ANOVA example

One way ANOVA

#  Sipping, sipping, sipping 3 Different user ratings in different cities 
from scipy.stats import f_oneway  
a = [10,9,9,8,8,7,7,8,8,9]        
b = [10,8,9,8,7,7,7,8,9,9]  
c = [9,9,8,8,8,7,6,9,8,9]  
f,p = f_oneway(a,b,c)  
print (f)  

0.101503759398
0.903820890369

  among p The value is 0.903820890369

It cannot be considered that the factors tested have a significant impact on the observed value

Multivariate analysis of variance

# #  Sipping, sipping, sipping 2 One factor ： Environmental grade , Food grade 
from scipy import stats  
import pandas as pd  
import numpy as np  
from statsmodels.formula.api import ols  
from statsmodels.stats.anova import anova_lm  

  
environmental =  [5,5,5,5,5,4,4,4,4,4,3,3,3,3,3,2,2,2,2,2,1,1,1,1,1]       
ingredients    = [5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1]    
score      =     [5,5,4,3,2,5,4,4,3,2,4,4,3,3,2,4,3,2,2,2,3,3,3,2,1]  
  
data = {'E':environmental, 'I':ingredients, 'S':score}  
df = pd.DataFrame(data)  
df.head()

                                                

Symbolic meaning ：

• （~） Isolate dependent and independent variables ( Left dependent variable , Right argument )
• （+） Separate the arguments
• （:） Indicates the interaction of two independent variables

formula = 'S~E+I+E:I'                           
                                                 
model = ols(formula,df).fit()                   
results = anova_lm(model)                       
print (results)  

            df  sum_sq    mean_sq           F        PR(>F)
E          1.0    7.22   7.220000   54.539568  2.896351e-07
I          1.0   18.00  18.000000  135.971223  1.233581e-10
E:I        1.0    0.64   0.640000    4.834532  3.924030e-02
Residual  21.0    2.78   0.132381         NaN           NaN

explain ： E Of F value 2.896351e-07,I Of F value 1.233581e-10 Very small ,E and I Have a significant impact on the results , There is no interaction