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A DAY AT THE OFFICE
Mary is very short
What makes you say that she is short?
Meet Mary. She
is 12 years old.
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Mary’s peers
You think Mary should be like
everybody else.
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Mary’s peers
You compare Mary with everybody else
Is Mary’s height and ”everybody else’s”height all you know in order to make aconclusion?
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Mary’s peers
NO, you also have an idea in your mind that
Mary’s height is farther away fromeverybody else than random variation
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Mary’s peers
You make an estimate that Mary is
more different than randomvariation should account for
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Formula:
Mary’s height
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Formula:
Mary’s height - Everybody else’s height
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Formula:
Mary’s height – Everybody else’s height
Random variation
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A high figure leads you to think thatMary can not be like everybody else
You start looking for a specific «reason»
for her low height, maybe a medicalcondition.
Mary’s height - Everybody else’s height
Random variation
Formula:
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Girls with Turner’s syndrome
Mary is not like everybody else. but she is like everybody else if you only comparewith other girls with Turner’s syndrome
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Girls with Turner’s syndrome
Mary is not like everybody else, but she is like everybody else if you only comparewith other girls with Turner’s syndrome
Mary’s height- Everybody else’s height
Random variation
for girls with Turner’s syndrome
for girls with Turner’s syndrome
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Important!!!
THIS IS BASICALLY ALL THERE IS TO
STATISTICAL TESTINGREMEMBER, you do it every day just by«eye-balling»
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Formula:
Mary’s height – Everybody else’s height
Random variation
This measurement carries few difficulties
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Formula:
135 cm - Everybody else’s height
Random variation
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Formula:
135 cm - Everybody else’s height
Random variation
What is everybody else’s height?
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Formula:
ModeThe value occurring most often
Median
The middle value when all values are rankedMean
Sum of all values divided by number of values
!x/N = µ
Measures of centrality:
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Formula:
If Mary’s peers are a statistical”population” of 10 twelve-year olds :
Measures of centrality:
10
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Formula:
135 cm - 154 cm
Random variation
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Formula:
135 cm - 154 cm
Random variation
What is random variation?
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Formula:
Difference between highest andlowest value: 162 cm - 147 cm =15 cm
#his is called RANGE
Utilizes only a small part of the
available information
Measures of spread:147
151
151
152
153
154
155
156
159
162
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Formula:
Mean distance from the mean Measures of spread:
What is the value of this mathematical expression?
"( x #µ )
N
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Formula:
Mean distance from the mean: Measures of spread:
"( x #µ )
N =
0
10= 0
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Formula:
Mean distance from the mean: Measures of spread:
Is it possible to ignore the sign?
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Formula:
Absolute mean distance from themean:
Measures of spread:
" | ( x #µ ) |
N =
32
10= 3,2
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Formula:
Mean distance from the mean: Measures of spread:
Is there another way of getting rid ofthe sign?
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Formula:
Mean squared distance from themean:
Measures of spread:
This is called:
VARIANCE
"( x #µ )2
N =
166
10=16.6
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Formula:
Variance is in this case expressed in cm2
This is not very practical when the meanheight is expressed as cm
Measures of spread:
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Formula:
Square root of the mean squareddistance from the mean:
Measures of spread:
This is called:
STANDARD DEVIATION
"( x #µ )2
N =16.6
"( x #µ )2
N = 4.1
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Formula:
Measures of spread:
The STANDARD DEVIATION
carries the symbol
This is the measure of spread in a population
"( x #µ )2
N
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Formula:
135 cm - 154 cm
4.1 cm
Mary’s height is four and a half times furtheraway from the mean than the standarddeviation (random variation)
This value is called z
- 4.63SO WHAT??
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Normal curve:
Histogram of the height of Mary’s peers
Most of the girls fall in the middle, a few further out.
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Normal curve:
Histogram of the height of Mary’s peers
Most of the girls fall in the middle, a few further out.
-2 +2
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Normal curve:
68.3%
95.4%
99.7%
-3 +3
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Normal curve:
68.3%
95.4%
99.7%
-3 +3
The exact probability of
any number of standard deviations
from the mean can be calculated
and are given in statistical tables or in your
computer’s statistical packages.
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Normal curve:
Histogram of the height of all Mary’s peersand Mary
Most of the girls fall in the middle, a few further out.Mary is way out there: The statistics agree with ourprevious «eye-balling»
-2 +2
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Yes, the principlesof statistical testing
arenot more than this.
Was that all?
