ","metadata":{"id":"vTKwJdvBhvUu","outputId":"423fc59b-f27d-4fbf-8513-aff9b970b025"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"proportions_ztest(count=23, nobs=1000,value=.03,alternative=\"larger\") ","metadata":{"id":"bQanaXIRh9Ta","outputId":"012af8d8-7d91-454a-83eb-f015e27cf7f9"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"proportions_ztest(count=23, nobs=1000,value=.02,alternative=\"larger\") ","metadata":{"id":"AagYKIKFiPb3","outputId":"5f1e57b3-d81c-4c5e-8d65-7ac076f6c7ff"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"proportions_ztest(count=m[1], nobs=1000,value=.02,alternative=\"larger\") ","metadata":{"id":"6EvMYETziZvo","outputId":"09d2aa27-0ef3-4cd7-e2f0-6f471333d276"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# confidence interval  calculation\np=23/(23+977) # sample proportion\nn=len(df.Run1) # sample size\n\nstats.norm.interval(alpha=0.95,                   # confidence level\n                    loc=p,                        # sample proportion\n                    scale=math.sqrt((p*(1-p)/n))) # standard error of proportion","metadata":{"id":"3O3PM47BoY8P","outputId":"3394ce14-9eee-4aee-f3d6-668f877c73f6"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# confidence interval for mean ***********\ncarpet=pd.read_csv(\"/content/drive/My Drive/python_data/Hypothesis_Test/carpet.csv\")\ncarpet.head()","metadata":{"id":"oyFvYN1oqArL","outputId":"d5cacd51-7e33-42cb-df0b-4d55a98eaa69"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"m=carpet.Durability.mean() # point estimate of mean\ns=carpet.Durability.std()  # sample standard deviation\nn=len(carpet.Durability)   # sample size\n\nstats.t.interval(alpha=0.95,           # confidence level\n                 df=n-1,               # degree of freedom\n                 loc=m,                # sample mean\n                 scale=s/math.sqrt(n)) # standard error of mean","metadata":{"id":"FyYVuJA6qWL8","outputId":"6d694f25-d814-463f-da49-be8ca65b6997"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# Chi-square test of independence\ndf=pd.read_csv(\"/content/drive/MyDrive/Data/DBA_lecture/Industry-data/python_data/Hypothesis_Test/Biscuits_Chi.csv\")\ndf.head()","metadata":{"id":"f-8FHsv9sJNR","outputId":"b1409b6c-f8e2-40fe-d70c-3a28f12403bc"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"df.tail()","metadata":{"id":"IgUmPzNgseF_","outputId":"ea8302bd-ee53-4a0a-e86e-2fb599110c7b"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"table=pd.crosstab(df.Crackers,df.Bloat) \ntable","metadata":{"id":"t6q8ERnHshDe","outputId":"8d4e0451-81c7-476b-cf15-2d051e7b75c2"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"chi2,p,dof,exp=stats.chi2_contingency(table)\nexp # expected frequency","metadata":{"id":"adZpiBuWtYGU","outputId":"d5b08edc-0279-46f4-8ad2-8da50cad37d6"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"dof\n","metadata":{"id":"712ZOppTdUHh","outputId":"268b3a1f-182f-47b1-a6d8-b58b33fbfcec"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"print(\"Chisquare=\",chi2,\"p-value=\",p)","metadata":{"id":"JEYY8mOStvu1","outputId":"676de522-08e8-4021-de83-69930d387be0"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# now run the new file taking the 'combo' out\ndf=pd.read_csv(\"/content/drive/My Drive/python_data/Hypothesis_Test/Biscuits2_Chi.csv\")\ndf.head()","metadata":{"id":"rj30fc3Tt-ZF","outputId":"8865bf80-0cf8-402d-fecc-e340010b332e"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"table=pd.crosstab(df.Crackers,df.Bloat)\ntable","metadata":{"id":"r06D6HtmuV0U","outputId":"191c2464-d6cb-4d36-e2b9-cf82145a7ece"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"chi2,p,dof,exp=stats.chi2_contingency(table)\nexp # expected frequency","metadata":{"id":"WW1n54P2ub9-","outputId":"d88f34ff-e226-4d75-e4ab-028796d71f30"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"print(\"Chisquare=\",chi2,\"p-value=\",p)","metadata":{"id":"rqouzeAKufNK","outputId":"17e67563-9621-426f-bed0-1676b0ba0364"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# Non-parametric alternative to two-sample t-test\n\ncar=pd.read_csv(\"/content/drive/MyDrive/Data/DBA_lecture/Industry-data/python_data/Hypothesis_Test/Car.csv\")\npd.options.display.max_columns=15\ncar.head()","metadata":{"id":"5OMfEzG47JNv","outputId":"84fad2eb-2d45-4441-a96b-d656c0b0fc8f"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"car.Make.unique()","metadata":{"id":"Kfv8l_vG-2uf","outputId":"da8d9349-a137-4e66-911a-ea98f8ed1fd1"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"Price_Door_2=car[car.Doors==2].Price\nPrice_Door_4=car[car.Doors==4].Price\nstats.shapiro(Price_Door_2) ","metadata":{"id":"AaTsF0zzAdKZ","outputId":"884a099e-c48e-4aa9-ba2e-13724208e831"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"stats.shapiro(Price_Door_4)","metadata":{"id":"AcZrhuvBAnCo","outputId":"a9c189e0-a216-4064-93cc-f5aa215811fb"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# stats.mannwhitneyu(Price_Door_2,Price_Door_4) #Wilcoxon rank-sum test/Mann–Whitney U test\nstats.mannwhitneyu(Price_Door_2,Price_Door_4,alternative='two-sided') #Wilcoxon rank-sum test/Mann–Whitney U test","metadata":{"id":"oQCDv7o7AqJr","outputId":"af9e21d5-ff9a-4e74-f6fb-e091d8d7babb"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# Non-parametric alternative to anova\nstats.kruskal(car[car.Make=='Buick'].Price,car[car.Make=='Cadillac'].Price,car[car.Make=='Chevrolet'].Price) # Kruskal–Wallis test ","metadata":{"id":"JPRuigNw7eIJ","outputId":"4d8db36e-9231-4e3f-a4ec-7149a01ea1d3"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"# Non-parametric alternative to Paired t-test\ndf=pd.read_csv(\"/content/drive/My Drive/python_data/Hypothesis_Test/paired_wilcoxon_testScores_fullSheet.csv\")\npd.options.display.max_columns=6\ndf.head()","metadata":{"id":"qM0-5jOOE6ai","outputId":"9bb2642c-8b40-4220-f9c8-3b79089eef21"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"stats.wilcoxon(df.Score_1,df.Score_2)  # wilcoxon signed-rank test","metadata":{"id":"6JpUDVxKH68X","outputId":"f0eb2c47-551a-4e91-80a0-7b9247a42d4c"},"execution_count":null,"outputs":[]}]}