Jenness Enterprises - Statistical Distributions; Summary Statistics

Mexican Spotted Owl, stretching...

Field Summary Statistics:

This function produces similar values to those produced by the “Summarize” function in the “Field” menu, except with a few more options and a higher level of precision. Open the “Summary Statistics” dialog by opening your table, selecting the field you are interested in, and then clicking on the button. This button will not be enabled unless a numeric field has been selected. Then, select your summary statistics and click “OK”. The output will open in a Report window and the data will automatically be copied to the clipboard for you to paste into other applications.

This tool is designed with a dialog interface to make it easy for users to get and view a variety of statistics describing a set of data. This tool can also be accessed with Avenue code which enables more advanced users to pass these statistics to variables, and then use the calculated values in other places. Please review Calculating Summary Statistics with Avenue for details on how to do this.

Mean:

Std Error of the Mean:

Minimum: The lowest value in the data set.

Confidence Interval: The confidence limits for population mean mu with a confidence coefficient (1 - alpha), given a sample population mean X-bar, are calculated as:

Quartiles and Median: Those values at which at most (P)% of the data lie below the value and at most (1 – P)% of the data lie above the value. There are different ways to calculate quartile values, which produce similar but different results. Some methods draw the quartile values from the data set itself so that the value called the “quartile” will always be found in the data. This script uses a different method which occasionally calculates a quartile value which represents the midpoint between two values from the data set, applying the following algorithm:

Maximum: The highest value in the data set.

Range

Maximum - Minimum

Variance:

Standard Deviation:

Average Deviation:

Skewness: Measures the degree of asymmetry of the sample data around the mean.

Skewness (Fisher’s G1): There are alternative methods to calculate skewness measures of the data. S-PLUS uses the Fisher’s G1 variation, calculated as:

Kurtosis: Measures the “peakedness” or “pointedness” in a distribution, and calculated as:

Kurtosis (Fisher’s G2): As with Skewness, there are alternative ways to calculate kurtosis. S-PLUS uses the Fisher’s G2 variation, calculated as:

Number of Rows: The total number of rows of data examined during the analysis.

Number of ‘Null’ Values: The total number of cases of missing data. These are represented as “null” numbers in the table, which are different than zeros.

Total Sum:

Back to Statistics/Distributions | Probability Calculators | References

Calculating Summary Statistics with Avenue

Discussion of Distribution Functions:
Probability Density Functions | Cumulative Distribution Functions | Quantile Functions

Download Statistics Extension Manual (Adobe PDF, version 5)

Please visit Jenness Enterprises ArcView Extensions site for more ArcView Extensions and other software by the author. We also offer customized ArcView-based GIS consultation services to help you meet your specific data analysis and application development needs.