自定义双因素方差分析

####双因素方差分析，可进行有交互作用与无交互作用    
def f_twoway(df_c,col_fac1,col_fac2,col_sta,interaction=False):
    df=df_c.copy()
    list_fac1=df[col_fac1].unique()
    list_fac2=df[col_fac2].unique()
    r=len(list_fac1)
    s=len(list_fac2)
    x_bar=df[col_sta].mean()
    list_Qa=[]
    list_Qb=[]
    for i in list_fac1:
        series_i=df[df[col_fac1]==i][col_sta]
        xi_bar=series_i.mean()
        list_Qa.append((xi_bar-x_bar)**2)
    for j in list_fac2:
        series_j=df[df[col_fac2]==j][col_sta]
        xj_bar=series_j.mean()
        list_Qb.append((xj_bar-x_bar)**2)
    Q=((df[col_sta]-x_bar)**2).sum()
    df_res=pd.DataFrame(columns=['方差来源','平方和','自由度','均方','F值','Sig.'])
    if interaction==False:
        Qa=s*sum(list_Qa)
        Qb=r*sum(list_Qb)
        Qw=Q-Qa-Qb
        Sa=Qa/(r-1)
        Sb=Qb/(s-1)
        Sw=Qw/((r-1)*(s-1))
        sig1=stats.f.sf(Sa/Sw,r-1,(r-1)*(s-1))
        sig2=stats.f.sf(Sb/Sw,s-1,(r-1)*(s-1))
        df_res['方差来源']=[col_fac1,col_fac2,'误差','总和']
        df_res['平方和']=[Qa,Qb,Qw,Q]
        df_res['自由度']=[r-1,s-1,(r-1)*(s-1),r*s-1]
        df_res['均方']=[Sa,Sb,Sw,'-']
        df_res['F值']=[Sa/Sw,Sb/Sw,'-','-']
        df_res['Sig.']=[sig1,sig2,'-','-']
        return df_res
    elif interaction==True:
        list_Qw=[]
        t=len(df[(df[col_fac1]==list_fac1[0]) & (df[col_fac2]==list_fac2[0])])
        for i in list_fac1:
            for j in list_fac2:
                series_ij=df[(df[col_fac1]==i) & (df[col_fac2]==j)][col_sta]
                list_Qw.append(((series_ij-series_ij.mean())**2).sum())
        Qa=s*t*sum(list_Qa)
        Qb=r*t*sum(list_Qb)
        Qw=sum(list_Qw)
        Qab=Q-Qa-Qb-Qw
        Sa=Qa/(r-1)
        Sb=Qb/(s-1)
        Sab=Qab/((r-1)*(s-1))
        Sw=Qw/(r*s*(t-1))
        sig1=stats.f.sf(Sa/Sw,r-1,r*s*(t-1))
        sig2=stats.f.sf(Sb/Sw,s-1,r*s*(t-1))
        sig3=stats.f.sf(Sab/Sw,(r-1)*(s-1),r*s*(t-1))
        df_res['方差来源']=[col_fac1,col_fac2,col_fac1+'*'+col_fac2,'误差','总和']
        df_res['平方和']=[Qa,Qb,Qab,Qw,Q]
        df_res['自由度']=[r-1,s-1,(r-1)*(s-1),r*s*(t-1),r*s*t-1]
        df_res['均方']=[Sa,Sb,Sab,Sw,'-']
        df_res['F值']=[Sa/Sw,Sb/Sw,Sab/Sw,'-','-']
        df_res['Sig.']=[sig1,sig2,sig3,'-','-']
        return df_res
    else:
        return 'interaction参数错误'

实例测试：

dic_t3=[{'燃料':'A1','推进器':'B1','射程':58.2},{'燃料':'A1','推进器':'B1','射程':52.6},
       {'燃料':'A1','推进器':'B2','射程':56.2},{'燃料':'A1','推进器':'B2','射程':41.2},
       {'燃料':'A1','推进器':'B3','射程':65.3},{'燃料':'A1','推进器':'B3','射程':60.8},
       {'燃料':'A2','推进器':'B1','射程':49.1},{'燃料':'A2','推进器':'B1','射程':42.8},
       {'燃料':'A2','推进器':'B2','射程':54.1},{'燃料':'A2','推进器':'B2','射程':50.5},
       {'燃料':'A2','推进器':'B3','射程':51.6},{'燃料':'A2','推进器':'B3','射程':48.4},
       {'燃料':'A3','推进器':'B1','射程':60.1},{'燃料':'A3','推进器':'B1','射程':58.3},
       {'燃料':'A3','推进器':'B2','射程':70.9},{'燃料':'A3','推进器':'B2','射程':73.2},
       {'燃料':'A3','推进器':'B3','射程':39.2},{'燃料':'A3','推进器':'B3','射程':40.7},
       {'燃料':'A4','推进器':'B1','射程':75.8},{'燃料':'A4','推进器':'B1','射程':71.5},
       {'燃料':'A4','推进器':'B2','射程':58.2},{'燃料':'A4','推进器':'B2','射程':51.0},
       {'燃料':'A4','推进器':'B3','射程':48.7},{'燃料':'A4','推进器':'B3','射程':41.4},]
df_t3=pd.DataFrame(dic_t3,columns=['燃料','推进器','射程'])
f_twoway(df_t3,'燃料','推进器','射程',interaction=True)

结果：