Raw Data Analysis

Raw Data Analysis

Graphs

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.
The above graph shows the amount of Uca minax fiddler crabs counted on bot the North and South sides of Spermaceti Cove on Sandy Hook, New Jersey during the 2017-2018 data collection set.
The above line graph shows the amount of fiddler crabs counted on the North side of Sperrmaceti Cove on Sandy Hook, New Jersey throughout the two years that this study has been conducted, from 2016-2018.

Correlation Between Temperature and Crabs Counted

Calculating the correlation between the temperature and number of crabs gives me more information about the Uca minax fiddler crab population on Sandy Hook. The following is a equation for correlation: AB/sqrt(A^2)(B^2). The column X represents the temperature at the time of counting, while column Y shows the amount of crabs counted. Columns A and B represent the numbers one gets when he or she subtracts the mean temperature or crabs counted from the day's temperature or day's count, respectively. Column AB is what one receives when he or she multiplies A and B of the same day, A^2 is the square of that day's A, and B^2 is the square of that day's B.

Above is a table of all of the numbers necessary to calculate the correlation between temperature and amount of crabs counted.

Using these numbers, I calculated a .31056 correlation between temperature and amount of crabs counted. To put this number into perspective, 1 is a perfect positive correlation, 0 is no correlation, and -1 is a perfect negative correlation. With this being said, temperature and the amount of crabs counted has a slightly positive correlation. 

Calculating Data Spread

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.

Statistical Comparison of the Summer Months

I was able to discover whether or not my null hypothesis should be accepted or voided by using a t-test. The formula is as follows: [(ED)/N]/sqrt[(ED^2)-(ED)^2/N]/(N-1)N. 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. I made a chart of the six dates in the 2016-2017 data set and the six dates in the 2017-2018 data set that took place during June, July, and August, with the amount of crabs counted during each of the sets during each of the dates. Since there are six counting sessions being analyzed, N=6 in the formula.

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.
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. I then plugged my values into a calculator to receive an answer of 1.943. N-1 gives me the degrees of freedom, so my degrees of freedom are 5 degrees.

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.
Using the t-test table, shown above, I found that the t-test number with an alpha level of .05 and 5 degrees of freedom should have been 2.015. 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.

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