ASYMMETRY MEASURES AND POINTING

ASYMMETRY MEASURES AND POINTING

1. The objective of these measures is to determine, without need to draw the frequency distribution, the horizontal warping of variable values analyzed with respect to a central value (Montero, 2007)

2. Asymmetry characteristics

   • symmetrical
     • If the distribution is symmetric: g1 = 0
   • positive asymmetric
     • If the distribution is positive asymmetric or to the right: g1 > 0
   • negative asymmetric
     • If the distribution is asymmetric negative or to left: g1 < 0

3. Asymmetry measures

   • coefficients are used. although it is frequent get the so-called asymmetry coefficient (from Fisher)
     • named g1
       • is defined as the ratio between the central moment of order 3 and the standard deviation cubed.

4. Pointing measures look at whether a distribution of frequencies is more pointed or less when comparing this with a standard distribution, the Normal distribution with its same mean and variance. (Garcia, 2005)

5. Types and Characteristics of aiming

   • If the distribution is mesokurtic or equal pointed out that the normal: g2 = 0
   • If the distribution is platykurtic or less pointed out that the normal : g2 < 0.
   • If the distribution is it leptokurtic or more targeted than normal: g2 > 0.

6. Pointing measures (kurtosis)

   • A measure that allows know this degree pointing is the kurtosis coefficient
     • which is denoted by g2
       • is defined in this case for an X-variable