Two FORTRAN II Programs for the Univariate and Bivariate Analysis 



of Morphometric Data 



Abstract 



Two computer programs, written in FORTRAN II for the 

 IBM 7094, perform univariate and bivariate analyses of 

 morphometric data and plot bivariate scatter diagrams of 

 pairs of data. Basically, the programs are designed to process 

 arrays in which rows (up to 100) represent specimens and 

 columns (up to 52) represent measured and computed 

 variables. Alternatively, an input array may represent a single 

 organism, for example a coiled snail or a segmented arthro- 

 pod, with the rows representing, respectively, individual 

 whorls or segments. A high degree of adaptability to differ- 

 ent kinds of problems is achieved because of the numerous 

 control cards which specify input and output format, table 

 headings, and column numbers of variables on which opera- 

 tions are to be performed. 



Program devices allow for the elimination of zeroes rep- 

 resenting missing data and for the conversion of selected 

 columns to logarithms to the base 10. The computed uni- 

 variate statistics include the maximum, minimum, observed 

 range, arithmetic mean, standard deviation, standard error 

 of the mean, and coefficient of variation. Bivariate statistics 

 include the correlation coefficient, slopes and intercepts of 

 either regression lines or the reduced major axis, coefficients 

 of relative dispersion, and factors for the computation of 

 confidence intervals. Finally, the programs plot selected 

 pairs of data on bivariate scatter diagrams and furnish the 

 end points for the plotting of regression lines or reduced 

 major axes. 



Introduction 



Morphometry, or the measurement of form, is becoming in- 

 creasingly important in the study of fossil and living orga- 

 nisms. The uses and limitations of univariate and bivariate 

 techniques in the analysis of morphometric data in paleon- 

 tology have been summarized by Imbrie ( 1956) , and the ap- 

 plication of such analytic techniques in zoology has been de- 

 scribed by Simpson, Roe, and Lewontin (1960). 



In paleontology, it is often necessary to deal with fragmen- 

 tary specimens in order to obtain samples (groups of speci- 

 mens) which are large enough to be statistically treated. If 

 the missing data are represented by zeroes, these zeroes must 

 be eliminated from any statistical analysis. Furthermore, if 

 the data are transformed to logarithms, a zero representing 

 the logarithm of one to the base ten must be treated statis- 

 tically and must therefore be differentiated from a zero 

 representing missing data. 



Examples of other operations which may be required in 

 morphometric work are as follows: 



1. Subtract the thickness of a measuring platform from 

 a measurement where, in order to obtain the measurement, 

 this thickness had to be included. 



2. Convert certain measurements, which are invari- 

 ably in ocular micrometer units, to millimeters. 



3. Convert certain measurements, which are in ocu- 

 lar micrometer units only when the specimen is small, to 

 millimeters. 



4. Compute the cross-sectional area of a muscle or liga- 

 ment, where such an area can be approximated by a sim- 

 ple formula, e.g., the area of a circle or a triangle. 



5. Compute measurements which are the sums or dif- 

 ferences of other measurements. 



6. Convert any or all measurements to logarithms. 



7. Compute ratios of one measurement to another. 



8. Arrange data in order of decreasing size of one of the 

 measurements and /or preserve the order of specimens in the 

 input. 



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