# Ecology Lab 2 - Analyzing for Differences in annual Tree Growth 2011

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```					Ecology Lab #3 – Analyzing for Differences in Annual Tree Growth
Due: Thursday, Feb. 3 2011 (put in Bill’s mailbox if you wish to submit earlier)
One paper per team

A) Data Collection (each group measures four branches on each of TWO trees):

At each Ponderosa Pine tree, select four branches that are breast high and that are 90 o from each other. Let
the first branch (a) be one closest to the trail, then proceed clockwise 90 o for each of the next three branches
(b, c, d).

On each branch, measure the ACTUAL LENGTH of three youngest internodes. Note that 2010 growth will
be from the tip of the branch back to where the first branches emerge, the 2009 growth will be from this
node back to where the next series of branches emerge, and so on. Calculate the total length of each branch
as indicated in the table.

Tree #: _____

Branch                    2010 Actual             2009 Actual            2008 Actual             Total (cm)
Length (cm)             Length (cm)            Length (cm)
a
b
c
d

Tree #: _____

Branch                    2010 Actual             2009 Actual            2008 Actual             Total (cm)
Length (cm)             Length (cm)            Length (cm)
a
b
c
d

Tree #: _____

Branch                    2010 Actual             2009 Actual            2008 Actual             Total (cm)
Length (cm)             Length (cm)            Length (cm)
a
b
c
d

Tree #: _____

Branch                    2010 Actual             2009 Actual            2008 Actual             Total (cm)
Length (cm)             Length (cm)            Length (cm)
a
b
c
d
Tree #: _____

Branch                  2010 Actual          2009 Actual         2008 Actual           Total (cm)
Length (cm)          Length (cm)         Length (cm)
a
b
c
d

B) Data Scaling.

Using a calculator, calculate a SCALED LENGTH for each year’s growth on a branch. Do this by dividing
the ACTUAL LENGTH of each year’s growth by the TOTAL for that branch, then multiplying by 100.
Finally, calculate the MEAN (= average) scaled length for each year’s growth.

Tree #: _____

Branch                  2010 Scaled          2009 Scaled         2008 Scaled          Total Scaled
Length (cm)          Length (cm)         Length (cm)          Length (cm)
a                                                                  100
b                                                                  100
c                                                                  100
d                                                                  100
Mean

Tree #: _____

Branch                  2010 Scaled          2009 Scaled         2008 Scaled          Total Scaled
Length (cm)          Length (cm)         Length (cm)          Length (cm)
a                                                                  100
b                                                                  100
c                                                                  100
d                                                                  100
Mean

Tree #: _____

Branch                  2010 Scaled          2009 Scaled         2008 Scaled          Total Scaled
Length (cm)          Length (cm)         Length (cm)          Length (cm)
a                                                                  100
b                                                                  100
c                                                                  100
d                                                                  100
Mean
Tree #: _____
Branch                       2010 Scaled       2009 Scaled          2008 Scaled          Total Scaled
Length (cm)       Length (cm)          Length (cm)          Length (cm)
a                                                                     100
b                                                                     100
c                                                                     100
d                                                                     100
Mean

Tree #: _____

Branch                       2010 Scaled       2009 Scaled          2008 Scaled          Total Scaled
Length (cm)       Length (cm)          Length (cm)          Length (cm)
a                                                                     100
b                                                                     100
c                                                                     100
d                                                                     100
Mean

C) Data Compilation (= Pooling of Data)

Obtain mean values for 2009, 2008 and 2006 growth for each of your trees and fill in the box below. These
are the data you will use in your data analysis.

Tree #       Mean 2010 Scaled        Mean 2009 Scaled           Mean 2008 Scaled
Length (cm)             Length (cm)                Length (cm)
1
2
3
4
5
D) Data Analysis.

You will now test whether or not a difference exists somewhere among 2009, 2008 and 2006 twig growth.

    Enter LAST THREE columns in the data compilation table above (including column labels) into
    Select Data, Data Analysis, ANOVA: Single Factor
    For Input Range, highlight all data (including column labels)
    Select alpha = .05
    Indicate that the highlighted area has labels
    Select a blank area of spreadsheet for Output
    Examine your output. Write down the value of F, the Between Group df, the Within Group df, and
the p-value. [Note: If the p-value reads something like 5.59E-07, this means 5.59 x 10-7 =
.000000559.
    If the p value > .05, conclude that the null hypothesis, i.e., twig growth among the years 2009,
2008, 2006, is true. You are done with statistical analysis.
    If the p value ≤ .05, reject the null hypothesis and conclude that the data support an alternate
hypothesis that a difference exists somewhere among twig growth in 2009, 2008 and 2006. [We
will learn how to pinpoint the location of this/these differences next week]
E) Write a summarizing paragraph as follows ..

We tested for differences in twig growth in ponderosa pine trees at Little Walnut Picnic Area among the
years 2010, 2009 and 2008. To do this, we conducted a single factor Analysis of Variance (ANOVA). We
conclude (F = 2.01, df = 2, 18, p = .45) that the data support our null hypothesis of no difference in twig
growth among the three years.

OR

We tested for differences in twig growth in ponderosa pine trees at Little Walnut Picnic Area among the
years 2010, 2009 and 2008. To do this, we conducted a single factor Analysis of Variance (ANOVA). We
reject (F = 12.3, df = 2, 18, p = .02) the null hypothesis and conclude that a difference in twig growth exists
somewhere among the three years.

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