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Chapter 6
The Normal Curve and
Sampling Error
Difference between SD & SE?
SD is the sum of the squared deviations
from the mean.
SE is the amount of ERROR in the
estimate of the population based on the
sample.
Need for Standard Scores
In the Olympics the last place finishers are
all superior to non-Olympic athletes.
How good is a 4 m long jump in high
school?
Given mean = 5, we know that 4 m was
below the mean.
More than 95% of scores fall between ± 2 SD
Z of 1.96 is the 95% value
Z Scores
Computing Confidence Intervals
Area
Under
Normal
Curve
Z = 1.96
is 95%
level.
2.5% in
each tail.
50 - 2.5 =
47.50
T Score
Skewed Distribution
Interpretation of Skew
Skew is acceptable
as long as the Z score
is less than 2.0 [p 89]
Interpretation of Kurtosis
Kurtosis is
acceptable as
long as the Z
score is less
than 2.0 [p 89]
SPSS Interpretation of Skew
From Table 6.2 p 87
Statistics
Skew_Kurt
N
Valid
Mis sing
Mean
Std. Error of Mean
Std. Deviation
Skewness
Std. Error of Skewnes s
Kurtos is
Std. Error of Kurtos is
12
0
3.6667
.35533
1.23091
-.988
.637
.649
1.232
A skew that is more than twice it’s SE is taken as a
departure from symmetry.
In this case the Skew of -.988 is not greater than
2 * .637 = 1.274
See p 287 of SPSS Base Manual
Confidence Intervals
Using SE for Confidence Interval
Computing Confidence Intervals