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# Qstats

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

 (3.1)

An estimate of the skewness is

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:

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This is for -trait 1 called szfreq
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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
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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.

Subsections

Next: Command Line Options Up: Analysis Previous: Analysis   Contents   Index
Christopher Basten 2002-03-27