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

• 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

p 45

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):

MSD=143.54

nXX

nd

ii

22

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):

= 11.98

• 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

nXX

MSDRMSD i

2

• Standard deviation S or SX

= 12.01 (3.6)

• n-1 is known as the degrees of freedom in calculating SX

Univariate Statistics: Dispersion

1

2

n

XXs iX