92 BELL SYSTEM TECHNICAL JOURNAL 



Logarithmic Probability Charts. Cumulative curves for rent dis- 

 tributions may be plotted on logarithmic probability paper® in which 

 case the resulting graph is a straight line for a large number of cities. 

 Such a graph will be said to represent a logarithmic skew distribution. 

 In the appendix there is given a discussion of frequency curves, 

 with special reference to curves of this type. The essential point 

 in reading charts on logarithmic probability paper is that the slope 

 of the line determines both the spread or dispersion of the data and 

 the skewness or lack of symmetry of distribution. Since the hori- 

 zontal scale is logarithmic it follows that the dispersion is represented 

 on a percentage and not a linear basis. A steep slope indicates a 

 close concentration of the data, a less steep slope indicates a wider 

 distribution, and parallel lines indicate distributions which are identical 

 on a percentage basis. As explained in the appendix, the most con- 

 venient index or coefficient for expressing the spread or dispersion 

 of a distribution is the ratio of the upper quartile'^ to the median rent. 

 If the curves for a given city are closely parallel for successiv'e surveys 

 it follows that there has been no material change in the character of 

 the distribution. In other words, rents have increased approximately 

 proportionately at all points of the scale. 



Examples of charts of this kind (Figs. 2-4) are shown for twelve 

 cities for which successive surveys are available. Curves for suc- 

 cessive surveys are nearly parallel in eight of the twelve cities. For 

 Cleveland, Dallas and Houston there are distinct differences in the 

 curves for the two dates, indicating changes in the distribution of 

 rents, which changes may be measured since horizontal distances 

 between points on the curves for two dates represent the percentage 

 increases in rents. 



When a rent distribution is plotted on logarithmic probability 

 paper the points do not always lie on a straight line, but a straight 

 line of best fit may be chosen by eye, giving greatest weight to points 

 near the middle of the scale of ordinates. Of the rent distributions 

 for large cities which have been plotted on this paper, nearly one- 

 third are very closely represented by straight lines, an equal number 

 are slightly concave upward, and the remainder are more or less 

 concave downward. Most of the deviations from straight lines are 

 slight. The examples submitted herewith (cities in which successive 

 surveys have been made) are rather poorer than the average in this 



"See an article by G. C. Whipple in the Journal of the Franklin Institute for July 

 ajid August, 1916, for a description of this paper and some examples of its use in the 

 field of sanitation. 



' See Appendix. 



