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2. Effect of Individual Pollutants on Recreational Use
3. Joint Effect of All Pollutants on Recreational Use
We analyzed the effect of four different forms of pollution on recreational use of the BNR. Most effects were not "significant" in the statistical sense of having a 95% confidence level. We will report the less significant results, to point out the trends which appear to be occurring. We analyzed total visitation, boating days, and fishing days; the forms of pollution only affect water-based recreation, so we did not analyze effects on land-based recreation except its inclusion in total visitation. We will describe our methodology and then present our data.
First, we calculated the correlation between each form of pollution and each form of recreation. Tables E-1, E-2, and E-3 indicate the effect that a unit change in each pollutant level has on each recreational activity, as well as the confidence level in the correlation. We used a standard technique called "ordinary least squares regression" to make the correlations between pollution and recreation, holding month and year constant (see Figure 4-1 for monthly trends). Our raw data is available upon request but is not presented here.
Second, we established a "baseline" pollution level, of what the average monthly level has been for the entire period from 1989 to 1992. The baseline is the arithmetic average of the monthly pollution levels. The monthly pollution levels are the average of all of the readings done in that month (usually five to ten for each pollutant). The pollution readings are averaged from whichever sites they were taken; we do not break down pollution by section of the river.
Third, we establish a "worst case" pollution level, by averaging the worst month of each of the four years 1989 to 1992. The worst case level, therefore, represents a level of pollution that has actually been recorded already. We assume as the worst case that the pollution level of the worst month would occur for the entire year. Typically, the worst pollution levels occurred in the springtime, because those months have the most severe rain events. We averaged the worst month from each year to establish the overall "worst case." We established a more conservative "possible worst case" by summing the worst January, the worst February, and so on, into a "possible worst case" year.
Fourth, we multiplied the effect of the unit change in pollution on each form of recreation (from our correlation in part 1), by the change in pollution between the baseline and the worst case (from our levels in part 2 and part 3). That indicates how much recreational use would decrease, if pollution levels were increased from their current averages to the level in the worst month of the year. We report those numbers as the amount of reduction in recreational use that could occur, if pollution levels were to increase to their plausible worst level.
Finally, we report only the effects which have a reasonably probable effect. In statistical terms, we report only those correlations which have a confidence level higher than 60%-70%. That level of confidence is below "statistical significance," which means that we cannot assuredly rule out that the reduction in recreational use is not due to some factor other than the pollutant we are addressing, but it is high enough to indicate that some connection is probably present (it specifically means that 70% of the time, the effect of the pollutant on recreation is above zero). We correlated each pollutant independently, and then in combination with all the pollutants. In some cases, we omit a pollutant from our "probable" list because we have no confidence in its effect in combination, even though it had a strong effect separately. We report the unit change from the independent correlation as our measure of loss of recreational activity.
Effect of Individual Pollutants on Recreational Use
In general, pollution levels do not have a statistically significant effect on recreational use of the BNR. That means that we cannot state with 95% confidence that any pollutant would reduce recreational use by a specific amount, or at all. However, with somewhat lower confidence, we can state the effect that increasing pollution would have, and assign a numerical loss in recreational use, which although not "statistically significant," indicates that there is a probable connection. With that caveat in mind, we present the results of our correlation analysis.
Losses in Visitation due to Pollution Table E-1 Average Average of Loss due Loss due Confidence Confidence in Pollutant 1989-1992 Worst to Unit to Worst Level Combination Months Change Change Fecal Coliform 75.3 506.4 -143.2 -61,749 64% 32% Turbidity 2.5 9.1 -13,439 -87,597 67% 33% Dissolved 9.9 8.1 30,644 -55,155 77% 71% Oxygen Acidity (pH) 8.0 7.6 18,520 -8,862 11% 6% Total of 3 confident -204,501 69% 45% pollutants Three pollutants -135,008 45% simultaneously
The loss in visitation due to DO fulfills our criteria for probable connection -- it has over a 70% confidence in the independent correlation and over a 60% in the simultaneous correlation. We therefore report in Finding 4.3.1 the reduction in recreational visitation which would be caused by an decrease in DO from 9.9 (the baseline average) to 8.1 (the average of the worst month from each of the four years). FC levels and turbidity levels seem to have some effect as well, but only when measured independently. Because of their low confidence in combination, we do not report the loss in visitation due to FC and turbidity, but we do note its possible effect.
