Effect of acid rain on diversity

This question was administered in 96 November

Acid Rain is a serious problem in Canada. As acidification progresses, the eco-system simplifies, i.e., the number of different species of fish, plant life, insects declines, until eventually, the lake is virtually sterile - no fish and few water plants. To investigate the effects of acid rain, an experiment has been running for the last decade in the Experimental Lakes Area (ELA), a series of small lakes just north of Kenora, Ontario about 250 km east of Winnipeg. These experiments have been instrumental in helping scientists understand the processes involved in acidification and have won world wide acclaim. [You might be interested to know that, as usual, the response of Canadian governments has been to cut funding for this very successful experimental program!] The following questions are based upon actual experiments conducted at the lakes.

A series of 20 small lakes (each less than 10 ha in area) were selected. These lakes were randomly assigned to either the control group or the treatment group. The treatment group was acidified by dumping sulfuric acid into the lakes at rates comparable to what would occur during acid rain. After one year, the lakes were sampled and measures of diversity were computed for each lake. Higher values of the diversity imply more types of living organisms occur which indicates, in general, a more healthy lake.

Here is summary information as presented by JMP:

1. Why did we randomize the lakes to either the treatment or the control group? Why didn't we apply the treatment to all of the lakes?

   Randomization is done so that the effects of any uncontrollable factors that might influence the results will roughly equal in both groups. Note that randomization does not eliminate the effects of other factors - it only makes them roughly equal in all groups.

   If only the treatment were applied to all the lakes, there would be no group to compare the changes with. The researchers would not know if the changes would have occured without any intervention.
   

2. Show how the standard error of the mean was computed for the Control Group. Interpret this value.

   The estimated se(control group) was found as s/ = 9.81835/sqrt(10) = 3.1048.

   The estimated se is an estimate of how much the sample mean () would vary if other, identical experiments were conducted.
   
   

3. Using the summary statistics above, construct an approximate 95% confidence interval for the mean diversity of the Experimental lakes (it is not necessary to use the t-distribution). Interpret this interval.

   An approximate 95% confidence interval is found as
   ± 2 se of = 45.9 ± 2(2.05724) = (41.78 to 50.01).

   We are 95% confident that the true diversity index (over all lakes treated similarly) is in this interval.
   

4. Below are side-by-side box plots of the data. Plot confidence intervals (either diamonds or vertical lines) on the plots.

   
   

5. What is the difference between a box-plot and a confidence interval (mean diamond) plot?
   

   A box plot show the distribution of individual values. A confidence interval shows a plausible range for the true population mean.

6. Based on the summary statistics and your graph in (d), what do you conclude?

   Because the intervals do not overlap very much, there is good evidence that the respective population means differ. We conclude that acid rain is reducing species diversity.
   

7. Consider the control lakes. Explain the difference between _control and µ_control and how the c.i. links the two.
   

   _control measures the mean of the sample. µ_control is the mean of the population. The confidence interval is a range of plausible values for µ based on sample statistics.