Interactive effects

Performing Experiments in Python

Luke Hayden

Instructor

Additive model

Density plot of potato production in relation to potato variety and fertilizer type (additive model)

Performing Experiments in Python

Interactive effects

Density plot of potato production in relation to potato variety and fertilizer type (interactive effect present)

In this example:

  • Fertilizer D only better for Rooster potatoes
Performing Experiments in Python

Interactive effects

Density plot of potato production in relation to potato variety and fertilizer type (interactive effect present)

In this example:

  • Fertilizer E is best for Roosters

  • Fertilizer F is best for Records

Performing Experiments in Python

Implementing ANOVA with interactive effects

import statsmodels as sm
formula = 'Production ~ Fertilizer + Variety + Fertilizer:Variety'
model = sm.api.formula.ols(formula, data=df).fit()
aov_table = sm.api.stats.anova_lm(model, typ=2)
print(aov_table)

                          sum_sq      df             F  PR(>F)
Fertilizer                           1.0                   p-value
Variety                              1.0                   p-value
Fertilizer:Variety                   1.0                   p-value
Residual                                           NaN     NaN
Performing Experiments in Python

Example 1

Density plot of potato production in relation to potato variety and fertilizer type (interactive effect present)

Performing Experiments in Python

Interactive effect

import statsmodels as sm
formula = 'Production ~ Fertilizer + Variety + Fertilizer:Variety'
model = sm.api.formula.ols(formula, data=df).fit()
aov_table = sm.api.stats.anova_lm(model, typ=2)
print(aov_table)

                          sum_sq      df             F  PR(>F)
Fertilizer          56425.833205     1.0  60222.992593     0.0
Variety             56049.056459     1.0  59820.860770     0.0
Fertilizer:Variety  55385.556078     1.0  59112.710332     0.0
Residual             3744.045584  3996.0           NaN     NaN
Performing Experiments in Python

Example 2

Density plot of potato production in relation to potato variety and fertilizer type

Performing Experiments in Python

No interactive effect

import statsmodels as sm
formula = 'Production ~ Fertilizer + Variety + Fertilizer:Variety'
model = sm.api.formula.ols(formula, data=df).fit()
aov_table = sm.api.stats.anova_lm(model, typ=2)
print(aov_table)

                          sum_sq      df             F    PR(>F)
Fertilizer          15468.395105     1.0  15172.001139  0.000000
Variety             16010.275045     1.0  15703.497977  0.000000
Fertilizer:Variety      1.464654     1.0      1.436589  0.230763
Residual             4074.064210  3996.0           NaN       NaN
Performing Experiments in Python

Beyond 2-way ANOVA

Two-way ANOVA

formula = 'Production ~ 
Fertilizer + Variety + Fertilizer:Variety'
  • 3 variables, 3 p-values
  • 2 factors, 1 interaction

Three-way ANOVA

formula = 'Production ~ Fertilizer + 
Variety + Season + Fertilizer:Variety +  
Fertilizer:Season + Variety:Season + 
Fertilizer:Variety:Season'
  • 7 variables, 7 p-values
  • 3 factors, 4 interactions
Performing Experiments in Python

Let's practice!

Performing Experiments in Python

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