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Introduction to Inferential Statistics
Statistics is based on observations of large data sets. In this reading we will
make some observations on large data sets and then apply them to small data
sets (samples).
DISTRIBUTION CURVE FOR LARGE DATA SETS
a. Earlier we saw that the mathematical equation for a normal distribution
curve is
y
=
e
"
(
x
i
"
μ
)
2
/ 2
#
2
$
Equation 1
b. The equation for the normal distribution curve can be simplified by
introducing a new variable, z.
z
=
x
i
"
Equation 2
making:
y
=
e
"
z
2
/ 2
Equation 3
c. Figure 1 shows that the introduction of z also changes the normal
distribution curve to the
standard
normal distribution curve in which the x
axis is given in zscores or distances from the mean (which is now 0) in
standard deviation units.
Figure 1. Standard normal distribution curve. Eeling, D.L., Introduction to
the normal distribution,
http://www.comfsm.fm/%7Edleeling/statistics/notes007.html
, accessed
6/5/10.
d. Integration of the equation for the standard normal distribution curve
between limits of any two zscores makes it possible to determine the area
under the total curve and the area under any portion of the curve. The
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View Full Documentratio of these areas is then the probability of x being within that span. The
percent probabilities are referred to as l
evels of confidence
. Figure 2
shows those probabilities.
Figure 2. Fractional probabilities between z values on a standard normal
distribution curve.
Eeling, D.L., Introduction to the normal distribution,
http://www.comfsm.fm/%7Edleeling/statistics/notes007.html
, accessed 6/5/10.
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 Summer '11
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