# Microsoft PowerPoint Viewer - ConfidenceIntervals_update5

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```					Confidence Interval around a Percentile (CIP): Impaired <10% of the time (EPA guidelines),
with 80% confidence (TCEQ currently controls Type I error at 20% on listing).
If the confidence interval (CI) region is below the maximum criteria value for a parameter,
or is above the minimum critera value for a parameter, the waterbody is not considered
impaired.

A waterbody is an impairment concern if the CI region overlaps the criterion
for the parameter of interest.

A waterbody is impaired if the CI region is above the maximum criteria value for a parameter,
or is below the minimum criteria value for a parameter.
H1 = There is less than a 20% chance of falsely impairing a water body that is supporting
the criterion 90% of the time (or 75% of the time for bacteria).

26 Oct, 2004             TCEQ Austin, SWQM Stakeholders Meeting                      1
Various confidence intervals around a percentile...

50% C.I.

50% C.I.
60% C.I.

60% C.I.
70% C.I.

70% C.I.
90th

80% C.I.
80% C.I.

90% C.I.
90% C.I.
Probability

Parameter value

26 Oct, 2004                 TCEQ Austin, SWQM Stakeholders Meeting                                                                  2
Start/finish
80% C.I.                           FS
Criteria

Probability
Delist
Parameter value
NS       80% C.I.
80% C.I.               T2
90th                                        90th percentile                                             90th
Probability

Probability
Determining impairment
Parameter value                               by evaluating the                                         Parameter value
Confidence Interval
NS            80% C.I.                              around a Percentile (CIP)
90th                                                                                              80% C.I.          T2
Probability

90th

Probability
Parameter value
Parameter value
NS                      80% C.I.
90th
Probability

List

Parameter value
Start/finish
80% C.I.                           FS
Criteria

Probability
Parameter value
NS       80% C.I.
80% C.I.              T2
50th                                        50th percentile                                           50th
(ie: median)
Probability

Probability
Determining impairment
Parameter value                                 by evaluating the
Parameter value
Confidence Interval
around a Median (CIM)
NS            80% C.I.

50th                                                                                           80% C.I.          T2
Probability

50th

Probability
Parameter value
Parameter value
NS                      80% C.I.
50th
Probability

Parameter value
Summary

When a parameter is not currently listed, assess with recent data:
To avoid the expense and distraction of falsely listing a water body when it is not impaired,
the Type I error is currently controlled at < 20%

Missing an impairement: the Type II error is high for small samples, especially near the criteria.

Null Hypothesis: Not impaired
Alternate Hypothesis: Is impaired

When a water body is on the current list, assess with recent data:
To avoid delisting a water body when it it still impaired, the Type I error could be controlled at < 20%

Erroneously continuing the listing: the Type II error is high, especially near the criterion.

Null Hypothesis: Still impaired
Alternate Hypothesis: No longer impaired

26 Oct, 2004                 TCEQ Austin, SWQM Stakeholders Meeting                                  5

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 views: 3 posted: 12/1/2011 language: English pages: 5