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Statistical Analysis of Woody Plant Communities Across Different Plots using ANOVA

## What data do we have?

In this week’s lab, we will analyze our PHAE data, comparing woody plant communities across our different plots from all sites and lab sections. Your tasks for lab are to complete the statistical analyses and make the figures described in this packet. In addition, you will decide as a class on additional analyses/comparisons that you would like to make using our data, and complete those analyses. At the end of lab, you will submit an Excel sheet with all your calculations, analyses, and figures. You will use these analyses and figures as the basis of a written paper on this project (due on your lab day in Week 9, October 26-28).

Remember that we started with the following information in each plot: (1) Identity of each woody plant; (2) DBH of each woody plant; (3) % human-made structures in the viewscape; (4) % impervious surface If we want to compare plots, we first need to summarize the characteristics of each plot. For instance, we might want to examine the relationship between abundance of human-made structures and number of plants in the plot. To do that, we would need to calculate these summary values within each plot (How many woody plants in total? What’s the average of the 36 viewscape measurements?), and then use a statistical analysis to quantify the relationship between those variables.

Alternatively, we might want to see if the number of species per plot differs across our three site types (campus, old golf course, and forest). To do that, we would need to calculate the number of species in each plot, and use a statistical analysis to compare the three groups.  These summary calculations have already been completed, so you can focus on making comparisons among plots in this lab. As a class, you will discuss an analysis strategy for your data, and then work in groups to complete these analyses. You will submit these analyses and associated figures at the end of the class. You will decide as a group on any additional analyses or plots beyond those outlined here. Your analyses and plots will become part of the scientific paper that is a major assignment for this lab course. More information on the paper will be provided separately.

A file containing

Your ANOVA results for # trees in the three plot types, with bar graph

Your ANOVA results for DBH in the three plot types, with bar graph

A scatterplot relating species richness to % impervious surface

A scatterplot relating species richness to % human impact

You should also keep a copy of this file so you have these analyses and figures for your lab report.

We will use a type of statistical analysis called analysis of variance (ANOVA) to compare our plot types. The instructions below explain how an ANOVA works, and how you will conduct this analysis, using some example data. There are then specific instructions on what you should do with your PHAE data. In addition to the analyses described here, as a class, you will discuss any additional analyses you might wish to make, and your instructor will provide guidelines.

ANOVA stands for Analysis of Variance. We use this statistical test to compare multiple groups of measurements of a continuous variable, to help us infer whether those groups are different.

For now, assume there’s no difference among our three forests – in other words, if we had measured every single tree, the average tree diameter would be the same for each forest. (This is our null hypothesis.)

What is the probability that we’d get the differences among forests we see in our dataset, if the null hypothesis is really true? In other words: if all three forests really have the same average tree diameter (if I’d measured every single tree), what is the probability (when I’m sampling 5 plots per forest) that I would find a range of observed averages across forests like in the table above?

ANOVA calculates this probability for you, based on the differences in mean values among each of your groups, and the variation in individual values within each of those groups. We call the probability the p-value.

We then make conclusions based on that probability. If that probability is very low, we conclude that we reject the null hypothesis, and say that there is a statistically significant differenceamong the three forests.