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. SOME STATISTICAL TOOLS IN HYDROLOGY 37 . , on the time of year. Thus, the duration curve is merely the distribution of daily means that has occurred. It can be considered an estimate of the distribution during a future period sev- eral years long. On the other hand, frequency curves of annual flood peaks can be interpreted as prob- ability curves because the individuals are unrelated and homogeneous. Most low-flow frequency curves can be similarly interpreted, but occasionally a serially correlated sample will be found. The effect of using nonhomogeneous data in a regression problem is shown by figure 25 in which is plotted 4 years of monthly mean dis- charge for ea9h of the 12 calendar months for two stations," one in Turkey and one in Idaho. The relation looks fairly good, but there is actually no relation between the two streams for a particular calendar month. The apparent relation using all calendar months arises be- cause the yearly cycle of streamflow in Idaho resembles that in Turkey" Discharges in winter months are low and in spring snowmelt months are high. . 500 I ! 0 o Z ~8 oiJJ Zoo ~::e o "'", ~oo o~ ~~100 ~~ r", 0::> <!!o Oz z- ~r;:i "'" oo >::> ~.... r . ....'" tSir "g ~ 0010 100 1000 4000 MONTHLY MEAN DISCHARGE OF SOUTH FORK BOISE RIVER NEAR FEATHERVILLE~ IDAHO, IN CUBIC FEET PER SECOND o Oct x Nav '" Dee o Jan .(l Feb x March ... Apr IJ May . June . July . Aug Ell Sept Figure 25.-Spurious relation using nonhomogeneous data. . Less extreme conditions are shown by rela- tions between monthly mean discharges from contiguous basins. For example, there is no relation between monthly mean discharges of Lake Fork above Moon Lake, Utah, and Duchesne River at Provo River Trail, Utah, for the calendar month of January; there is a fair relation for the calendar month of June (fig. 26). With few exceptions the relation be- tween monthly discharges from two adjacent drainage basins for a particular calendar month is not the same as the relation for a different calendar month. When monthly discharges for all calendar months are used together, the computed correlation coefficient will be too high and the computed standard error will be an average of the standard errors for the individual calendar-month relations. Outliers Many factors influence the flow of a stream; some exert great influence at one time and none at another; most exert effects which are inter- related with effects of other factors. Only a few factors can be included in a regression used to estimate streamflow, and the effects of these factors are only approximated. Consequently there is a scatter of points about the regression line and occasionally a wild point occurs (see fig. 18 for an example). Such wild points are called outliers in statistics, and statistical tests are available for use in determining whether or not a particular point should be rejected as not belonging to the group. It seems questionable whether outliers in hydrologic analyses should be rejected on the basis of a statistical test. Consider the wild point in figure 18. If the precipitation had been about 7 inches instead of 3.4 inches, the point would not be wild. It is possible that precipitation at thc higher elevations in the Jarbidge River basin was much greater than at Three Creek. If it were, the same thing could happen again and more weight should have been given to that point in the analysis. However, if some of the data for that year are found to be unreliable we could reject the point. Acton (1959) devoted a short chapter to thc rejection of unwanted data. He says, in part, "But the plain truth is that physical scientists and engineers need not be encouraged to ignore obstinate outlying data-rather they need to be held in check".