Home Reports Start

Acquisition Activity and Raw Data Report on 1997 Annual Water Level Measurements: Kansas Geological Survey's Portion

Prev Page--Data Acquisition || Next Page--Appendix A--Water Levels

II: QA/QC Statistics

John Davis

General Statistical Assessment

This initial statistical analysis of the quality of water well depth measurements is based on the 1997 drawdown; that is, the difference between the water level measured in 1996 and that measured 1997. In this way, the effect of depth to water table, which so large that it tends to overwhelm all other sources of variation, is removed from the analysis. Unfortunately, this also limits the statistical analysis to those wells for which measurements are available in both 1997 and the previous year. There are 499 of these wells in the data base, but one well (USGS ID 380351099461501) has such an aberrant 1996 measurement that it was excluded from the analysis.

An initial assessment of the quality of 1997 measurements can be made by examining the distribution of drawdowns. We would not expect the distribution to be normal, but values should be clustered around some average value and extreme drawdowns should be rare. In particular, we would not anticipate large positive drawdowns (increases in water level). Figure 5 summarizes the distribution of '97-'96 drawdowns in three forms: as a histogram, a box-and-whisker plot, and as a cumulative normal distribution. Measurements that deviate in an extreme manner from the expected pattern are indicated by open circles. The twelve observations so indicated are listed below by USGS ID number. These are the only samples among the 498 examined that seem to merit extensive additional checking.


Influence of ExogenousVariables

Several possible exogenous variables were identified prior to the 1997 field season. Exogenous variables are "suspicious factors" that may have an influence on the measurements obtained, even though they do not directly enter into the measurement process. Before a statistical analysis, it's not possible to know if these variables will have a significant influence on the results or not, but their contribution to the total variation in drawdown can be assessed by a statistical procedure called Analysis of Variance. The exogenous variables considered in this study are

  1. Date of measurement
  2. Person making the measurement
  3. Quality of access to well
  4. Quality of downhole access
  5. Presence of weight on tape
  6. Use of the well
  7. Oil on the water in well
  8. Quality of the chalk cut
  9. Aquifer
We anticipate that the identity of the aquifer being measured will prove to be the largest exogenous source of variation in drawdown, but unfortunately no information was made available to us about the identity of aquifers in individual wells. When such information becomes available, it should be possible to significantly improve this statistical analysis.

The first two variables may be interrelated because individuals were assigned to small teams that worked in specific areas on specific days. This possible interaction will be resolved in a subsequent analysis.

Variables 2 and 6 are nominal categories; that is, there is no implication of rank or relative superiority of any class. Variables 3, 4, 5, and 7 are bivariate nominal states corresponding to "good" versus "bad" or "yes" versus "no." Variable 8 is an ordinal property whose ranks are "excellent," "good," and "fair."

Variables 2 through 8 were used to predict '97 drawdown in an analysis of variance. The fitted model is highly significant, although the exogenous variables account for only 8% of the total variation in drawdown. The variables, in declining order of importance, are

1. Use of the well1.80*
2. Quality of the chalk cut2.45*
3. Oil on the water in well6.08*
4. Presence of weight on tape6.43*
5. Person making the measurement14.64
6. Quality of access to well52.11
7. Quality of downhole access92.28

The values on the right describe the probability that the observed effect could arise by random chance. Those marked with an asterisk are considered statistically significant.

Results of this analysis can be summarized in the following manner.

  1. If a well is used for household supply or stock watering, there tends to be a drawdown that is about 2 1/2 feet greater than expected. Wells of unknown use tend to have about 1 1/2 feet of greater than expected drawdown.
  2. Measurements with "fair" quality chalk cuts tend to be about 1 1/4 feet higher (less drawdown) than expected.
  3. If there is oil on the water in the well, the measurement tends to be about 3/4 foot higher (less drawdown) than expected.
  4. If there is no weight on the tape, the drawdown tends to be about 1 foot greater than expected.
This analysis detects bias, or shifts in average value attributable to the exogenous variables. It also is possible that an exogenous variable may increase (or reduce) the scatter in the measurements without causing a shift in their average value. Although this does no harm overall, an increase in variance does reduce the precision with which groundwater levels can be estimated at specific locations. A "quick and dirty" test for increase in variance as a function of exogenous influences can be made by regressing the absolute magnitudes of drawdown against the exogenous variables. Again, although the fitted model is highly significant, only about 8% of the total variance can be attributed to these influences. The variables, in declining order of importance, are

1. Quality of the chalk cut0.84*
2. Use of the well1.11*
3. Quality of downhole access17.28
4. Presence of weight on tape18.89
5. Person making the measurement42.96
6. Quality of access to well68.33
7. Oil on the water in well72.14

These results can be summarized:

  1. If there is oil on the water in the well, measured drawdowns are slightly more variable than expected.
  2. Drawdowns in wells pumped for stock watering purposes are somewhat more variable than expected.

Initial Statistical Assessment of Well Measurement Quality

A number of wells were measured more than once because the measurement team was unsatisfied with the initial attempt. In addition, a selection of wells were remeasured at a later time to be used for quality assessment purposes. This is an initial evaluation of these replicated measurements. Table 2 below lists all of the remeasured wells by USGS ID number, and gives the average 1997 drawdown, the standard deviation of the drawdown measurements, and the standard error of the estimated mean drawdown. The standard errors should be regarded as highly conservative (that is, they suggest greater scatter than probably exists) because of the small number of replicates. Only nine wells (indicated above by boldfaced type) have more than two measurements.

Half the resampled wells have standard deviations in drawdown of less than one-quarter foot, and 90% of the resampled wells have standard deviations of less than three-quarters of a foot. The true variation between repeated measurements made under conditions of the 1997 field season seems to be well within acceptable limits for all except a few wells. Further analysis will be necessary to determine how much of the variation in replicates can be attributed to exogenous factors. We suspect that much of the variation can be accounted for by considering the aquifer being measured, but these data are not yet available and more detailed analysis is not warranted without this information.

Table 2--Means and Standard Deviations of Quality Assessment Measurements

USGS IDNo.MeanStd DevStd Err
* Standard error over 1/4 foot
**Standard error over 1/2 foot


Miller, R.D., 1996, The acquisition of annual water levels in Kansas sponsored through a cooperative agreement between the KGS and USGS: Kansas Geological Survey Open-file Report 96-39.

Prev Page--Data Acquisition || Next Page--Appendix A--Water Levels

Kansas Geological Survey, Water Level CD-ROM
Send comments and/or suggestions to webadmin@kgs.ku.edu
Updated Feb. 19, 1997
Available online at URL = http://www.kgs.ku.edu/Magellan/WaterLevels/CD/Reports/OFR9711/rep02.htm