MGMT650  Statistics for Managerial Decision
Making
Week 5 Lecture
The Normal Distribution
Hey, I thought this week's lecture was about sampling?
It is!
But one very important concept that we need to cover on our way to talking about
why we can draw conclusions about a population based on our study of only a sample is
the normal distribution.
It is, as they say, statistics' raison d'etre (reason for being).
Recall that social scientists are concerned with finding a sample that will represent the
population, so that the research results will be generalizable to the population. One tool
for making such generalizations is
the normal distribution
, or,
the normal curve
. There
are certain features of the normal curve that you must simply accept as "true" if you are to
use the normal curve to your benefit. The normal curve can be of tremendous assistance
in understanding human behavior, if you are willing to accept a few basic "givens," listed
below.
The givens:
1.
It is assumed that most variables are "normally distributed" in the population. Thus, if
you collect enough data points (have a large enough sample), your participants' scores on
your variable will form a normal curve also. For instance, let's consider the variable, "Self
esteem." In the population, there are people who have high self esteem, people who have
low self esteem, and lots of people in between. If you conduct a study that includes the
variable "self esteem" and your sample size is adequate, the same features will emerge
among your sample participants  some will be high, a few will be low, and the largest
proportion will be somewhere near the middle.
Note:
Not all variables are normally
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distributed in the population, but most are. We will later learn how to deal with those that
are not.
2.
It is assumed that, when a variable (like "self esteem") is normally distributed in the
population, the bulk of the population will score at or about the mean, and very few will
score "really high" or ”low" on the variable.
In fact, the normal curve stipulates that
about 68% of the population will score very near the mean.
That leaves 32% who
score somewhere away from the mean (68% + 32 % = 100% of the population). The
useful fact about the normal curve is that both sides of the curve are mirror images of
each other. Thus, we know there will be equal numbers of”high" and”low" scores.
Whatever happens above the mean will also happen below the mean.
Thus, if you cut 32% in half (half for the high scores and half for the low scores), that
means 16% of the population will score moderately high (a bit above the mean) and 16%
will score moderately low (a bit below the mean).
3
.
The normal curve is meant to be a tool for understanding which percentage of the
population will score at the mean, below the mean, and above the mean, because it is
assumed that if a sample's scores form a normal curve, so will the population's scores.
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 Fall '14

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