gosset, william sealy 1876-1937
DESCRIPTION
GOSSET, William Sealy 1876-1937. The t-distribution is a family of distributions varying by degrees of freedom ( d.f. , where d.f. = n -1). At d.f. = , but at smaller than that, the tails are fatter. X - . X - . _. _. z = . t = . -. -. X. s X. s. -. s X = . N. - PowerPoint PPT PresentationTRANSCRIPT
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GOSSET, William Sealy 1876-1937
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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.
![Page 3: GOSSET, William Sealy 1876-1937](https://reader033.vdocuments.net/reader033/viewer/2022051002/56815f3e550346895dce1296/html5/thumbnails/3.jpg)
_
z = X -
X-
_
t = X -
sX-
sX = s
N
-
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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.
![Page 5: GOSSET, William Sealy 1876-1937](https://reader033.vdocuments.net/reader033/viewer/2022051002/56815f3e550346895dce1296/html5/thumbnails/5.jpg)
df = N - 1
Degrees of Freedom
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Problem
Sample:
Mean = 54.2SD = 2.4N = 16
Do you think that this sample could have been drawn from a population with = 50?
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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-
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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.
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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.
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Population
SampleA
SampleB
SampleE
SampleD
SampleC
_
XY
rXY
rXY
rXYrXY
rXY
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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 =