From 23ef4221300b3bc33b55a6656ff5c08c8036b76e Mon Sep 17 00:00:00 2001 From: Vikas Rawal Date: Fri, 29 Nov 2019 09:57:37 +0530 Subject: [PATCH] Minor --- bsample2.png | 4 +-- bsample3.png | 4 +-- statistical-inference.org | 55 ++++++++++++++++++++------------------- 3 files changed, 32 insertions(+), 31 deletions(-) diff --git a/bsample2.png b/bsample2.png index 6d4b357..d5eae24 100644 --- a/bsample2.png +++ b/bsample2.png @@ -1,3 +1,3 @@ version https://git-lfs.github.com/spec/v1 -oid sha256:a2c03497f7a23fda4d406bffd38f632c3131e924857dd32fd9ca45c27f043c63 -size 175928 +oid sha256:3a1bdd5e69d2c9d15bac557524888eb11f802d48433b1ef7f786f5c99cda8319 +size 175327 diff --git a/bsample3.png b/bsample3.png index 140e3c1..f3c4bc8 100644 --- a/bsample3.png +++ b/bsample3.png @@ -1,3 +1,3 @@ version https://git-lfs.github.com/spec/v1 -oid sha256:29117e9a332272abc02bdfc69c1829a6a01609809e3d79d8f9abe69da2de1162 -size 114841 +oid sha256:1b72b0d1f379e06273c79daaa9dadabd77f66f145862c82a9268011c6d22443c +size 114764 diff --git a/statistical-inference.org b/statistical-inference.org index 11d93d0..3bdc225 100644 --- a/statistical-inference.org +++ b/statistical-inference.org @@ -49,7 +49,7 @@ paste("Sample size 5: mean = ", round(mean(t1$meancol)), "; stdev = ", - round(sqrt(var(t1$meancol))),sep="")->lab + round(sd(t1$meancol)),sep="")->lab p+annotate("text",x=450,y=0.030,label=lab,colour="blue")->p p @@ -67,7 +67,7 @@ paste("Sample size 20: mean = ", round(mean(t0$meancol)), "; stdev = ", - round(sqrt(var(t0$meancol))),sep="")->lab + round(sd(t0$meancol)),sep="")->lab p+annotate("text",x=450,y=0.033,label=lab,colour="darkolivegreen")->p p @@ -85,7 +85,7 @@ paste("Sample size 50: mean = ", round(mean(t$meancol)), "; stdev = ", - round(sqrt(var(t$meancol))),sep="")->lab + round(sd(t$meancol)),sep="")->lab p+annotate("text",x=450,y=0.036,label=lab,colour="red")->p p @@ -103,7 +103,7 @@ paste("Sample size 200: mean = ", round(mean(t4$meancol)), "; stdev = ", - round(sqrt(var(t4$meancol))),sep="")->lab + round(sd(t4$meancol)),sep="")->lab p+annotate("text",x=450,y=0.039,label=lab,colour="pink")->p p #+end_src @@ -113,13 +113,14 @@ + $Standard.error = \frac{\sigma}{\sqrt{mean}}$ - -| Standard deviation of population ($\sigma$) | 130 | -| Standard errors of samples of size | | -| 5 | 58 | -| 20 | 29 | -| 50 | 18 | -| 200 | 9 | +| Variable | Value | +|---------------------------------------------+-------| +| Standard deviation of population ($\sigma$) | 130 | +| Standard errors of samples of size | | +| 5 | 58 | +| 20 | 29 | +| 50 | 18 | +| 200 | 9 | @@ -140,7 +141,7 @@ library(ggplot2) worker->t9 - (t9$wage-mean(t9$wage))/sqrt(var(t9$wage))->t9$wage + (t9$wage-mean(t9$wage))/sd(t9$wage)->t9$wage ggplot(t9,aes(wage))+geom_density(colour="black",size=1)->p p+scale_y_continuous(limits=c(0,0.75))->p p+scale_x_continuous(limits=c(-15,15) @@ -159,7 +160,7 @@ c(t1,mean(s1$wage))->t1 } - data.frame(sno=c(1:10000),meancol=(t1-mean(worker$wage))/sqrt(var(t1)))->t1 + data.frame(sno=c(1:10000),meancol=(t1-mean(worker$wage))/sd(t1))->t1 p+geom_density(data=t1,aes(meancol),colour="blue",size=1)-> p p @@ -172,7 +173,7 @@ c(t0,mean(s1$wage))->t0 } - data.frame(sno=c(1:10000),meancol=(t0-mean(worker$wage))/sqrt(var(t0)))->t0 + data.frame(sno=c(1:10000),meancol=(t0-mean(worker$wage))/sd(t0))->t0 p+geom_density(data=t0,aes(meancol),colour="darkolivegreen",size=1)-> p p @@ -185,7 +186,7 @@ c(t,mean(s1$wage))->t } - data.frame(sno=c(1:10000),meancol=(t-mean(worker$wage))/sqrt(var(t)))->t + data.frame(sno=c(1:10000),meancol=(t-mean(worker$wage))/sd(t))->t p+geom_density(data=t,aes(meancol),colour="red",size=1)-> p p @@ -198,7 +199,7 @@ c(t4,mean(s1$wage))->t4 } - data.frame(sno=c(1:10000),meancol=(t4-mean(worker$wage))/sqrt(var(t4)))->t4 + data.frame(sno=c(1:10000),meancol=(t4-mean(worker$wage))/sd(t4))->t4 p+geom_density(data=t4,aes(meancol),colour="pink",size=1)-> p p #+end_src @@ -220,7 +221,7 @@ worker[sex!=3,]->worker worker->t9 - (t9$wage-mean(t9$wage))/sqrt(var(t9$wage))->t9$wage + (t9$wage-mean(t9$wage))/sd(t9$wage)->t9$wage ggplot(t9,aes(wage))+geom_density(colour="black",size=1)->p p+scale_y_continuous(limits=c(0,0.75))->p p+scale_x_continuous(limits=c(-15,15) @@ -236,19 +237,19 @@ rbind(t4,data.frame( sno=i, meancol=mean(s1$wage), - sterr=sqrt(var(s1$wage))/sqrt(samplesize) + sterr=sd(s1$wage)/sqrt(samplesize) ) )->t4 } (t4$meancol)/t4$sterr->t4$teststat - (t4$meancol)/sqrt(var(t4$meancol))->t4$teststat2 + (t4$meancol)/sd(t4$meancol)->t4$teststat2 data.frame(modelt=rt(200000,samplesize-1,ncp=mean(t4$teststat)),modelnorm=rnorm(200000,mean=mean(t4$teststat2)))->m - var(t4$teststat) - var(m$modelt) - var(m$modelnorm) - var(t4$teststat2) + sd(t4$teststat) + sd(m$modelt) + sd(m$modelnorm) + sd(t4$teststat2) mean(t4$teststat) mean(m$modelt) mean(m$modelnorm) @@ -260,18 +261,18 @@ p+geom_density(data=t4,aes(teststat),colour="blue",size=1)-> p p+geom_density(data=m,aes(modelt),colour="darkolivegreen",size=1)->p p+annotate("text",x=-30,y=0.42, - label=paste("Normal distribution, with standard deviation",round(sqrt(var(m$modelnorm)),2)), + label=paste("Normal distribution, with standard deviation",round(sd(m$modelnorm),2)), colour="black",hjust=0)->p p+annotate("text",x=-30,y=0.40, label=paste("Statistic with known population variance, standard error =", - round(sqrt(var(t4$teststat2)),2)), + round(sd(t4$teststat2),2)), colour="red",hjust=0)->p p+annotate("text",x=-30,y=0.38, - label=paste("t distribution, with standard deviation =",round(sqrt(var(m$modelt)),2)), + label=paste("t distribution, with standard deviation =",round(sd(m$modelt),2)), colour="darkolivegreen",hjust=0)->p p+annotate("text",x=-30,y=0.36, label=paste("Statistic with unknown population variance, standard error =", - round(sqrt(var(t4$teststat)),2)), + round(sd(t4$teststat),2)), colour="blue",hjust=0)->p p+scale_x_continuous(limits=c(-30,30))+theme_bw()->p p