U.S. Dept Commerce/NOAA/NMFS/NWFSC/Publications
NOAA-NMFS-NWFSC TM-9: Effectiveness of Predator Removal for Protecting Juvenile Fall Chinook Salmon Released from Bonneville Hatchery, 1991

APPENDIX D

Statistical Analysis of Juvenile Recovery Data

A.
Chi-square goodness of fit analysis was used to evaluate differences among observed recoveries (Appendix Table C2) through time for different treatment groups released on the same day (Sokal and Rohlf 1981). A nonsignificant result indicated that there was equal probability of capture at Jones Beach for each treatment group (i.e., that the groups were adequately mixed). For additional details of this procedure see Appendix D in Dawley et al. (1989).
Ho: There was homogeneity between recovery distributions of treatments.
Release date Seine type Chi-square df P
24 June purse 15.025 18 0.6602
28 June purse 5.349 15 0.9887
24 June beach 9.331 8 0.3151
28 June beach 6.721 6 0.3474
24 June total 17.625 18 0.4806
28 June total 7.943 15 0.9260

Conclusion: No evidence to suggest there is nonhomogeneity between treatment recovery distributions.

B.
Paired difference z-tests were used to evaluate the benefits of midstream Columbia River release over Tanner Creek release and to evaluate the effects of northern squawfish removal efforts on the difference between midstream and Tanner Creek releases.

Consider the following notation:

Ptc1
= true survival to and recovery at Jones Beach of fish released in Tanner Creek before squawfish removal on 24 June

ptc1
= estimate of Ptc1 = recovery proportion at Jones Beach of fish released at Tanner Creek on 24 June.

Similar explanations follow for Ptc2, ptc2, Pmc1, pmc1, Pmc2 and pmc2

where: tc denotes Tanner Creek

mc denotes midstream Columbia River

1 denotes before squawfish removal

2 denotes after squawfish removal

Rij
= release number for group i, j

where i = tc, mc and j = 1, 2

v(pij) = pij(1-pij) ¸ Rij is the estimated variance of pij.

For the three null hypotheses tested below, we will assume z (as defined below) follows a standard normal distribution.

1)
The null hypothesis for testing whether recoveries of midstream Columbia River-released fish were different than Tanner Creek-released fish for the first release pair is as follows:

Ho: (Pmc1 - Ptc1) = 0

The test statistic is as follows:

The relevant statistics for the first release pair are the following:

pmc1 = 344 ¸ 93679 = 0.003672

ptc1 = 285 ¸ 95542 = 0.002983

Then,

Conclusion: The recovery rate for midstream Columbia River-released fish was significantly higher than for Tanner Creek-released fish; the difference was 23.3%.
2)
The null hypothesis for testing whether recoveries of midstream Columbia River-released fish were different than Tanner Creek-released fish for the second release pair is the following:

Ho: (Pmc2 - Ptc2) = 0

The test statistic is as follows:

The relevant statistics for second release pair are the following:

pmc2 = 377 ¸ 96017 = 0.003926

ptc2 = 320 ¸ 97666 = 0.003276

Then,

Conclusion: The recovery rate for midstream Columbia River-released fish was significantly higher than for Tanner Creek-released fish; the difference was 18.2%.

3)
The null hypothesis for testing whether squawfish removal had a significant benefit for midstream Columbia River-released fish is the following:

Ho: (Pmc1 - Ptc1) - (Pmc2 - Ptc2) = 0

The test statistic is as follows:

The relevant statistics for the study are the following:

pmc1 = 344 ¸ 93679 = 0.003672

ptc1 = 285 ¸ 95542 = 0.002983

pmc2 = 377 ¸ 96017 = 0.003926

ptc2 = 320 ¸ 97666 = 0.003276

Then,

Conclusion: The effect of removing northern squawfish from the migration route of Tanner Creek-released fish was insignificant; the reduction was 21.9% ((23.3% - 18.2% ¸ 23.3) * 100).

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