Abstract

The intent of this report is to compare 2 different variables’ means in order to test whether or not there is a significant difference in them. T-tests are performed in Stata in order to obtain results. The significant results of this report are that the differences in the means between 2012 and 2017 are statically significant, as are the means of dissolved oxygen at the top and bottom of the testing location.

Introduction

While the previous report focused on creating confidence intervals for the population means of the variables, this report goes further in estimating the differences in those means and confidence intervals in order to better understand the New York Harbor Data Set, and water quality in general [1]. This report will also be examining the amount of dissolved oxygen (mg/L) at the tops and bottoms of test locations during 2012 and 2017. This is an important variable to be consistently measuring in order to ensure the sustainability of aquatic life [2].

Methods

In order to use the paired ttest method of comparing sample means, we must first make sure that the data we are analyzing is close to being normally distributed. I have elected to use histograms of the data graphed against the theoretical normal distribution. These figures are presented in the following Results and Discussions section. Because the higher number of observations in this data set, we can expect that the data be close to normal due to the central limit theorem. After analyzing the data, paired t-tests were performed on the 2012 top and bottom data, the 2017 top and bottom data, thr 2012 top and 2017 top data, and finally the 2012 bottom and 2017 bottom data. The are good choices because it allows the viewer to see the difference in dissolved oxygen depending on the depth of the water, and also the change in dissolved oxygen at the same depth over 5 years.

Results and Discussion

The distributions of the data are presented below:




The distributions are mostly normal with some minor flaws, which should not affect the validity of using the paired t-test to compare means.
The t-tests were performed and produced the following 4 results:

Based on Table 8, we can see that all four tests display extremely high t-values which indicate that we can reject the null hypothesis that the difference in means is 0. This implies a few different things. The first is that the difference in dissolved oxygen measure at the top and bottom are greatly different. This could mean that aquatic life that requires a higher amount of oxygen would likely exist closer to the surface of the water, while life that does not require as much oxygen may likely be found towards the floor of the body of water. The second implication is that over the past 5 years, there has been a significant increase dissolved oxygen levels both at the top and bottom of the harbor. Generally, this is a good thing as dissolved oxygen helps sustain life and promote the decay of organic materials[2].This could also cause a change in where certain aquatic life will form their habitats, if lower depths of water now have enough oxygen to support life that it once could not, this could lead to changes in the overall ecology of aquatic life.

Conclusion

Based on the results of this report, it is nearly certain that there is a difference in the means of dissolved oxygen in the top and bottom depths of the test locations, and that over time, these values have significantly increased. While the data does not perfectly fit the assumptions of using the ttest, it is close, and no data set will ever be perfect. If continuing this research, I would try to obtain data from a major city in China and compare that data with the presently used data, this would tie in nicely with the previous work in this overall report, and allow for more scientific comparison between the two countries rather than simply relying on year as the only regressor.

References

[1]“Harbor Water Sampling Data.” Gowanus Canal – History, www.nyc.gov/html/dep/html/harborwater/harbor_water_sampling_results.shtml.
[2] “What Is Dissolved Oxygen in Water?” Environmental Measurement Systems, 4 Feb. 2014, www.fondriest.com/news/whatisdissolvedoxygen.htm.