Transcript Understanding Your Data

Understanding and Presenting
Your Data
OR
What to Do with All Those
Numbers You’re Recording
Comparison of Means
 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
 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
 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
 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
Example - Sea Slugs
 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
 Based on a journal article you’ve read, and some
preliminary observations, your team predicts that:
 Sea slugs living on a rocky substrate will show more
head bobs/month than sea slugs living on a silty
substrate.
Example - Sea Slugs
 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
 Here are your raw data:
Sea
Slug
1
2
3
4
5
# Head Bobs/Month  Each set (rocky or silty)
Rocky
Silty
of 5 values represents a
3
6
specific sample of sea
1
3
slugs from the two
7
5
5
3
populations of sea slugs
11
15
 Remember, we use the
you are interested in (all
sea slugs living on rocky
sample data to make
substrates or all sea
inferences about the
slugs living on silty
population
substrates)
 Raw data:
Sea
Slug
1
2
3
4
5
# Head Bobs/Month
Rocky
Silty
3
6
1
3
7
5
5
3
11
15
 What would be your first steps in summarizing
these data?
Sea
Slug
1
2
3
4
5
AVG
# Head Bobs/Month
Rocky
Silty
3
6
1
3
7
5
5
3
11
15
5.4
6.3
 The first step would be to
calculate the mean
(average) number of head
bobs/month for each
substrate treatment
 The sample mean is a
measure of the central
 The AVERAGE function
in Excel will calculate
this for you
tendency of a population ;
i.e., where the center of
the population of interest
tends to be located for the
variable in question
Sea
Slug
1
2
3
4
5
AVG
SD
# Head Bobs/Month
Rocky
Silty
3
6
1
3
7
5
5
3
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15
5.4
6.3
3.8
5.1
 The STDEV function in
 The next step would be
to calculate the standard
deviation (SD) for each
substrate treatment
 The SD is a measure of
the dispersion (spread) of
your data; that is, a value
Excel will calculate this
that summarizes how far
for you
individual values are from
the mean value
Sea
Slug
1
2
3
4
5
AVG
SD
SE
# Head Bobs/Month  Another important step is
Rocky
Silty
to calculate the standard
3
6
1
3
error of the mean (SE) for
7
5
each substrate treatment
5
3
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15
5.4
6.3  The SE is a measure of
3.8
5.1
how far the “true”
1.7
2.3
(population) mean is likely
no. of individual s to be from the calculated
SE 
SD
sample mean (remember
the “grain of salt”)
Sea
Slug
1
2
3
4
5
AVG
SD
SE
# Head Bobs/Month
Rocky
Silty
3
6
1
3
7
5
5
3
11
15
5.4
6.3
3.8
5.1
1.7
2.3
 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)
Sea
Slug
1
2
3
4
5
AVG
SD
SE
# Head Bobs/Month  Question for you:
Rocky
Silty
For the silty substrate sea
3
6
1
3
slugs, what is the range
7
5
5
3
within which the
11
15
population mean has
5.4
6.3
3.8
5.1
about a 90% chance of
1.7
2.3
being located?
 1.7 and 10.9 head bobs/month
1.7 = (6.3 - 2*2.3)
10.9 = (6.3 + 2*2.3)
Sea
Slug
1
2
3
4
5
AVG
SD
SE
# Head Bobs/Month
Rocky
Silty
 Once all these statistics
3
6
(mean, SD, SE) have
1
3
7
5
been calculated for your
5
3
sample, the next step is
11
15
5.4
6.3
to visually describe your
3.8
5.1
data
1.7
2.3
 This is done using a figure of the proper sort
# Head Bobs/Month
20
15
Rocky
10
Silty
5
0
1
2
3
4
5
Sea Slug
 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?
# Head Bobs/Month
20
15
Rocky
10
Silty
5
0
1
2
3
4
5
Sea Slug
 What kind of graph would be a better way to
visually summarize on which of the two substrates
sea slugs do more head bobbing?
# Head Bobs/Month
10
8
6
4
2
0
Rocky
Silty
 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?
# Head Bobs/Month
10
8
6
4
2
0
Rocky
Silty
 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?
# Head Bobs/Month
10
8
6
4
2
0
Rocky
Silty
 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
# Head Bobs/Month
10
8
6
4
2
0
Rocky
Silty
 If our data looked like this instead, the SE bars of the
2 groups would not overlap by a substantial amount
 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
# Head Bobs/Month
10
8
6
4
2
0
Rocky
Silty
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)
# Head Bobs/Month
10
8
6
4
2
0
Rocky
Silty
 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
Recap
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
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