The article “Effects of Short-Term Warming on Low andHigh Latitude Forest Ant Communities” (Ecoshpere,May 2011, Article 62) described an experiment in which observations on various characteristics were made usingminichambers of three different types: (1) cooler (PVCframes covered with shade cloth), (2) control (PVC framesonly), and (3) warmer (PVC frames covered with plastic).One of the article’s authors kindly supplied the accompanyingdata on the difference between air and soil temperatures(°C).Cooler Control Warmer1.59 1.92 2.571.43 2.00 2.601.88 2.19 1.931.26 1.12 1.581.91 1.78 2.301.86 1.84 0.841.90 2.45 2.651.57 2.03 0.121.79 1.52 2.741.72 0.53 2.532.41 1.90 2.132.34 2.860.83 2.311.34 1.911.76a. Compare measures of center for the three differentsamples.b. Calculate, interpret, and compare the standard deviationsfor the three different samples.c. Do the fourth spreads for the three samples conveythe same message as do the standard deviationsabout relative variability?d. Construct a comparative boxplot (which was includedin the cited article) and comment on any interestingfeatures.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The article “Effects of Short-Term Warming on Low and
High Latitude Forest Ant Communities” (Ecoshpere,
May 2011, Article 62) described an experiment in which
observations on various characteristics were made using
minichambers of three different types: (1) cooler (PVC
frames covered with shade cloth), (2) control (PVC frames
only), and (3) warmer (PVC frames covered with plastic).
One of the article’s authors kindly supplied the accompanying
data on the difference between air and soil temperatures
(°C).
Cooler Control Warmer
1.59 1.92 2.57
1.43 2.00 2.60
1.88 2.19 1.93
1.26 1.12 1.58
1.91 1.78 2.30
1.86 1.84 0.84
1.90 2.45 2.65
1.57 2.03 0.12
1.79 1.52 2.74
1.72 0.53 2.53
2.41 1.90 2.13
2.34 2.86
0.83 2.31
1.34 1.91
1.76
a. Compare measures of center for the three different
samples.
b. Calculate, interpret, and compare the standard deviations
for the three different samples.
c. Do the fourth spreads for the three samples convey
the same message as do the standard deviations
about relative variability?
d. Construct a comparative boxplot (which was included
in the cited article) and comment on any interesting
features.
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