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# "Are We the Problem?"

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In Chapter 8 of Watershed 4: "Are We the Problem?"
1. Is the equation, I=PAT true for all environmental problems. If yes, how? If no, why? Please, support your arguments with two practical examples from the course textbooks.

2. Who proposed this equation? Explain the equation

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In Chapter 8 of Watershed 4: "Are We the Problem?"
1. Is the equation, I=PAT true for all environmental problems. If yes, how? If no, why? Please, support your arguments with two practical examples from the course textbooks.
The equation I=PAT is not true for all environmental problems. This equation is true for environmental impact caused by human beings. There can be substantial impacts caused by natural disasters. For instance, there may be huge changes in the topography because of earthquakes and these could lead to washing away of valuable topsoil by subsequent rains. There would be substantial impact on the environment but these would not be caused by population, affluence or the use of technology. Similarly, large forests are destroyed because of fires caused by volcanic activity; these fires are not related to human population, affluence and technology. However, their impact on the environment is substantial. In the same vein we can consider the ...

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## ANOVA Problem

When we want to test two samples to determine if it is likely that the population means (estimated by the sample means) are different, we typically use a t-test. If the samples are large, we can also use a z-test. (Note that the formulas for computing s, t and/or z in the case of a two-sample test are different than the formulas for computing the same values in a one-sample test. Use Excel data analysis to conduct tests comparing two sample means.)

Using ANOVA (short for Analysis of Variance), however, we can test 3 or more sample means to determine if at least one of the sample means comes from a population with a mean that is significantly different from all of the others in the test. We actually do this by estimating a combined population variance two different ways and comparing the two estimates (the ratio of these two variance estimates follows the so-called "F distribution").

Question:

Why do we need a new test method to compare the means of 3 or more populations? Why can't we just use a series of z-tests or t-tests to compare all of the possible pairs of population means to see if one (or more) is different?

Most of the testing is to determine one or two things:

1. Is there a statistically significant difference between two or more population means? (based on comparison of 2 or more sample means)

2. Is there a statistically significant relationship between two or more variables? We can use regression analysis or chi-square tests to answer this second question.)

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