First extensive published use of normal qqplots. Hazen uses a=1/2 to make the p values for the plots. Hazen doesn'tplot zeros but has them contribute to the sample size. The context of use is in a study of the relation between the water storage provided in a reservoir on any stream and the quantity of water that can be continuously supplied by it. To quote the paper: ... treat all the remaining variations on the basis of probabilities, using all data from a number of streams; and to study them in comparison with the normal law of error."
WachusettReservoirA data frame with 15 rows and 6 variates:
Computed storage, in millions of gallons per square mile of land area, given a draft of 100,000 gallons per square mile daily.
Computed storage, in millions of gallons per square mile of land area, given a draft of 200,000 gallons per square mile daily.
Computed storage, in millions of gallons per square mile of land area, given a draft of 400,000 gallons per square mile daily.
Computed storage, in millions of gallons per square mile of land area, given a draft of 600,000 gallons per square mile daily.
Computed storage, in millions of gallons per square mile of land area, given a draft of 800,000 gallons per square mile daily.
Computed storage, in millions of gallons per square mile of land area, given a draft of 1,000,000 gallons per square mile daily.
qqtest(WachusettReservoir$draft800,dist="uniform", a=1/2,type="o") will effect Hazen's original plot for a draft of 800,000 gallons per square mile daily.
qqtest(WachusettReservoir$draft800,dist="normal", a=1/2, type="o") will effect Hazen's normal qq plot for a draft of 800,000 gallons per square mile daily.