High values of correlation coefficients and residual variance of estimated variables are shown to be sometimes caused by "mingling" of samples.
HIGH CORRELATION BETWEEN AIR TEMPERATURE AND PAN EVAPORATION
In Volume 3 (3/4) of Agricultural Meteorology, GRIFFITHS (1966) presented a short communication under the title of "Another evaporation formula" concerning a simple method for estimating the monthly evaporation from a pan with the help of the monthly mean temperature, which method is said to be adequate for practical purposes. This method is based upon the high correlation between the monthly pan evaporation (y) and the monthly mean temperature data (x). We were surprised by the high values of the correlation coefficients because all 28 Texas stations show a correlation coefficient in excess of + 0.79 (24 stations exceeding + 0.95).
INFLUENCE OF ANNUAL COURSE
The paper by Griffiths suggests that the data came from successive months in successive years; the number of months is not mentioned. Then there are two meteorological variables both following the same annual course, each on the average taking high values in summer and low values in winter. This means that, with m years of measurements, the m months of January give a sample of m paired values x~,yl, (with means: :~,371; standard deviations: s(x~), s(yl) and a correlation coefficient r(xj,yO) drawn from a bivariate xl,y I population (with corresponding theoretical values p(xl), p(y~), a(x0, a(yl) and p(xl,Yl) ) whereas the m months of February give rn paired values x2,Y2 (with ff2,.92 etc.) drawn from a bivariate xz,y2 population (with/~(x2), P(Yz), a(x2), a(y2) and P(xz,yz)), etc.
It is statistically not correct to combine (to mingle) all these k = 12 samples to kin = 12 m paired values p,q (with b,q, s(p), s(q) and r(p,q)) because the k = 12 bivariate populations are not identical. This incorrectness implies the following.
Taking for simplicity k = 2 populations, say n pairs x,y and n pairs u,v