The Data Summary window provides standard descriptive statistics for the variates defined in the Data Worksheet window. Information is provided for both the Z-variate (as below), for the coordinate variates in a separate X,Y Coordinates tab, and when a covariate is being analyzed, for the regression of Z vs. the Covariate Z2 in a separate Regression tab.
For the Z-variate it is also possible to specify a lognormal (base e) or square-root transformation in order to better normalize the variatedistribution prior to geostatistical analysis. If you do transform the variate, you may choose to have GS+ report the interpolated (Kriged) values either in transformed form or back-transformed to the original measurement domain. The back-transformation occurs after all analyses have been performed, and it is not applied to autocorrelation results.
Also from the Data Summary window you can access a full-window frequency distribution, a cumulative probability distribution, or a normal probability distribution by clicking on the small frequency distribution image.
It is often helpful to apply a lognormal or a square root transformation to a Z variate in order to normalize for skewed frequency distributions. It can also be useful to scale data to a range of 0-1 if the values are extremely large. The transformation specified is applied to every Z value in the data set prior to geostatistical analysis; the values in the data worksheet are not transformed. View the effectiveness of the transformation by viewing the Frequency Distribution or a probability distribution and the values for skewness and kurtosis in the data summary.
If your z-variates span the range of <1 to >1 (e.g. 0.3 to 20.1) and you decide to apply a lognormal or square root transform, you should make all values >1 prior to transformation by adding an offset value (e.g. ln(z+1), where the offset is 1). This is because of the discontinuous nature of the lognormal transformation across the <1 to >1 range.
When a transformation is chosen, after analysis of the transformed data the output data are customarily (but not necessarily) back-transformed to the original data domain when reported. You may choose among three potential back-transformation choices: None, Standard, or Weighted. The standard back-transformation is simply the converse of the transformation: scaled values are rescaled to the original range, logn-transformed values are raised to the natural exponent e, and squared values are raised to the 0.5 (square root). Offset values are subtracted from the back-transformed values.
The Weighted back-transformation is a complex back-transformation that more closely approximates true population statistics than simple back transformations. See Haan (1977) and Krige (1981) for further details.
Back transformations are applied only to final data. These include statistics on the Data Summary screen (mean, standard deviation, etc.), and all kriging results. Individual semivariance values are not back-transformed prior to display (as noted by semivariogram axis labels).
Click on a frequency distribution image to view an enlarged version of the frequency distribution. From the Frequency Distribution window you will also be able to view a normal or cumulative probability distribution of the data.
Descriptive statistics appear in the box noted. Note that n refers to the number of active data items currently in the analysis (128 in the screen above); n missing refers to the number of worksheet records that were excluded from the analysis because they contained a missing x, y, or z value or because they were excluded from the analysis by the Filter command (4 values, in the example above). If duplicate values were averaged (see the Duplicate Values dialog), then all the duplicates for a given location count as a single record, and the duplicates will not be counted as missing.
Numbers in parentheses following skewness and kurtosis are standard errors.
When analyzing data sets with a covariate (Z2) present, the following rules apply:
• Only records with a valid Z and a valid Z2 value will be included in the analysis of Z;
• All records with a valid Z2 value will be included in the analysis of Z2;
This is because covariance analysis expects all sample points for Z to be accompanied by a covariate Z2, which will also be sampled at places other than where Z is sampled. The summary statistics and autocorrelation analysis for Z will thus be performed only for those values of Z accompanied by a Z2. The summary statistics and autocorrelation analysis for Z2, on the other hand, will be performed for all values of Z2 regardless of whether a matching Z value is present.
Press Exit to close the window.