❓ A WA parliamentary question probes the statistical confidence levels of a fisheries research bulletin on the impact of trawling on pink snapper in Denham Sound. The Minister provides detailed responses, including R-squared and P-values, and defends the statistical methods used.
AnsweredQoN 2272Legislative Assembly
QuestionView source ↗
(1) Has the statistical confidence levels of the various statistical analyses presented in the
Fisheries Research Bulletin No. 31
‘The effects of the trawl fishery on the stock of pink snapper,
Pagrus auratus,
in Denham Sound, Shark Bay’ been determined as part of this research report?
(2) If yes, where in the Bulletin are the statements of statistical confidence shown?
(3) In particular, what are the P or confidence levels for each of the equations shown in Figure 10 on page 19 of the report?
(4) Similarly, what are the P or confidence levels for the various statistical analyses contained in Table 2 on page 23 of the report?
(5) Why has graph E in Figure 10 on page 19 been determined using a linear regression analysis when a best fit curve appears to provide a far more statistically confident fit to the four data points?
(6) Is it not more accurate to interpret the data points in graph E in Figure 10 on page 19 as showing that the cumulative catch of 16 to 33 cm snapper maintains an initial relatively flat plateau which then crashes to virtually zero after a cumulative catch of between 20 and 30 fish has occurred?
Fisheries Research Bulletin No. 31
‘The effects of the trawl fishery on the stock of pink snapper,
Pagrus auratus,
in Denham Sound, Shark Bay’ been determined as part of this research report?
(2) If yes, where in the Bulletin are the statements of statistical confidence shown?
(3) In particular, what are the P or confidence levels for each of the equations shown in Figure 10 on page 19 of the report?
(4) Similarly, what are the P or confidence levels for the various statistical analyses contained in Table 2 on page 23 of the report?
(5) Why has graph E in Figure 10 on page 19 been determined using a linear regression analysis when a best fit curve appears to provide a far more statistically confident fit to the four data points?
(6) Is it not more accurate to interpret the data points in graph E in Figure 10 on page 19 as showing that the cumulative catch of 16 to 33 cm snapper maintains an initial relatively flat plateau which then crashes to virtually zero after a cumulative catch of between 20 and 30 fish has occurred?
AnswerView source ↗
Answered
3 December 2003
Responded by
Parliamentary Secretary to the Minister for Agriculture, Forestry and Fisheries
Response time
14 days
(1) Yes. The statistical analyses, which underlie the estimation of the effect of trawling on the stock of pink snapper, are regression analyses. The standard method used in scientific literature to express the reliability of regression analyses is to give the R squared value. This denotes the proportion of the variation in the data which is explained by the regression model. R squared ranges from zero which is a very poor fit, to one which is a perfect fit. These values are displayed in the report.
(2) For the estimation of the proportion of snapper in the path of the net that is caught, the R squared values for each of the regressions are shown on each of the graphs in Figure 10, page 19. For the estimation of the instantaneous rate of natural mortality (M) for juvenile snapper, the data are shown graphically in Figure 13 on page 24 and the resultant M values are shown with the R squared values in Table 2 on page 23.
(3) In Figure 10, the R squared value for each of the equations is shown directly below the equation. The only one of these equations in Figure 10 used later in the bulletin to calculate the effect of trawling on juvenile snapper is the one in Figure 10 D for 10-15 cm snapper, the size-range of pink snapper exposed to the trawl fishery. The R squared value in Figure 10 D is 0.999. This corresponds to a P value of less than 0.01 (that is, highly significant).
(4) The P values for year classes 1998, 1999 and 2000 in Table 2 on page 23 are all < 0.01. The P value for the 2001 year class is > 0.05, so the instantaneous mortality rate (M) is estimated with less confidence than for the other three year classes. The reliability of the data sets for the different year-classes was taken into account in calculating the mean M over all the year-classes by using a weighted mean, whereby a higher weighting is given to those estimates of M which are based on a larger number of points and are therefore more reliable.
