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Matched Pairs

A study compared tree growth measurements for trees close to and far away from the location of an aluminum processing plant for periods before and after the plant opened. The mean tree ring sizes were
Preoperational Years Operational Years
Year Within 8 km Beyond 8 km Year Within 8 km Beyond 8 km
1962 3.3 3.3 1967 2.6 3.2
1963 3.4 3.4 1968 2.4 3.1
1964 3.0 3.1 1969 2.0 2.9
1965 2.9 2.9 1970 2.3 3.2
      1971 2.3 3.1
      1972 2.1 2.9
      1973 1.9 2.6
      1974 2.2 2.8
      1975 2.0 2.9

To test whether there is a significant difference between tree growth close to and far from the plant site before the plant began operation, use

The results should be
         Paired t-test 

data:  before.close and before.far 
t = -1.633, df = 4, p-value = 0.1778 
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -0.10800874  0.02800874 
sample estimates:
mean of the differences 
                  -0.04
There is no evidence of a difference (though keep in mind that the sample size is quite small).

To test whether grown is loser close to the plant in the years the plant was operational, use

The results are
         Paired t-test 

data:  after.close and after.far 
t = -17.9252, df = 8, p-value = 4.809e-08 
alternative hypothesis: true difference in means is less than 0 
95 percent confidence interval:
         NA -0.6970915 
sample estimates:
mean of the differences 
             -0.7777778
These is very strong evidence for lower growth near the plant in the years of plant operation.

Try some examples of your own in the work area below.

Work Area
Enter your own commands here; then click the Submit button.

next up previous
Link to Statistics and Actuarial Science main page
Next: Two Independent Samples Up: Confidence Intervals and Tests Previous: Single Samples
Luke Tierney 2006-08-23