2. Understanding and Presenting Your Data OR What to Do with All Those Numbers You’re Recording

3.  The primary question underlying many biology experiments is whether, on average, one condition (treatment) has a greater effect on a certain variable than another condition  This type of question is answered by comparing the mean (average) response of a group of organisms under two or more treatments  Does your experiment involve this kind of question? Comparison of Means

4.  If we could measure the variable of interest in every animal from our chosen population (for example, a species exposed to a certain treatment) we could calculate the variable’s “true” mean (average of all individuals) in that population  If we did this for each population we wanted to compare, we could tell for sure whether these populations differed by seeing if their “true” means differed for the variable in question Comparison of Means

5.  As you might guess, it would be impossible to measure each individual of each population involved in our hypothesis!  We solve this problem by measuring a very small, but representative, subset of each relevant population  This specially selected subset is called a sample  We use data from a sample to make inferences (predictions) about the population Comparison of Means

6.  Because a sample is so much smaller than the population from which it is taken, the values we calculate from the sample (for example, the sample mean) should be “taken with a grain of salt” when using them to predict population values  Statistics is a set of calculations and rules that tell us how probable it is that our sample-based predictions will hold true for the population  Now we’ll discuss an example where we use statistics to test a hypothesis about sea slugs

7.  Say that you have observed sea slugs for some time and noticed that these slow-moving animals signal their readiness to mate by performing a simple “head bob”  Your team wants to determine what factors have the greatest effect on how often this simple courtship display occurs in sea slugs Example - Sea Slugs

8.  Based on a journal article you’ve read, and some preliminary observations, your team predicts that: Example - Sea Slugs  Sea slugs living on a rocky substrate will show more head bobs/month than sea slugs living on a silty substrate.

9.  To test this hypothesis, you randomly select 5 sea slugs for each of two treatment tanks - one with a rocky substrate and one with a silty substrate  For 1 month, you record the number of head bobs that you see during observation periods for each sea slug and then calculate the number of head bobs/month for each slug Example - Sea Slugs

10.  Here are your raw data:  Each set (rocky or silty) of 5 values represents a specific sample of sea slugs from the two populations of sea slugs you are interested in (all sea slugs living on rocky substrates or all sea slugs living on silty substrates)  Remember, we use the sample data to make inferences about the population

11.  Raw data:  What would be your first steps in summarizing these data?

12.  The first step would be to calculate the mean (average) number of head bobs/month for each substrate treatment  The AVERAGE function in Excel will calculate this for you  The sample mean is a measure of the central tendency of a population ; i.e., where the center of the population of interest tends to be located for the variable in question

13.  The next step would be to calculate the standard deviation (SD) for each substrate treatment  The STDEV function in Excel will calculate this for you  The SD is a measure of the dispersion (spread) of your data; that is, a value that summarizes how far individual values are from the mean value

14.  Another important step is to calculate the standard error of the mean (SE) for each substrate treatment  The SE is a measure of how far the “true” (population) mean is likely to be from the calculated sample mean (remember the “grain of salt”)

15.  For small samples (such as ours), the range of values 2 standard errors (2*SE) on either side of the sample mean has about a 90% chance of containing the “true” (population) mean  Thus, for the rocky substrate sea slugs, the population mean has about a 90% chance of being between 2.0 and 8.8 head bobs/month 2.0 = (5.4 - 2*1.7) 8.8 = (5.4 + 2*1.7)

16.  Question for you: For the silty substrate sea slugs, what is the range within which the population mean has about a 90% chance of being located?  1.7 and 10.9 head bobs/month 1.7 = (6.3 - 2*2.3) 10.9 = (6.3 + 2*2.3)

17.  Once all these statistics (mean, SD, SE) have been calculated for your sample, the next step is to visually describe your data  This is done using a figure of the proper sort

18.  This column graph shows the value for each sea slug from each substrate tank  Can you tell on which substrate sea slugs show more head bobs per month?  What is the meaning of the sea slug # on the X-axis?

19.  What kind of graph would be a better way to visually summarize on which of the two substrates sea slugs do more head bobbing?

20.  This column graph shows the sample mean for each substrate group  Now can you tell on which substrate sea slugs show more head bobs per month?  Is the answer completely clear or could two reasonable people disagree?

21.  If you measured 5 other sea slugs in each of the two substrate tanks would the sample means be the same as in the first experiment?  What could you add to this graph to give a sense of how well these sample means predict the mean of the population from which they come?

22.  Now we’ve added error bars representing 1 SE on either side of the sample mean  Even though the means of these two samples differ, because the SE bars for the two groups overlap (the upper bar for rocky overlaps the lower bar for silty), we have no good evidence that the “true” means for the rocky and silty substrates actually differ

23.  In this case, we would have fairly certain evidence of a difference between groups -- that is, that the “true” means for the rocky and silty substrates differ  If our data looked like this instead, the SE bars of the 2 groups would not overlap by a substantial amount

24. Rules of thumb for using SE bars to judge significant diffs :  Two means will never be significantly different if:  their SE intervals overlap -- at all  the gap between the two SE intervals is < 1/3 the length of the shorter SE interval  When the gap between the two SE intervals is > 1/3 the length of the shorter SE interval, the two means may be significantly different (you will need to use a statistical test to know with more certainty)

25.  Thus, SE bars give us an accepted standard for judging how certain we are that two treatments produce different effects on the variable of interest  In other words, two reasonable people should now agree that substrate type does not produce a significant difference in the number of head bobs per month in sea slugs

26. Once you have collected your raw data:  calculate the mean, standard deviation (SD), and standard error of the mean (SE) for each treatment group sample  graph the mean values for each treatment group in a column graph, adding error bars above and below the mean equal to 1 SE  use the rules of thumb about SE interval overlap to determine how probable it is that any means you are comparing are actually different Recap

27. How to Get the PP Presentation  Website where PowerPoint file “Understanding and Presenting Your Data” can be downloaded: http://minerva.stkate.edu/offices/academic/ biology.nsf/pages/myersgb  Tutorial Written By:  Dr. Marcie J. Myers  College of St. Catherine  St. Paul, MN