Results

            All of the data that was recorded from the field research in Nahant was entered into an excel spreadsheet for further analysis (Table 1).  While in the field, the amount of wave exposure was recorded on a scale from 0-10.  In order to keep the samples completely random and unbiased, the observations were changes from the 0-10 scale to a simpler classification as either: sheltered, moderate, or severe ocean exposure. 

            Furthermore, after all the recorded data from Nahant was entered into a spreadsheet, the photographs of the barnacle quadrats had to be counted to obtain a measure of density.  In order to be as accurate as possible, the photos were counted using Microsoft paint.  For each quadrat, the number of live, dead, and total barnacles was counted and recorded (Table 2).  Once all the quadrats were counted it was possible to obtain a measure of barnacle density in each quadrat.  The density of barnacles was calculated by first converting the average sizes obtained from millimeters to centimeters.  This value was then divided by 2 to determine the radius of the operculum.  The formula for the area of a circle, πr², was used to determine the area of the average operculum.  This area was then multiplied by the number of live barnacles specific to that quadrat.  Since the quadrat was 25cm x 25cm, the area of the quadrat was calculated to be 625cm².  Thus, the percent cover of live barnacles in a given quadrat was determined by dividing the area of live barnacles by the total area of the quadrat, and multiplying that number by 100%.  A simplified illustration of the math is shown below:

         Area of operculum = πr²                            (πr²) x (# of live barnacles) = Area of live barnacles within quadrat

 (25cm) x (25cm) = 625cm²

            Both the percent cover and the average size of the barnacles (mm) were analyzed for any correlation with the 6 different variables that examined: slope, direction, wave exposure, intertidal range, temperature, and substrate surface.  First, a regression analysis was performed for the percent cover with each of the six variables mentioned above.  The results were summarized and the significant values are shown below (Table 3).  An addition regression analysis was also performed for the average size of the barnacles with each of the six variables (Table 4).   
           

Regression Analysis Summary Using the Average Size (mm) of the Barnacles
Variable	F	df	P Value	R² Value
Slope	4.982532966	44	0.030866132	0.103840557
Direction	1.187516961	44	0.281900446	0.02687449
Wave Exposure	13.62185444	44	0.000625087	0.240575915
Intertidal Range	0.453871444	44	0.504107614	0.010444902
Temperature	2.83231701	44	0.099633274	0.061797378
Substrate Surface	0.510918476	44	0.482829485	0.011742305

Table 4: The table above shows the significant values for each regression analysis for average barnacle size(mm) that was performed.  The values of significance that are summarized above are: the F values, the degrees of freedom (df), the P value, and the R² Value.    
   

            In addition to performing a regression analysis for both percent cover and average size of the barnacles, the data of each was plotted to determine any additional correlations that could be determined.  Not all graphs are included because some of them did not show any correlation between percent cover or average size and the six different variables.  By comparing the percent cover with the slope values, it appeared that some slopes were favored over others (Graph 1).  When comparing the directions with the percent cover it also appeared that some directions had a higher percent cover than others (Graph 2).  The intertidal range of the barnacles was recorded as low, mid, and high.  The comparison of this location within the intertidal zone with the percent cover showed a higher percent cover in the mid and high zones (Graph 3).  It is important to note these comparisons because the obtained P values for these variables indicate that there is no correlation.  The P values obtained for both wave exposure and substrate surface show that there is a significant correlation with the percent cover.  By comparing wave exposure with percent cover, it appears that that greater wave exposure correlates with increased percent cover (Graph 4).  Also, when comparing the surface of the substrate with the percent cover it appears that rough surfaces have a higher percent cover than smooth surfaces (Graph 5).             
          
            Comparisons between average barnacle size and all six variables were also performed.  There appears to be a possible correlation between the East and South directions and average size (Graph 6).  The recorded values for temperature, intertidal range, and substrate surface were all compared with average size, but there appeared to be no significant correlations.  From the regression analysis data in table 4 above, there is a significant correlation between both slope and wave exposure.  When comparing the slope with the average size it appears that may be some correlation, but it difficult to determine and more data points are needed (Graph 7).  The regression analysis of average size and wave exposure yielded a very low P value.  This indicates that there is a very strong correlation between exposure and the size of the barnacles.  When the two were compared, the strong positive correlation could be seen (Graph 8).