Statistical Characterization of Data

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Computer Implementation of Statistical Characterization of Data

 

All this is fine and good but how do we implement these procedures using a computer?

Let us begin using Excel.  There are three ways to implement that procedures we have discussed using Excel.  The first is to code each of the formulas discussed in a spreadsheet.  The second method is to use the Function Wizard in Excel in which many of these procedures are defined and can be called up from menus.  The third method is to use the commands, Tools, Data Analysis which gives one access to a menu of commands to execute the common statistical functions.

 

Let’s work an example that shows the use of the Function Wizard.

 

The spreadsheet presented below shows the results of several statistical analyses of experimental data.  The first tab or sheet shows the results of a blood analysis for sodium.

The data has been characterized using the spreadsheet functions AVERAGE, STDEV and CONFIDENCE. 

 

The next tab or sheet shows data on thiol concentration.  It illustrates the calculation of the t-test and F-test quantities along with standard statistics.  The t-test and F-test statistics were coded as simple calculations along with the use of the functions COUNT, AVERAGE and STDEV. 

 

The tabs (sheets) for t-test and F-test were made using the Data Analysis Tool Pack.  The command is Tools-Data Analysis.  (If you do not find this command on your spreadsheet, then go to Tools-AddIns and add the data analysis tools to your setup.)  To interpret the results of the t-test, note that a t value of 8.5 is greater than the critical value of 2.57—which means the means of the two measurements are statistically significant.  Similar for the F-test, note that an F value of 33.955 is greater than a critical value of 4.387 –which means that the variances of the two distributions are different.

 

Click here to see Excel examples

Mathematica

 

Let us use problem 5 as an example of how to use the statistical functions in Mathematica

The first command calls the file grades.dat and reads it in.  Next one calls the appropriate statistical package in Mathematica.  The next command computes the average as a fraction and the following command evaluates the fraction numerically.  The standard deviation is calculated and evaluated using the next two commands.  Finally the content of the statistics package is displayed.

 

Click here to see the Mathmatica Example

FORTRAN90

 

The following programs in FORTRAN90 are taken from Numerical Recipes and illustrate how to: (a) calculate the mean and higher moments of the data (b) calculate the t statistic and to interpret it, (c) to calculate the F-statistic and interpret it, (d) to calculate chi-squared and how to interpret it and (e) finally to make an elegant implementation of smoothing using Savitsky-Golay filters.

 

 

 

 

 

 

References

 

1.                  Numerical Recipes, Chap. 14, Chapter B14

2.                  W.E. Deming, Statistical Adjustment of Data, Chapter III

3.                  Diamond and Hanratty, Spreadsheet Applications in Chemistry Using Microsoft Excel, Chapter 2.

4.                  Bevington and Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd Edition, Chap 1-4, 11

5.                  C. Pidgeon, Tutorials for the Biomedical Sciences, Chap. 2.