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+In [20]:
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+import pandas as pd
+import numpy as np
+from scipy.stats import chi2
+from scipy.optimize import minimize
+from scipy.stats import norm
+from plotnine import *
+
+chickens=pd.read_table("chickwts.txt", delimiter=",")
+
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+In [21]:
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+means=dict()
+
+for i in np.unique(chickens.feed):
+ means[i]=np.mean(chickens[chickens.feed == i][["weight"]])[0]
+
+means_df=pd.DataFrame(means, index =[0])
+means_df
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+Out[21]:
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+In [22]:
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+ggplot(chickens, aes(x="feed",y="weight")) + geom_boxplot() + theme_classic()
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+Out[22]:
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+4. Test Null and alternative hypotheses using chi-2 likelihood test¶
Create a data "sun_soy_chickens" containing only data of interest (chickens fed on soybean or sunflower feed). Add a column "Factor" to this new data frame, containing a 1 for chickens fed with sunflower feed, and a 0 for chickens fed with soybean feed.¶
+
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+In [23]:
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+sun_soy_chickens=chickens[(chickens.feed == "sunflower") | (chickens.feed == "soybean")]
+
+sun_soy_chickens["Factor"]=0
+for i in range(0, len(sun_soy_chickens.feed)):
+ if sun_soy_chickens.feed.iloc[i] == "sunflower":
+ sun_soy_chickens.iloc[i,2]=1
+ else:
+ sun_soy_chickens.iloc[i,2]=0
+
+sun_soy_chickens
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+Define null and alternative hypothesis functions¶
+
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+In [24]:
+
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+def nllalt(p,obs):
+ B0=p[0]
+ sigma=p[1]
+ B1=p[2]
+
+ expected=B0+B1*obs.Factor
+ nll=-1*norm(expected,sigma).logpdf(obs.weight).sum()
+ return nll
+
+
+def nllnull(p,obs):
+ B0=p[0]
+ sigma=p[1]
+
+ expected=B0
+ nll=-1*norm(expected,sigma).logpdf(obs.weight).sum()
+ return nll
+
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+
+Make guess, use minimize function to find optimal coefficients for alternative and null hypothesis functions. T test to determine the significance of the factor (presence of sunflower seed) in determining the weight of chickens in this study¶
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+In [25]:
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+
+guess=[1,1,1]
+
+fit_alt=minimize(nllalt, guess, method="Nelder-Mead", options={'disp': True},args=sun_soy_chickens)
+fit_null=minimize(nllnull, guess, method="Nelder-Mead", options={'disp': True},args=sun_soy_chickens)
+
+D=2*(fit_null.fun-fit_alt.fun)
+1-chi2.cdf(x=D, df=1)
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+Out[25]:
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