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| Fig. 1. Mean growth rate for ten Acer palmatum seedlings. Measurements began one week following germination. Height was measured as the distance from soil level to base of the top leaf of the seedling. |
We have made the fonts uniform in style and size, there are fewer numbers indicating the axis scale, and the scales do not extend far beyond the range of either variable. These changes simplify the presentation, making it easier to see the relationship itself.
When we collect replicate data and then report mean values, we are usually obligated to report a measure of experimental error, that is, a measure of the tendency of the data to deviate from the mean. For a more complete story behind errors and their representation see our document on error analysis and significant figures [http://www.owlnet.rice.edu/~labgroup/pdf/references.htm] or, better, consult a good introductory statistics test or take a basic statistics course. Meantime, here are three formulas with which we are concerned when working with figures.
sample mean |
sample standard deviation |
s.e.m. |
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If you look past the mathematical symbols you will recognize the first expression as the formula for the average, or mean (
). The second expression is the formula for sample standard deviation (sx). Provided that the sampled data are distributed randomly, if the measurement is repeated many times then approximately 68% of the measured valves will fall in the range± sx.
Sx is a realistic estimate of the influence of random error on a collection of data. It gives us a measure of confidence that the mean value is close to the true mean for the population of data that were sampled. In our example, if we sampled all of the seedlings then we would be sampling the entire population. We usually report a mean value with its corresponding standard deviation when we describe data in text or in a table. For example, you would write, "Seedlings reached a mean height of 5.9 ± 1.9 inches after 13 weeks of growth. When data are presented this way the reader can assume that the error is the sample standard deviation, unless it is otherwise noted. Notice that these data were rounded to two significant figures.
The third expression describes what is commonly known as the standard error of the mean (s.e.m.), although it is more properly called the standard deviation of the mean. As you will see in a moment, the s.e.m. (symbol,
) gives a better measurement of confidence in the mean value of a sample than does the standard deviation.
Now it is your turn. Complete the sentence in quotation marks below. For the study, mean weight losses for group 1 and 2 were 7.3 and 11.1 pounds, respectively, with respective sample standard deviations of 2.4 and 2.7 pounds.
"The average weight loss for individuals in group 1 was pounds compared with for group 2."
NOTE: If you study statistics you find the symbol 
used
for standard deviation, and the symbol 
used
for standard error of the mean. The formula for substitutes
N for (N-1). is
the theoretical standard deviation. The sample standard
deviation sx approaches as
N approaches infinity. For realistic sample sizes, sx is
a more realistic estimate of the error.
Time is the independent variable, to be plotted on the x axis; height (a measured quantity) is a dependent variable, to be plotted on the y axis.
A good choice for plotting these data is to use a scatter plot (XY scatter) of mean values verus time, rather than a scatter plot of raw data; other plot types are not suitable for this kind of data set.
"Computer clutter" should be replaced by X and Y axis labels, a figure caption, and perhaps an appropriate trend line.
A good caption includes just enough information to permit it to stand apart from text.