Report to Mentor

INTRODUCTION

The intent of this report is to inform you of my progress on my longitudinal study of the Uca minax fiddler crab species at Spermaceti Cove on Sandy Hook, New Jersey. I will discuss my methods for collecting the data I use to prove or disprove my hypothesis, which is that the population will increase as time goes on, how I organized the data in order to analyze it more efficiently, which statistical methods I used to analyze my data, and finally, what else I still need to complete. 

BODY OF REPORT

Data Collection

This project began in early June, when the fiddler crab counting began, and has continued to present. Since counting has seized in early October, I have began writing my scientific research paper and analyze the amount of fiddler crabs I counted during each counting site through statistics in order to prove or disprove my hypothesis, which is as follows: as the years continue, the amount of Uca minax fiddler crabs at Spermaceti Cove on Sandy Hook, New Jersey will increase. I will do this by taking the baseline data from 2016-2017 and comparing it to the 2017-2018 data, to see if there are any trends.

I researched and read over forty scientific papers and primary sources about the Uca minax fiddler crab, as well as its habitat, the coastal wetland. This helped me to learn more about the species and its environment as a whole. I took notes on all of the sources, which is proving to be very useful during the writing of the paper.

After there were no longer fiddler crabs spotted at the cove, I compiled all of the data into a spreadsheet (see Figure 1) in order to easily see all of the information collected at once.

Figure 1: The table above shows all of the data collected during the 2017-2018 collection year in a neat and organized fashion in order to encourage easy access to the information.

Then, I plotted the amount of fiddler crabs at the cove against the counting session on a line graph (see Figure 2) to see if there were any trends as the breeding season progressed. All of this was useful when I began working on the statistics and raw data analysis.

Figure 2: The line graph above shows all of the counting sessions, from 2016-2018, and the amount of crabs counted at both the North and South sites at Spermaceti Cove.

Statistical Analysis

In order to better see the amount of fiddler crabs counted each counting session, I put the data into bar graphs (see Figures 3 and 4), because the line graphs were not as descriptive as I first imagined they would be.


Figure 3: The above graph shows the amount of Uca minax fiddler crabs counted on both the North and South sides of Spermaceti Cove on Sandy Hook, New Jersey during the 2016-2017 data collection set. This is the baseline data for this longitudinal study.

Figure 4: The above graph shows the amount of Uca minax fiddler crabs counted on both the North and South sides of Spermaceti Cove on Sandy Hook, New Jersey during the 2017-2018 data collection set.


For the raw data analysis portion of this project, I completed a correlation between the temperature of the counting session day against the amount of crabs seen (see Figure 5 for a table of the calculations made for this correlation). The correlation between these two variables was calculated to be .31056; this means there is a slightly positive correlation between the temperature and the amount of crabs counted.

Figure 5: The table above shows all of the necessary calculations in order to derive the correlation between the temperature of the counting day in Celsius against the amount of fiddler crabs counted at both of the counting sites.

Several different types of statistical analysis were conducted in order to see the spread of data among both years of this longitudinal study, 2016-2017 and 2017-2018. These statistics include average number of crabs counted each year, as well as the standard deviation and variance (see Figure 6).

Figure 6: This table breaks up the data from the 2016-2017 and 2017-2018 data collection sets, which are then further broken down into the amount of crabs counted on the North and South side of Spermaceti Cove during each counting session. Then the columns were totaled and the amount of crabs found on each side of the cove were averaged, which was then used to derived the variance and standard deviation of each set. The higher the variance and standard deviation, the bigger the spread of the data, meaning there is a considerably large difference between each counting session and the amount of crabs spotted on each side of the cove.

The higher the variance and standard deviation, the bigger the spread of the data, meaning there is a considerably large difference between each counting session and the amount of crabs spotted on each side of the cove. The variance of both years varied greatly between both sides of Spermaceti Cove. For example, the variance of the North side of the cove during 2016-2017 is 28,835.8, while the variance during 2017-2018 is only 5,586.5, meaning that the amount of crabs counted in the latter data set have values much closer together than in the 2016-2017 data set. On the other hand, the difference in variance between the South side of the cove between both data sets is significantly less, with a variance of 48,062.8 in the 2016-2017 data set and 47,435.1. This means that the amount of crabs spotted on the South side were relatively close to each other each counting session. The same is true of the standard deviation between both sides of Spermaceti Cove, with a bigger difference of standard deviation on the North side than on the South side in both data sets.

I, then, statistically compared the summer months of both data sets, by using the formula [(ED)/N]/sqrt[(ED^2)-(ED)^2/N]/(N-1)N, where ED is the sum of the different counting sessions, (ED^2) is the sum of the square of the different counting sessions, and N is the sample size, or amount of counting sessions being taken into consideration. The months of June, July, and August were compared during the summers of 2016 and 2017, thus the sample size, or N, was 6. Following the formula for conducting a t-test, I subtracted the amount of crabs counted from each counting session in 2016-2017 from the crabs counted from that same session in 2017-2018, and then totaled this. Afterwards, I squared each of my results, and totaled this column (see Figure 7 for my calculations). I plugged my values into a calculator to receive an answer of 1.943.

Figure 7: Above is a table of all of the necessary numbers to conduct a t-test. Here, the value of ED is shown, 1015, and the value of (ED)^2 is also shown, 399203.

N-1 gives me the degrees of freedom, so my degrees of freedom are 5 degrees. Using a t-distribution table (see Figure 8), I found that the t-test number with an alpha level of .05 and 5 degrees of freedom should have been 2.015.

Figure 8: Above is a t-distribution table, which is used for comparing one's calculated t-test value against in order to determine whether or not the null hypothesis is correct.

Since my calculated t-test is lower than the t-table value, the null hypothesis, that there will be no significant change in fiddler crab population as the years progress, should be accepted as true.

SUMMARY

In total, I collected data from June 2017 to the beginning of October 2017 and used statistics in order to compare my data to the baseline data collected during the Uca minax breeding season in 2016-2017. When it comes to the statistics used, I used a t-test to disprove my hypothesis, compared the summer months of both data collecting sets, conducted a correlation between the temperature in Celsius against the amount of crabs counted, and calculated the spread of the crab counts using variance, standard deviation, and average.

Throughout this process, I learned a lot about statistics. I did not know much of anything about this field of mathematics prior to conducting this study. All of the statistics I completed thus far, I have learned to do as I went. 

CONCLUSION

While a lot of work has been completed to date, there is still much to accomplish. For starters, I must write up an abstract, as well as a materials and methods for my paper. The abstract is a brief summary of the subject of the scientific research paper; in this case, it would regard the longitudinal study at Spermaceti Cove on Sandy Hook, New Jersey of the Uca minax fiddler crab species. The materials and methods describes how the project and study was conducted in such detail that it is able to be replicated by the reader. Continuing, I need to write the actual body of the paper in general, as well as including in-text citations of where I found the information I did not think of or discover on my own. All of this work needs to be completed by late May and early June.