Losses in Boating Days due to Pollution Table E-2 Average Average Loss due Loss due to Confidence Confidence Pollutant 1989-1992 of Worst to Unit to Worst Level Combination Months Change Change Fecal 75.3 506.4 -13.0 -5,618 29% 10% Coliform Turbidity 2.5 9.1 -2,569 -16,743 61% 46% Dissolved 9.9 8.1 6,118 -11,012 72% 63% Oxygen Acidity (pH) 8.0 7.6 16,655 -7,970 42% 25% Total of 2 confident -27,755 66% 55% pollutants Two pollutants -25,204 55% simultaneously
Again, with boating days, only DO has a probable effect when measured both independently and in combination. There is perhaps some effect from turbidity, but we report in Finding 4.3.2 only the more confident probable loss due to DO.
Losses in Fishing Days due to Pollution Table E-3 Average Average of Loss due to Loss due to Confidence Confidence Pollutant 1989-1992 Worst Months Unit Change Worst Change Level Combination Fecal Coliform 75.3 506.4 -7.4 -3,189 74% 1% Turbidity 2.5 9.1 -1,128 -7,354 96% 85% Dissolved 9.9 8.1 656 -1,180 45% 17% Oxygen Acidity (pH) 8.0 7.6 8,246 -3,946 85% 77% Total of two confident -11,300 90% 81% pollutants Two pollutants -10,042 81% simultaneously
For fishing days, there is a statistically significant effect due to turbidity levels. That means we can state with over 95% confidence that a reduction in fishing activity is due to the increase in turbidity, and not due to some other effect that might be occurring at the same time. To the degree that deforestation in the watershed affects turbidity, it will certainly reduce the amount of fishing in the BNR.
Both turbidity and pH fulfill our criteria for probable effect, so we report their sum as the loss in fishing activity due to pollution, in Finding 4.3.3.
Note that the confidence level of the effect of FC and DO both dropped dramatically from their independent measurement to when they were measured in combination. Evidently, these pollutants are strongly correlated with the other pollutants, and hence their independent effect is really just reporting the effect of other pollutants which occur simultaneously with them. Hence we ignore the FC loss, even though it would appear to be a "probable effect" by our "over 70%" criterion if viewed only as an independent pollutant.
Joint Effect of All Pollutants on Recreational Use
Lastly, we checked if pollution in the BNR affected tourism when all the pollutants were considered jointly. This was partially achieved by our simultaneous regressions above, but here we directly address the joint effect, while above we addressed the individual effect of pollutants when considered in combination with other pollutants. To perform a test of the joint effect of pollutants, we used a statistical tool called an "F-test." The F-value is calculated as:
F = [ SSRur - SSRr ] / q ÷ [ (1 - SSRur) / (N - k) ] where:
R2 = sum of the squares of the residuals of the regression equation (explanatory power);
SSRur = R2 for the equation with no pollution variables (unrestricted case);
SSRr = R2 for the equation with all pollution variables in combination (restricted case);
q = number of variables added between restricted and unrestricted case (here, 4);
N = number of observations (here, 48, or one per month from 1989 to 1992);
k = number of regression variables (here, 17 = constant + year+11 months+4 pollutants);
F = F-value which is compared to a "critical value" to determine the joint significance.
The critical value is determined by the "degrees of freedom" of the numerator and the denominator of the F-equation; in this case:
dfnumer = q = 4 (the pollutants, D.O., turbidity, F.C., and pH);
dfdenom = (N - k) = 31 here.
The F-value criticality point for dfnumer = 4 and dfdenom = 31 is as follows:
Significance level: 1% 5% 10% 25%
Critical F-Value: 4.001 2.682 2.135 1.418
If the F-value is above the critical point, then the joint effect of the pollutants is significant, even if the individual effect is not, and even if each pollutant in combination does not itself have a significant effect (in statistical terminology, the null hypothesis is that all dropped variables have no effect). Here are the results of our F-test:
Visitation Boating Fishing
SSRr 95.36% 89.14% 79.46%
SSRur 95.67% 89.72% 82.70%
F-value 0.558 0.437 1.451
Our conclusion is that there is no joint effect for either visitation or boating. That is, the combined effect of our four pollutants, considered jointly, is not significant, and we should consider only their individual effects described above. For fishing, the joint effect is significant at just above the 25% level, which means that we can state with 75% confidence that our four pollutants have a joint effect on fishing. This confirms the conclusions from our individual regression analysis above. In summary, at the current levels of pollution, recreational use of the BNR is not significantly affected by pollution, except for fishing. However, pollution often shows a "threshold effect," where its effect dramatically increases when the pollutant reaches a certain level. This potential threshold effect is discussed in chapter 4.3.