Bios 331: Ecology
FORAGING EXPERIMENT DATA ANALYSIS
DESCRIPTIVE STATISTICS
To begin, you need to organize the data in your Excel spreadsheet to facilitate the analyses (Table 1). Then use the Excel functions to calculate means and standard error.
Day
Rich Food/ Risky place (e.g., away from tree)
Rich Food/ Safe place (e.g., nearer to tree)
Poor Food/ Risky place
Poor Food/ Safe place
Giving-up densities (grams)
1
5
1
4
5
2
6
2
8
5
3
7
3
8
5
Average
St. Error
Table 1. Example data table. Notice that there are two variables (Food Type & Spatial Location) each with two levels (Rich food vs Poor Food & Risky Place vs Safe Place). This means that there are four possible conditions, as expected of a 2×2 Factorial Design.
To calculate the average, you can use the Excel function “=AVERAGE(B4:B6)”. In the parentheses, select the cells you wish to calculate an average from. In this example, my data was in cells B4, B5, and B6.
Unfortunately, there is no function to calculate standard error, but recall that this statistic is calculated by dividing the standard deviation by the square root of the number of replicates. In other words: “=STDEV(B4:B6)/SQRT(COUNT(B4:B6))”
STDEV: Calculates Standard Deviation
SQRT: Calculates the Square Root
COUNT: Counts the number of Cells
Recall that experimentally you used a 2×2 factorial design. We have two factors (food quality and spatial location) and two levels of each factor (e.g., poor and rich for food quality). The design is factorial because we have a treatment for each possible combination of the levels of the two factors. This type of experimental design allows us to test the effect of food quality, spatial location of trays, and their interaction, on the foragers’ giving up density (GUD). An interaction describes non-additive effects of the two independent variables (e.g., food quality and spatial location) on the dependent variable (that is, GUD, the leftover food).
Before you perform the statistical tests of your hypotheses, you should graph your data to get an idea of the trends in the data set. This data set can easily be visualized using a bar graph with standard error bars (Figure 1).
Figure 1. Example GUD figure. Notice that one of the variables is illustrated on the x-axis and the other one as a legend. We could flip these variables to make the food type appear as the legend and the spatial location on the x-axis and it would not affect the result. Error bars represent standard error.
HYPOTHESIS-TESTING STATISTICS
To test your hypotheses about each factor and interaction between them, we can use ANOVA (analysis of variance). To conduct an ANOVA follow these steps:
Go to http://vassarstats.net/
On the left, click on “ANOVA”
Click on “Two-Way Factorial ANOVA for Independent Samples”
Scroll down to “Number of rows in analysis =” and type “2” in the box.
Scroll down to “Number of columns in analysis =” and type “2” in the box.
Click on “Setup”
Click on “Weighted”
Paste your raw data into the yellow boxes (Figure 2).
Click on “Calculate”
Scroll down to the box that says “ANOVA Summary”
The values for “Rows” correspond to the variable that varies by row. In my case, what differ between Row 1 and Row 2 is spatial location. Same logic for “Columns”. The “r x c” is telling you whether your variables interact or have additive effects (Table 2).
Figure 2. This is what the window where you input your raw data will look like. Make sure you know what box will hold what (example on the left) data so you can interpret the output later.
Source
SS
df
MS
F
p
Rows
10.08
1
10.08
5.5
0.047
Columns
24.08
1
24.08
13.13
0.0067
r x c
4.09
1
4.09
2.23
0.1737
Error
14.67
8
1.83
Total
52.92
11
Table 2. This is what our example data ANOVA Summary table looks like. I know that “Rows” corresponds to Spatial Location and “Columns” to Food Type because that is how we input the data earlier.
You will need the three F-values (F), Degrees of Freedom (df), and p-values (p) from the ANOVA summary table.
INTERPRETING AND WRITING STATISTICS
If your p-value is below 0.05, then conclude that there is a significant effect of the factor. For example, spatial location on the rows has a significant effect. Now look at your graph and see if the direction of the effect agrees with your hypothesis. In this example, increased distance from the tree yielded higher GUDs. In the lab report, you will report this result in a sentence with the relevant statistical values in a parenthesis at the end.
For example: “Average GUDs were higher when the trees were placed closer to the trees (F = 5.5, df = 1, p = 0.047).”
Note that the interaction (r x c) is not significant. This means that although food quality and patch location are significant, their effects are largely additive.
THE LAB REPORT
This is basically a short research paper, rather than a lab report, but you still use the Lab Report Guides available on Blackboard to structure your paper. It should be only up to 4-5 pages including one figure and one table with your raw data included in the Appendix section.
Introduction: There should be an introduction that states the importance and aims of the study. It gives some background on working with giving-up-densities (what a GUD is and why it is useful) and presents the three hypotheses that you tested.
Methods: Write all about the design and how you ran the experiment and the analysis (i.e., what descriptive and hypothesis-testing statistics did you use?)
Results: State the results in declarative ways without discussing what they mean. Do however interpret your statistics as outlined above. Include your figure in this section.
Discussion: Discuss your results and compare them to studies from literature (e.g., what do your results mean, what are the main conclusions, what did you learn about the rabbits or sparrows).
Literature Cited: Use at least 3. Arrange them in alphabetical order, and make sure to follow the instructions from Assignment 2. Also make sure that you actually cite them in the text!
Appendix: Include your raw data as a table here.
There’s no need for an Abstract, but make sure you make up a short title with a declarative statement about the experiment you performed.
Important notes:
Although team members will be using the same data, when it comes to writing the report for the experiment each person must write his or her own report.
Upload your completed report to Safe Assign on Blackboard.
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