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+Performing likelihood ratio test to find out if there is difference in weight when chicken is fed soybean vs. sunflower¶
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+The dataset in “chickwts.txt” has columns as chick weights and feed type¶
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+In [24]:
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+import numpy
+import os
+import pandas
+import plotnine
+from plotnine import *
+import scipy
+from scipy.optimize import minimize
+from scipy.stats import norm
+from scipy.stats import chi2
+from plotnine import *
+os.listdir('.')
+os.chdir('/Users/sampathkumarbalaji/EX_12/Intro_Biocom_ND_319_Tutorial12')
+chick_weights = pandas.read_csv("chickwts.txt")
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+And the dataset with columns being weight and feed looks like:¶
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+In [4]:
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+print (chick_weights)
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+The plot looks like:¶
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+In [22]:
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+ggplot(chick_weights,aes(x="weight",y="feed"))+geom_point(aes(x="weight",y="feed"))
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+Out[22]:
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+The question is to find if there is difference in weight of the chicken when they are fed soybean vs. sunflower feed. Null Hypothesis: "The weight remains the same (no difference)", Alternate hypothesis: "Yes the weights differ based off the feed type".¶
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+In [32]:
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+Sun_Soy_feed_DS = chick_weights.query('feed == "sunflower" or feed == "soybean"')
+Sun_Soy_feed_DS['x'] = [0 if feedtype == 'sunflower' else 1 for feedtype in Sun_Soy_feed_DS.feed]
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+Defining the null and alternate hypotheses functions¶
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+In [25]:
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+def null_hyp(p,obs):
+ B0=p[0]
+ sigma=p[1]
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+ expected=B0
+ nll= -1*norm(expected,sigma).logpdf(obs.weight).sum()
+ return nll
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+def alt_hyp(p,obs):
+ B0=p[0]
+ B1=p[1]
+ sigma=p[2]
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+ expected=B0+B1*obs.x
+ nll=-1*norm(expected,sigma).logpdf(obs.weight).sum()
+ return nll
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+In [27]:
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+initialGuess_null_hyp=numpy.array([1,1])
+initialGuess_alt_hyp=numpy.array([1,1,1])
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+Minimize functions for null and alt hyp¶
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+In [28]:
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+fitnull=minimize(null_hyp,initialGuess_null_hyp,method="Nelder-Mead",options={'disp': True},args=Sun_Soy_feed_DS)
+fitalt=minimize(alt_hyp,initialGuess_alt_hyp,method="Nelder-Mead",options={'disp': True},args=Sun_Soy_feed_DS)
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+Chi squared calculations and finding the p-value:¶
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+In [29]:
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+1-scipy.stats.chi2.cdf(x=-2*(fitalt.fun-fitnull.fun),df=1)
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+Out[29]:
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+Since the p-value is small (< 0.05), it means that the null hypothesis of there is no difference in weight gained based off the feedtype can be rejected.
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