Statistical Methods

Statistical Methods

As this is a longitudinal study, many data sets over the years must be analyzed in order to prove or disprove the hypothesis. The 2017-2018 data set will be compared to the baseline data set that was compiled between 2016 and 2017. As the years progress and this project continues to be conducted, more and more data will be compiled, allowing the conclusions to the experiment to be backed by more data.

Normal distribution will be used in order to see if there are any outliers in the data, or any unusually high or low counts. These outliers have the potential to throw off the data analysis. Standard deviation and variance alike will be useful when determining either the spread or the closeness of the data points. A higher standard deviation means that there is more spread among the data, decreasing the potential for correlation among the data set. This indicates that there would be a smaller chance of a trend among the data. Variance is the distance each data point is from the mean. In just the same manner, a higher variance means there is more spread among the data.

The hypothesis of this project is as follows: as the years progress, the population of Uca minax fiddler crabs at Spermaceti Cove on Sandy Hook, New Jersey will increase. To validate either this hypothesis or the null hypothesis, which claims that there will be no change in the population of Uca minax species as the years progress, many different hypothesis tests must be conducted, such as p-scores, t-tests, and z-scores. P-scores are useful when determining whether or not to accept the null hypothesis. If the p-score calculated is less than or equal to .05, then the null hypothesis should be rejected. On the contrary, if the p-score is greater than .05, then the null hypothesis should be accepted and the hypothesis should be rejected.

Continuing, the amount of error in the experiment and statistical analysis must be calculated to show the accuracy or inaccuracy of the study as a whole. Margin of error is inversely proportional to confidence levels, meaning that if there is a high margin of error, there is a low confidence level, thus the experiment is less accurate. The following formula is used to calculate margin of error, where p is the percent confidence interval and n is the sample size: √p(1-p)/n.

Using a line graph to plot the date of the counting sessions against the amount of Uca minax fiddler crabs counted allows one to see the fluctuations in the population as time progresses and derive any trends. A bar graph may also be used to show this in order to make the data more visually appealing for the viewer.