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Author: Morgan Micallef
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Compute Environment: Ubuntu 20.04 (Default)
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%matplotlib inline import numpy as np import seaborn as sns import matplotlib.pyplot as plt import pandas as pd
1. Covid Data


2. perform Chi Squared Test, null hypothesis is that both groups come from the same populations (i.e. vaccine has no effect) Results come back statistically insignificant but we know that that is not true, we need to measure the size of the effect
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Code Appendix
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#2 data=([8, 162],[18190, 18163]) df1 = pd.DataFrame(data, columns = ['Drug', 'Placebo'], index=['Infected', 'Not Infected']) df1
Drug Placebo
Infected 8 162
Not Infected 18190 18163
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#observed chi squared inf=[8, 162] notinf= [18190, 18163] covid=[inf,notinf] covidarr=np.array(covid) a=covidarr[0,0] b=covidarr[0,1] c=covidarr[1,0] d=covidarr[1,1] N=a+b+c+d DI=((a+b)/N)*(a+c) PI=((a+b)/N)*(b+d) DN=((c+d)/N)*(a+c) PN=((c+d)/N)*(b+d) ochisquared=(((a-DI)**2)/DI)+(((b-PI)**2)/PI)+(((c-DN)**2)/DN)+(((d-PN)**2)/PN) ochisquared
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#simulated chi squared result=[] drug=['d infected']*8+['d not infected']*18190 placebo=['p infected']*162+['p not infected']*18163 covidzeros=np.zeros([2,2]) for i in range(10000): drand=np.random.choice(drug, 18198) dinfected = drand == ['d infected'] dnot = drand == ['d not infected'] covidzeros[0,0]=np.sum(dinfected) covidzeros[1,0]=np.sum(dnot) prand=np.random.choice(placebo, 18163) pinfected = prand == ['p infected'] pnot = prand == ['p not infected'] covidzeros[0,1]=np.sum(pinfected) covidzeros[1,1]=np.sum(pnot) a=covidzeros[0,0] b=covidzeros[0,1] c=covidzeros[1,0] d=covidzeros[1,1] N=a+b+c+d DI=((a+b)/N)*(a+c) PI=((a+b)/N)*(b+d) DN=((c+d)/N)*(a+c) PN=((c+d)/N)*(b+d) chisquared=(((a-DI)**2)/DI)+(((b-PI)**2)/PI)+(((c-DN)**2)/DN)+(((d-PN)**2)/PN) result.append(chisquared)
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graph=sns.histplot(results) graph.axvline(ochisquared, color="red") count=results>=ochisquared p=np.sum(count=='True') p/10000
<ipython-input-43-45ee63c034bc>:4: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison p=np.sum(count=='True')
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