Post on 16-Feb-2016
description
GOSSET, William Sealy 1876-1937
The t-distribution is a family of distributions varying by degrees of freedom (d.f., whered.f.=n-1). At d.f. = , but at smaller than that, the tails are fatter.
_
z = X -
X-
_
t = X -
sX-
sX = s
N
-
The t-distribution is a family of distributions varying by degrees of freedom (d.f., whered.f.=n-1). At d.f. = , but at smaller than that, the tails are fatter.
df = N - 1
Degrees of Freedom
Problem
Sample:
Mean = 54.2SD = 2.4N = 16
Do you think that this sample could have been drawn from a population with = 50?
Problem
Sample:
Mean = 54.2SD = 2.4N = 16
Do you think that this sample could have been drawn from a population with = 50?
_
t = X -
sX-
The mean for the sample of 54.2 (sd = 2.4) was significantly different from a hypothesized population mean of 50, t(15) = 7.0, p < .001.
The mean for the sample of 54.2 (sd = 2.4) was significantly reliably different from a hypothesized population mean of 50, t(15) = 7.0, p < .001.
Population
SampleA
SampleB
SampleE
SampleD
SampleC
_
XY
rXY
rXY
rXYrXY
rXY
The t distribution, at N-2 degrees of freedom, can be used to test the probability that the statistic r was drawn from a population with = 0. Table C.
H0 : XY = 0
H1 : XY 0
where
r N - 2
1 - r2
t =