Russel-Research-Method-in-Anthropology

180 Chapter 7
What we need is a distribution that is a bit more forgiving than the normal
distribution. Fortunately, just such a distribution was discovered by W. S. Gossett,
an employee of the Guiness brewery in Ireland. Writing under the pseudonym
of ‘‘Student,’’ Gossett described the distribution known as Student’s t.
It is based on a distribution that takes into account the fact that statistics calculated
on small samples vary more than do statistics calculated on large samples
and so have a bigger chance of misestimating the parameter of a continuous
variable.
The t distribution is found in appendix C. Figure 7.7 shows graphically the
-2.571 +2.571
95%
t
z
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1.96 +1.96
Figure 7.7. Variability in a t distribution and a normal distribution.
difference in the two distributions. In a normal distribution, plus or minus 1.96
sd covers 95% of all sample means. In a t-distribution, with 5 degrees of freedom,
it takes 2.571 sd to cover 95% of all sample means.
The confidence interval for small samples, using the t distribution is given
in formula 7.3:
Confidence Interval x t /2n sd Formula 7.3
where alpha (α) is the confidence interval you want. If you want to be 95%
confident, then α .05. Since half the scores fall above the mean and half
below, we divide alpha by two and get .025.