SAMPLE REPORT – EXPLANATORY NOTES
The report on the following pages provides a recommended layout for your project reports. It is NOT intended as a perfect report.
• The opening page provides a title, a summary of the aims and a brief coverage of relevant background information followed by findings that highlight important features of the data. It is important to back your findings up with reference to tables and figures in the main body of the report.
• The language on the first page is non-technical to ensure that the information is accessible to a non-statistical readership.
• The body of the report defines the methods employed and describes any new variables that you have created. The results give detail in the form of tables and figures that back up the findings on the first page. All the tables and figures should be clearly labeled and have appropriate titles and captions.
• There is scope for examining the data in many different ways. What is included in this report is not to be taken as covering all possible statistical analyses.
Factors relating to mating success in female crabs Aims
• To identify factors which are related to the number of satellite males for female horseshoe crabs.
• To explore relationships between other characteristics of the female crabs. Background
In female horseshoe crabs of the species Limulus polyphemus there is considerable variation in the number of satellite male associated with each female. The number of satellite males is a measure of breeding success so it is of interest to explore what other characteristics of the female crabs are related to the number of satellite males. This report is based on a dataset containing measurements about a sample of 173 female crabs. For each female crab the number of satellite males was recorded. In addition the weight and width of the female crab was measured and two other characteristics (spine health and color) were recorded.
The data was originally collected in:
Findings
1. Biggercrabs,asmeasuredbybothweightandwidth,generallyhadmoresatellite males (Figure 1). As the width of a crabs shell increased, so did the weight of the crab (Table 1).
2. Asthecolorofthecrabsgoesfromlightesttodarkesttheaveragenumberof satellite males decreases. For instance, the lightest category of crabs had an average of 2 more satellite males than the darkest crabs (Table 2).
3. Crabswithundamagedspineshadanaverageof3.7satellitemalescomparedto 2.0 and 2.8 respectively for crabs with partially damaged or completely damaged spines (Table 2).
4. Lightercolouredcrabsweremorelikelytohaveundamagedspinesthanthedarker crabs, with 75% of the lightest crabs undamaged compared to just 5% of the darkest crabs (Table 3).
Brockmann, H. J. 1996: Satellite male groups
in horseshoe crabs, Limulus polyphemus. Ethology 102, 1–21.
Statistical methods and results Variables
A measure of weight which makes allowance for width variations is computed as ‘crab body mass index’ using the formula CBMI = weight/(width)2.
The lower and upper quartiles of the variable number of males were found using the QUARTILE function. The categorical variable successful was formed from the number of males variable by assigning crabs with a number of satellite males fewer than or equal to the lower quartile to the category “no”, crabs with greater than or equal to the upper quartile to “yes” and all other crabs to “average”. For example, the value of successful for the crab in row 2 of the spreadsheet was calculated using the formula
=IF(G2<=0,"no",IF(G2>=5,”yes”,”average”)) , where column G records the number of males.
Computational methods
All statistical calculations are undertaken using Microsoft Excel 2010.
Pearson product-moment correlations were obtained using the ‘Correlation’ option in the ‘Data Analysis’ tool pack.
Average values of quantitative variables for different combinations of categorical variables were computed as arithmetic means using the ‘Pivot table’ tool.
Counts of crabs having different combinations of categorical variables were computed as counts using the ‘Pivot table’ tool.
The scatterplot was initially constructed using the Chart wizard and the ‘XY(Scatter)’ option and further refined using the Select Data option. Data was pre-sorted on the basis of the variable successful so that three series could be shown on the same plot.
Results
Table 1. Correlation table for scaled variables
weight width CBMI males
weight width CBMI males
1 0.887 0.759 0.369
1
0.389 1
0.340 0.272 1
The number of satellite males has a weak but positive correlation with both weight and width of the female crabs. Weight of the crabs has a strong positive correlation with width of the crabs’ shell. The correlation with the variable CMBI, which attempts to normalize weight by width, is weaker than the correlation with weight or width individually but still positive.
Figure 1
Success as measured by number of satelitte males for different weights and widths of female crab
unsuccessful average successful
34
32
30
28
26
24
22
20
1000 1500
2000 2500
3000 3500 4000
Weight (gms)
4500 5000 5500
Width plotted against weight for 173 female crabs. Each female crab has been allocated as follows: ‘unsuccessful’ crabs (squares) have <1 satellite male, ‘successful’ crabs (circles) have >4 satellite males, and the ‘average’ group of crabs (triangles) have between 2 and 4 satellite males . Weight and width are generally highly correlated although there are several outliers with 3 unsuccessful crabs having unusually low weight for their width and one successful crab having a much higher weight than all the others. There is a higher density of unsuccessful crabs amongst the crabs with low weight and small widths.
Table 2. Average number of males by crab color and spine damage
Average
number of males
colour none one both
(lightest) 2 3
4 (darkest) 5
T otal
4.44 4.50 0.00 3.29 1.75 3.49 5.33 1.75 2.03 0.00 0.00 2.25
3.65 2.00 2.81
T otal
4.08 3.29 2.23 2.05
2.92
Damaged Spines
Average number of satellite males for female crabs with different combinations of color and spine health. The lightest colored female crabs have an average of 2.03 more satellite males than the darkest colored crabs. Female crabs with undamaged spines have more satellite males on average than crabs with damaged spines.
Width (cms)
Table 3. Comparison of crab color and spine damage
No. of crabs colour
(lightest) 2 3
4 (darkest) 5
Total
Damaged Spines one
9 (75%) 24 (25%) 3 (7%) 1 (5%)
37
none
both
1 (8%) 63(66%) 37 (84%) 20 (91%)
121
T otal
12 95 44 22
173
2 (17%) 8 (8%) 4 (9%) 1 (5%)
15
Counts of female crabs with different combinations of color and spine health. Percentages of row totals are shown in brackets. Lighter colored crabs are more likely to have undamaged spines than darker colored crabs.