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The Everglades wetland ecosystems are phosphorus limited. After the Everglades Agriculture Areas (EAA) were established (enabled by a series of federal government constructed water diversion systems for draining part of the Everglades wetland), phosphorus-rich agriculture runoff reached the Everglades wetland and resulted in dramatic changes in parts of the Everglades wetlands. To better protect the Everglades, many studies were conducted in the late 1980s and the 1990s to learn about the effects of phosphorus enrichment in the Everglades. One study focused on estimating the background level of phosphorus concentration. To identify which site is not affected by the agriculture runoff, researchers measured phosphatase activity (APA) in sites known to be affected (TP > 30 µg/L) and sites that are unaffected by agriculture runoff. Phosphatase is an enzyme produced by organisms in low P environment. Because producing this enzyme costs energy, organisms do not produce them when bio-available phosphorus are present. As a result, high APA is an indicator of P limitation. The data file apa.s contains both APA and TP concentrations. It can be imported into R using function source.

(a) Compare the distributions of APA from sites with The Everglades wetland ecosystems are phosphorus limited. After the Everglades Agriculture Areas...-1 and APA from sites with The Everglades wetland ecosystems are phosphorus limited. After the Everglades Agriculture Areas...-2 using graphical tools we learned in Chapter 3.

(b) What is the nature of difference between the two populations of APA?

(c) Use an appropriate test to determine whether the difference is statistically significant and describe the result in non-technical terms.

 
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In the Kemp’s ridley turtle example, we tested whether the sex ratio has shifted. The data were observational, that is, turtles used in the data set were not randomly selected from the population, rather, these were turtles stranded on the beach. One particular feature of the data is the large difference in the number of turtles observed during the two time periods. Suppose that the data from the first time period (1983– 1989) were collected by regularly scheduled beach patrols throughout the year, while the data in the second time period (1990–2001) also include observations reported by tourists. Discuss the possible causes of the observed sex ratio differences.

 
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Problems of a significance test with a low power.

Reproducible research findings are a cornerstone of the scientific method. However, studies have shown that results of published research can be difficult to replicate when only statistically significant results are published, particularly when the statistical significance tests are conducted with small sample sizes (hence with low statistical power). Let’s consider a one sample t-test with Problems of a significance test with a low power. Reproducible research findings are a cornerstone...-10Problems of a significance test with a low power. Reproducible research findings are a cornerstone...-2 versus Problems of a significance test with a low power. Reproducible research findings are a cornerstone...-1aProblems of a significance test with a low power. Reproducible research findings are a cornerstone...-4

(a) If the population standard deviation is 0.5, what is the power of the test when the effect size is δ = 0.1 and sample size is Problems of a significance test with a low power. Reproducible research findings are a cornerstone...-51 = 10?

(b) In order to reject the null hypothesis, how large must the sample mean Problems of a significance test with a low power. Reproducible research findings are a cornerstone...-6 be?

(c) If you rejected the null using data from one experiment, how likely can the statistically significant result be verified if you repeat the same experiment?

(d) Suppose that you realized that the test has a low power and you decided to repeat the experiment with a much larger sample size (e.g., Problems of a significance test with a low power. Reproducible research findings are a cornerstone...-52 = 100). What is the power of the new test?

(e) Assuming δ = 0.1, how likely is it that you will obtain a sample mean as large as the statistically significant result from the experiment with Problems of a significance test with a low power. Reproducible research findings are a cornerstone...-51 = 10?

 
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Eutrophication due to increased input of nitrogen in the Neuse River Estuary in eastern North Carolina, USA, was considered the primary cause of large scale fishkills in the late 1990s. The North Carolina General Assembly established laws to protect the estuary, including a requirement of reducing nutrient (particularly, nitrogen) input to the estuary. Because eutrophication in North Carolina is measured by the concentration of chlorophyll a, assessing the success of the nutrient reduction program relies on the demonstration of a reduction in chlorophyll a concentration in the estuary. Three institutions have water quality monitoring programs including chlorophyll a in the variables they measure: NC Division of Water Quality (DWQ), University of North Carolina Institute of Marine Sciences (IMS), and Weyerhaeuser Corp. (WEY). Because the estuary is large and chlorophyll a concentrations vary spatially, methods used in sampling and measuring can affect the reported chlorophyll a concentrations. To demonstrate the success of the nitrogen reduction program, we need to compare the chlorophyll a concentrations measured before and after the implementation of the program to the concentrations before. But which series of data should we use? To answer this question, we need to compare the reported chlorophyll a concentrations from the three institutions and determine whether they are different. If they are the same, we may want to combine the three sources of data to increase the power of any statistical test we will use. If they are different, we need to describe the nature of the difference and decide how to best use them to describe the effect of the nitrogen reduction program.

For this problem, we are to compare the chlorophyll a concentrations from the three institutions and discuss the differences among them:

• Exploratory data analysis – a summary of data distributions and potential problems with the data.

• A decision on whether a transformation is necessary. In general, we use log-transformation for environmental concentration variables.

• ANOVA to test whether the mean (or median, if log-transformed) varies by institution.

• Present the estimated differences (and interpret the differences in the original concentration scale)

• A short discussion on other factors that may affect the result of this comparison.

 
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