440 RESEARCH IN PROTOZOOLOGY 



to get a clear view of the entire series. For this reason, the statis- 

 tical treatment starts by arranging these measurements in order, 

 according to size. 



For example, if we were measuring the length in microns of 

 trophozoites of Giardia bradypi, as was done by Hegner and 

 Schumaker (1928), and we had taken measurements on 100 of 

 these forms, we would find it necessary to arrange these measure- 

 ments in what is called a frequency table. Such an arrangement 

 is illustrated in Table I, which gives the frequency distribution 

 of measurements found by these experimenters. 



TABLE I. 



Quantitative information of this sort is presented graphically 

 as in Fig. 29. Bars are used to indicate the frequency because 

 the measurements, although recorded as 10, 11, 12, etc., microns, 

 are in fact distributed at various points about these exact positions 

 and the set of measurements recorded at any particular position 

 such as 12 represents measurements of values that occurred 

 between 11.5 and 12.5.^ 



Such a table with its accompanying graph presents the facts with 

 regard to these measurements in a form that gives us consider- 

 able information as to the length of these organisms. We see 

 that they tend to center in size somewhere in the neighborhood 



* The centering of such measurements calls attention to a point that is 

 very often overlooked. In any problem, after we have decided on the finest 

 unit of measurement to be used, it is better to record any measurement not 

 to the nearest position on the scale, but at that scale value at the beginning 

 of the interval vi^ithin which the measurement falls. Such a practice has the 

 advantage of eliminating the necessity of estimating a mid-position between 

 two scale readings and in no way handicaps the statistical treatment of the 

 results. If such a method of recording results had been followed, the bars 

 in the frequency distribution of Fig. 29 would run over the intervals lo-ii, 

 11-12, etc., rather than over the intervals 9.5-10.5, 10.5-11.5, etc. 



