Download Chapter 3.a

AAEC 4302
ADVANCED
STATISTICAL METHODS IN
AGRICULTURAL RESEARCH
Descriptive Statistics: Chapter 3
Univariate Statistics of Central Tendency
• There are three alternative statistics (i.e.
formulas) to measure the central tendency of
a variable:
* The Mean
* The Median
* The Mode
Univariate Statistics of Central Tendency
• For example, if the 15 smallest deer weights
are ignored; the mean increases from 61.77
Kg to 64.0 Kg while the median only goes
from 64 Kg to 65Kg
• The mode may be a useful statistic in the
case of a discrete variable, but not for
continuous variables because each
observation value is likely to be unique
Univariate Statistics of Dispersion
p 45
• The range is a measure of dispersion given by the
difference between the greatest and the smallest
value of X in the n observations available
Univariate Statistics: Dispersion
The mean absolute deviation (MAD),
MAD in deer weight = 9.00 Kg;
max absolute deer weight deviation is
93 Kg - 61.77 Kg = 31.23 Kg
min absolute deer weight deviation is
32 Kg – 61.77 Kg = -29.77 Kg
Univariate Statistics: Dispersion
• An alternative way to address the
canceling out problem is by squaring the
deviations from the mean to obtain the
mean squared deviation (MSD):
 di
2
n

MSD=143.54

X  X 
2
i
n
Univariate Statistics: Dispersion
• Problem of squaring can be solved by taking
the square root of the MSD to obtain the root
mean squared deviation (RMSD):
RMSD  MSD 

X  X 
2
i
= 11.98
n
• When calculating the RMSD, the squaring of
the deviations gives a greater importance to
the deviations that are larger in absolute value,
which may or may not be desirable
Univariate Statistics: Dispersion
• Standard deviation S or SX
sX 
 X
X
2
i
n  1
= 12.01
(3.6)
• n-1 is known as the degrees of freedom
in calculating SX