(5) The data for all the size-groups in Figure 10 are fitted by linear regression because a specific model is being applied. The assumption of this model is that a certain proportion of the fish in the area are taken in each instance of trawling. That is, if half the fish are taken by the first fishing event, that would leave 50% of the original number. If half of the remainder are taken by the second fishing event, that would leave 25% of the original number and so on. In this kind of depletion experiment, the model is fitted by applying a linear regression to the numbers caught in each fishing event, plotted against the cumulative number caught prior to that fishing event. The negative slope of this regression is the model estimate of the proportion of the fish in an area taken by one fishing event.
(6) No. It is generally the case for experiments in nature that the data points do not perfectly fit the underlying model. In this depletion experiment, the underlying model is that a proportion of the fish are taken by the net on each trawl pass and the remainder evade the net. It would not be expected that exactly 46% of the fish in the area evade the net every time (particularly for a schooling fish such as snapper, where a whole school would tend to either be caught together or evade the net together). The level of variation in the data for 16-33 cm snapper in Figure 10 E is thus not surprising, given the schooling behaviour of pink snapper and the small number of fish of that size in the area and does not justify abandoning the depletion model underlying the linear regression.
Given the complex nature of this question, the Minister is prepared to make a Departmental Officer available to brief the Member if he so requires.
(2) For the estimation of the proportion of snapper in the path of the net that is caught, the R squared values for each of the regressions are shown on each of the graphs in Figure 10, page 19. For the estimation of the instantaneous rate of natural mortality (M) for juvenile snapper, the data are shown graphically in Figure 13 on page 24 and the resultant M values are shown with the R squared values in Table 2 on page 23.
(3) In Figure 10, the R squared value for each of the equations is shown directly below the equation. The only one of these equations in Figure 10 used later in the bulletin to calculate the effect of trawling on juvenile snapper is the one in Figure 10 D for 10-15 cm snapper, the size-range of pink snapper exposed to the trawl fishery. The R squared value in Figure 10 D is 0.999. This corresponds to a P value of less than 0.01 (that is, highly significant).
(4) The P values for year classes 1998, 1999 and 2000 in Table 2 on page 23 are all < 0.01. The P value for the 2001 year class is > 0.05, so the instantaneous mortality rate (M) is estimated with less confidence than for the other three year classes. The reliability of the data sets for the different year-classes was taken into account in calculating the mean M over all the year-classes by using a weighted mean, whereby a higher weighting is given to those estimates of M which are based on a larger number of points and are therefore more reliable.
(5) The data for all the size-groups in Figure 10 are fitted by linear regression because a specific model is being applied. The assumption of this model is that a certain proportion of the fish in the area are taken in each instance of trawling. That is, if half the fish are taken by the first fishing event, that would leave 50% of the original number. If half of the remainder are taken by the second fishing event, that would leave 25% of the original number and so on. In this kind of depletion experiment, the model is fitted by applying a linear regression to the numbers caught in each fishing event, plotted against the cumulative number caught prior to that fishing event. The negative slope of this regression is the model estimate of the proportion of the fish in an area taken by one fishing event.
(6) No. It is generally the case for experiments in nature that the data points do not perfectly fit the underlying model. In this depletion experiment, the underlying model is that a proportion of the fish are taken by the net on each trawl pass and the remainder evade the net. It would not be expected that exactly 46% of the fish in the area evade the net every time (particularly for a schooling fish such as snapper, where a whole school would tend to either be caught together or evade the net together). The level of variation in the data for 16-33 cm snapper in Figure 10 E is thus not surprising, given the schooling behaviour of pink snapper and the small number of fish of that size in the area and does not justify abandoning the depletion model underlying the linear regression.
Given the complex nature of this question, the Minister is prepared to make a Departmental Officer available to brief the Member if he so requires.
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