# Paired T-Test

Paired t-test
Very often the two samples to be compared are not randomly selected—they are paired.
To find out whether (and how much) pawpaws inhibit tree regeneration, we are comparing the tree
seedling density of plots with pawpaws to plots without pawpaws. Because other factors like slope,
soils, etc. also influence tree seedling density, it’s important to hold these other factors constant. We
are doing this by comparing the plots with pawpaws to adjacent plots without pawpaws. Thus the plots
are paired by location.
In SPSS, make a bar chart of tree seedling density with and without pawpaws (Graphs; Legacy Dialogs;
Bar). Display the descriptive statistics (Analyze; Descriptive Statistics; Descriptives). Make a histogram
of each variable to see its distribution (Graphs; Legacy Dialogs; Histogram).
Examine the means and standard deviations. Do the means look similar or different? How much
variability is there in the data used to calculate the means? Make an educated guess as to whether the
two means are significantly different (i.e., more different than you would expect by chance if they came
from populations having the same mean and variability). Write down your expectation:
_____________________________________________________________________________________
Now perform a paired t-test. What is the null hypothesis for the test? The alternative hypothesis?
Ho:__________________________________________________________________________________
Ha:__________________________________________________________________________________
Click Analyze; Compare Means; Paired Samples T Test.
Examine the results: t=_____________, df= ______________, P=______________.
Do we reject the null hypothesis? Yes or No
What does the outcome of the paired t-test tell us about the answer to our original ecological question
about pawpaws? Write a results statement in the format: Result (t=___, df=___, P=___; Figure 1). (This
statement refers to your bar chart as Figure 1).