Tables of the normal and t-distribution

(PDF)	Table of normal and \(t\)-distributions

<rst> <rst-options: 'toc' = False/> <rst-options: 'reset-figures' = False/>

The table is `available here for download <http://learnche.mcmaster.ca/wiki_4C3/images/a/aa/Statistical-tables.pdf>`_. **You are responsible for printing it out and bringing a copy to the final exam.**

If you are interested, the source code used to generate the *normal distribution* section:

.. code-block:: s

q <- c(seq(-3.0, -2.0, 0.25), c(-1.8, -1.5, -1.0, -0.5, 0, 0.5, 1.0, 1.5, 1.8), seq(2.0, 3.0, 0.25)) cumulative.quantile = pnorm(q)

p <- c(0.001, 0.0025, 0.005, 0.010, 0.025, 0.05, 0.075, 0.10, 0.3, 0.5, 0.7, 0.9, 0.925, 0.950, 0.975, 0.99, 0.995, 0.9975, 0.999) cumulative.probability = qnorm(p)

bitmap('pnorm-and-qnorm.png', type="png256", width=16, height=7, res=300, pointsize=14) layout(matrix(c(1,2), 1, 2)) par(mar=c(4.2, 4.2, 0.2, 1)) plot(q, cumulative.quantile, type="b", main="", xlab="z", ylab="q = cumulative area under the normal distribution", cex.lab=1.4, cex.main=1.8, lwd=4, cex.sub=1.8, cex.axis=1.8, ylim=c(0, 1)) grid(col="gray30") a1 = -0.6 arrows(a1, y=-0.2, x1=a1, y1=pnorm(a1), code=0, lwd=2) arrows(a1, y=pnorm(a1), x1=-3, y1=pnorm(a1), code=2, lwd=2) text(-2, pnorm(a1)+0.05, "pnorm(z)", cex=1.5)

plot(cumulative.probability, p, type="b", main="", xlab="z", ylab="q = cumulative area under the normal distribution", cex.lab=1.4, cex.main=1.8, lwd=4, cex.sub=1.8, cex.axis=1.8, ylim=c(0, 1)) grid(col="gray30") a1 = qnorm(0.65) arrows(a1, y=0, x1=a1, y1=pnorm(a1), code=1, lwd=2) arrows(a1, y=pnorm(a1), x1=-5, y1=pnorm(a1), code=0, lwd=2) text(-2, pnorm(a1)+0.05, "qnorm(q)", cex=1.5) dev.off()

And the source code used to generate the *t-distribution* section:

.. code-block:: s

   dof <- c(1, 2, 3, 4, 5, 10, 15, 20, 30, 60, Inf)
   tail.area.oneside <- c(0.4, 0.25, 0.1, 0.05, 0.025, 0.01, 0.005)

   n.dof <- length(dof)
   n.tails <- length(tail.area.oneside)

   values <- matrix(0, nrow=n.dof, ncol=n.tails)
   k=0
   for (entry in tail.area.oneside){
       k=k+1
       values[,k] <- abs(qt(entry, dof))
   }
   round(values,3)

   library(RSvgDevice)
   devSVG("t-distribution-raw.svg", width=10, height=10)
   par(mar=c(4.2, 4.2, 0.2, 1))  
   z <- seq(-5, 5, 0.01)
   probabilty <- dt(z, df=5)
   plot(z, probabilty, type="l", main="", xlab="z", ylab="Probabilities from the t-distribution", 
       cex.lab=1.4, cex.main=1.8, lwd=4, cex.sub=1.8, cex.axis=1.8)
   abline(h=0)
   z=1.5
   abline(v=z)
   abline(v=0)
   dev.off()

The resulting :math:`t`-distribution figure was enhanced in `Inkscape <http://inkscape.org/>`_ to add the shaded area. </rst>