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

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II: QA/QC Statistics

John Davis

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.

USGS ID
380609099540701
380530099551301
380504099504001
380352099550501
375958099530101
375953101553901
375307099492701
375150101304801
374048099474001
373652099575901
371904101223801
371503101251201

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

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 well	1.80*
2. Quality of the chalk cut	2.45*
3. Oil on the water in well	6.08*
4. Presence of weight on tape	6.43*
5. Person making the measurement	14.64
6. Quality of access to well	52.11
7. Quality of downhole access	92.28

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.

1. Quality of the chalk cut	0.84*
2. Use of the well	1.11*
3. Quality of downhole access	17.28
4. Presence of weight on tape	18.89
5. Person making the measurement	42.96
6. Quality of access to well	68.33
7. Oil on the water in well	72.14

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 ID	No.	Mean	Std Dev	Std Err
370057101324601	2	2.84000	0.00000	0.00000
370422101140501	2	3.37000	0.59397	0.42000*
370602100572601	2	1.20500	0.00707	0.00500
370931101280201	2	2.12500	0.41719	0.29500*
372220100203501	2	-0.08500	0.14849	0.10500
372359100224701	2	1.27000	0.01414	0.01000
372638100241701	2	1.52500	0.24749	0.17500
372825101041201	2	2.10000	0.08485	0.06000
373352100411301	2	3.80000	0.18385	0.13000
373841100115601	2	0.39500	0.00707	0.00500
374044100395001	2	2.89000	0.11314	0.08000
374046100520101	2	4.40500	0.62933	0.44500*
374304100032201	2	-0.53000	0.04243	0.03000
374404100064401	2	0.47000	0.04243	0.03000
374507101580601	2	2.29500	1.03945	0.73500**
374638101025601	2	5.37000	0.02828	0.02000
374645100481901	2	1.78500	0.13435	0.09500
374725099485601	2	-0.33500	0.43134	0.30500*
374931100453501	2	2.77000	0.14142	0.10000
375049101165801	6	-0.66500	0.10407	0.04249
375107100125801	3	-0.93667	0.00577	0.00333
375149101341601	2	-0.11500	0.10607	0.07500
375258100281701	2	2.00500	0.10607	0.07500
375446102013601	3	0.87333	0.00577	0.00333
380109100570201	6	-6.90500	0.80590	0.32901*
380135100081001	2	0.36000	0.01414	0.01000
380600100535701	2	-0.14000	0.69296	0.49000*
380758098550501	3	-0.19000	0.00000	0.00000
380945101014801	2	-0.64500	0.00707	0.00500
381047099185301	3	-4.72000	0.60918	0.35171*
381714098300701	2	-0.53500	0.04950	0.03500
381734098423001	4	-0.85500	1.84175	0.92087**
382137098493201	2	-0.57000	0.04243	0.03000
382307098345601	2	0.02500	0.19092	0.13500
390856100451901	2	-0.10500	0.03536	0.02500
391737101551301	3	3.85667	0.20502	0.11837
392016101274901	3	0.17333	1.16835	0.67455**
392112101592101	2	0.72000	0.11314	0.08000
392113101484901	2	0.69000	0.01414	0.01000
392456101333201	2	-1.44500	0.53033	0.37500*
392520101591901	2	1.14500	0.03536	0.02500
393225101401201	2	0.18500	0.02121	0.01500
393403101575901	2	1.46000	0.18385	0.13000
393955101574301	2	-0.36500	0.02121	0.01500
394132101351201	2	0.15000	0.01414	0.01000
394152101525901	2	-0.48500	0.09192	0.06500
394421101354501	2	-0.91500	0.00707	0.00500
395120101545301	2	-0.27000	0.01414	0.01000

* Standard error over 1/4 foot
**Standard error over 1/2 foot

References

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.

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