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PDNN9/E4/Hs7OxWrVqdc845jRo1Svd0AADpVM7CLoqiSpUqde/evXv37ukeBADg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\nVCndI1CK7G/Y7G/Y7G/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"text/plain": [ "Plot with title “Compare groups A and B”" ] }, "metadata": { "image/png": { "height": 420, "width": 420 }, "text/plain": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "# 2 independent sample test for the mean (2-sample t-test)\n", "# \n", "# Situation: Want to see if a new drug X is more effective than the existing drug Y.\n", "# We take 2 random groups of patients willing to participate in the study.\n", "# n1 patients in group X receive the new treatment, n2 patients in group Y receive the old one.\n", "# Let X_i be the observed time in days it takes patient X_i to heal, same for Y_j.\n", "# We assume the same variance for both treatments (not guaranteed!)\n", "\n", "# 2 groups: n1 samples X_1..X_n1, n2 samples Y_1..Y_n2\n", "\n", "# Generate some data to test on\n", "\n", "n1=50\n", "n2=50\n", "sigma= 4\n", "\n", "X=rnorm(n = n1,mean = 18,sd = sigma) #new drug on average reduces healing time, but variance is large\n", "Y=rnorm(n = n2,mean = 19,sd = sigma) #sd are equal, as assumed\n", "\n", "histx <- hist(X, breaks = seq(0,40,by=1),plot=\"FALSE\") # centered at 4\n", "histy <- hist(Y, breaks = seq(0,40,by=1),plot=\"FALSE\") # centered at 6\n", "plot( histx, col=rgb(0,0,1,1/4), xlim=c(0,40), ylim=c(0,max(c(histx$counts,histy$counts))), xlab = \"Days until cured\", main = \"Compare groups A and B\") # first histogram\n", "plot( histy, col=rgb(1,0,0,1/4), xlim=c(0,40), add=T) # second\n", "\n", "#1) Research hypothesis: new drug is better than old drug (which we know is true)\n", "#H1: mu_x < mu_y -->> H0: mu_x >= mu_y\n", "\n", "#2) significance\n", "alpha=0.05\n", "\n", "#3) Compute test statistic\n", "S= sqrt( ((n1-1)*sd(X)^2+(n2-1)*sd(Y)^2)/(n1+n2-2) )\n", "T= (mean(X)-mean(Y))/S * sqrt( (n1*n2)/(n1+n2))\n", "\n", "#4) Critical region\n", "\n", "#H0 will have to be rejected if mu_x K, reject H0, accept H1, your drug is better than the old at the significance level alpha.\n", "\n", "# Show all output:\n", "\n", "paste('Pooled Variance: ',S^2, ' True Variance: ',sigma^2 )\n", "paste('T :', T, ' Critical T: ', TK)\n", "if (T