**Qstats** is a good place to start in analyzing your data. It computes
some basic statistics on the quantitative traits and summarizes missing
data.
Let
be a vector of quantitative trait values. For each trait in turn, it calculates the
sample size (*n*),
mean (
),
variance (
),
standard deviation (
),
skewness,
kurtosis and average deviation,
. The coefficient of variation is the
sample standard deviation divided by the sample mean.

lynchwalsh@98 provide a lucid explanation of some of the
statistics calculated by **Qstats**.
Let the th sample moment be
. Clearly,
. Using the notation
, we can estimate the
sample variance with

The standard error of skewness depends on the underlying distribution but can be approximated by . The coefficient of skewness, is

where the sample standard deviation, is estimated from (3.1). Kurtosis is estimated by

and the coefficient of kurtosis is

Like skew, the standard error of kurtosis is dependent upon the population distribution. We give the estimate . A test of normality for the vector then involves the test statistic

which is distributed as a with two degrees of freedom. The critical values for the rejection of normality are 5.99 and 9.21 for tests at the 5% and 9% levels, respectively.

An example of the output follows:

------------------------------------------------------ ------------------------------------------------------ This is for -trait 1 called szfreq ------------------------------------------------------ Sample Size................ 119 M(1)....................... 0.4349 M(2)....................... 0.2184 M(3)....................... 0.1195 M(4)....................... 0.0694 Mean Trait Value........... 0.4349 Variance................... 0.0295 Standard Deviation......... 0.1718 Coefficient of Variation... 0.3951 Average Deviation.......... 0.1398 Skw..LW(24)................ -0.0010 .....Sqrt(6/n)............. 0.2245 Kur..LW(29)................ 0.0022 .....Sqrt(24/n)............ 0.4491 k3...LW(24)................ -0.1922 k4...LW(28)................ -0.5250 S (5%: 5.99, 1%: 9.21)..... 2.0992 ------------------------------------------------------ ------------------------------------------------------In the above example, LW(i) refers to a page number in lynchwalsh@98 where one can find an explanation of the quantity. The value of the test statistic is 2.0992, thus one would fail to reject the hypothesis that this trait is normally distributed.

After the basic statistics, **Qstats** draws a histogram
of the quantitative trait. It is a simple histogram in that the range of the
data are divided into 50 equally sized bins, and the number of data points falling into
each bin are counted and plotted. A small table following the
histogram gives the sample size, minimum, first quartile, median, second quartile and maximum.