understanding and presenting your data or what to do with all those numbers you’re recording

Understanding and Presenting Understanding and Presenting Your DataYour Data

OR

What to Do with All Those What to Do with All Those Numbers You’re RecordingNumbers You’re Recording

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

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

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:

Example - Sea Slugs

Sea slugs living on a rocky substrate will show

more head bobs/month than sea slugs living

on a silty substrate.

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

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

Sea # Head Bobs/MonthSlug Rocky Silty

1 3 62 1 33 7 54 5 35 11 15

Raw data:

What would be your first steps in

summarizing these data?


1 3 62 1 33 7 54 5 35 11 15

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


1 3 62 1 33 7 54 5 35 11 15

AVG 5.4 6.3 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

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


1 3 62 1 33 7 54 5 35 11 15

AVG 5.4 6.3SD 3.8 5.1

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

Another important step is

to calculate the standard

error of the mean (SE) for

each substrate treatment

s individual of no.

SDSE


1 3 62 1 33 7 54 5 35 11 15

AVG 5.4 6.3SD 3.8 5.1SE 1.7 2.3

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”)

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)


1 3 62 1 33 7 54 5 35 11 15

AVG 5.4 6.3SD 3.8 5.1SE 1.7 2.3

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)


1 3 62 1 33 7 54 5 35 11 15

AVG 5.4 6.3SD 3.8 5.1SE 1.7 2.3

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


1 3 62 1 33 7 54 5 35 11 15

AVG 5.4 6.3SD 3.8 5.1SE 1.7 2.3

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?

What kind of graph would be a better way to

visually summarize on which of the two

substrates sea slugs do more head bobbing?

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?

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?

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

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

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)

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

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

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

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