Statistics as a tool... things to keep in mind:
- It's almost always helpful to graphically display the data before you start running
any kind of statistical test. It can help think about the steps to follow: How should
I plot my data to give me insight into what it means?
- Different statistical methods lend themselves to different types of questions
and, hence, data. What is most appropriate for my data?
- Most tests require that certain assumptions be met. What are those assumptions
and how can I ensure they are met?
- You don't usually need all the output from your analysis in your report. What
summary statistics are most important in describing my results?
Read through the following exercises and think about the above questions. Together we
will determine the best analysis approach.
- Effect of herbicide application on tamarix.
Two herbicide manufacturers want a biologist to use their products in a
proposed spraying of tamarix plants to reduce plant cover. A small hillside is
used in a test of the two sprays. The biologist notes a difference in the soil
type, depth, and available moisture at the bottom, middle, and top of the slope.
Because of these differences, the biologist feels these changes must be accounted
for in the experimental design. One hectare plots at the top, middle, and bottom
of the slope are sprayed with Herbicide A with other similar plots sprayed with
Herbicide B. Control plots of untreated tamarix are also located at each position
on the slope to compare with the treated plots. One month after spraying, the
number of cm2 of ground cover in each m2 of ground in
each experimental plot is measured with the following results:
| Herbicide A | Herbicide B | Control |
|---|
| Top | 37 | 38 | 36 |
|---|
| Middle | 88 | 76 | 81 |
|---|
| Bottom | 51 | 42 | 47 |
|---|
Question: Is there any difference in the effectiveness of the three treatments
(2 herbicides and the control)?
- Create a plot of these data in some meaningful way. What can you tell from
this plot? Does it look like there is a difference between the herbicides and the control?
- What conclusions can you make? Does this agree with what you thought from looking
at your plot? If not, was there a mistake made somewhere? Do you need to redo anything?
Help! Which test
- Relationship between sagebrush density and sage grouse.
A biologist has noted an apparent association between the density of sagebrush plants
and the density of sage grouse in a certain mountain basin. Based on this association,
the biologist wishes to predict the number of sage grouse per km2 from the
number of sagebrush plants per hectare and has collected the following data:
| Location | Sagebrush | Sage Grouse |
|---|
| 1 | 200 | 21 |
| 2 | 600 | 29 |
| 3 | 500 | 30 |
| 4 | 100 | 12 |
| 5 | 700 | 32 |
| 6 | 700 | 27 |
| 7 | 100 | 17 |
| 8 | 500 | 32 |
| 9 | 900 | 37 |
| 10 | 200 | 18 |
| 11 | 300 | 25 |
Question: What is the relationship between sagebrush and sage grouse?
- Plot these data. What are the 'dependent' and 'independent' terms?
- Does there appear to be a relationship? How would you describe it? Does this make
sense in light of what you know or can guess about how sagebrush and sage grouse
might be related?
- What are your conclusions? Do they agree with what you thought? If not, why not?
- Use your results to predict the number of sage grouse
per km2 you would expect on average with 400 sagebrush plants per hectare.
Help! Which test
- Classification of elk habitat and cattle range quality.
Twenty-five separate mountain valleys can be grazed either by cattle or elk. By an
arbitrary system, each valley has been classified as good, fair, or poor elk range and as
good, fair, or poor cattle range. The specialist is interested in determining whether the two
classifications are independent of each other, or whether good elk range tends to also be
good cattle range. The number of valleys falling into the two classifications are as follows:
| Elk Classification |
|---|
| Good | Fair | Poor |
|---|
Cattle
Classification | Good | 2 | 3 | 1 |
|---|
| Fair | 4 | 2 | 5 |
|---|
| Poor | 5 | 0 | 3 |
|---|
Question: Does good elk range tend to also be good cattle range?
- Is there a good way to plot these data? Does there appear to be any relationship?
- Enter these data into Quattro and run your analysis.
- What can you conclude. Is this what you expected? Is this surprising?
Help! Which test
SAS has traditionally been a fairly intimidating statistics package to learn.
It is a very powerful program, having more modules and manuals than several other programs
combined. But, as with most computer applications, having that power means an increase
in complexity. In order to accomodate all sorts of analyses and datasets, there is of
necessity a large number of commands and options available. However, you don't have
to learn everything at once. Let's start with some basic analyses and see how it goes.
Most analyses with SAS take a two-step approach.
- First you need to get the data in
shape so SAS understands it. Here you can read in the data values and give each a
name, such as 'abundance' or 'time'. You can also select only specific cases or do
transformations on the data, such as take the log of 'abundance'.
- The second step is the actual analysis, whether it's regression, analysis of
variance, or a simple t-test. Each general type of analysis has its own procedure,
or as SAS calls them, a PROC. You will typically need to identify which variables
are class or categorical data as opposed to continuous or ordinal data. Then you
specify a model, which variable is the response, which are the explanatory variables,
and any interaction terms to consider. Then, let it rip and check out your results.
Up until now, you had to become somewhat of a programmer to use SAS. The commands
were laid out in a program that was then submitted to SAS to execute. If something
didn't work, you had to rewrite the program and run it again. Well, things are a
little easier now. SAS has a helpful utility called "SAS/ASSIST"
from the 'GLOBALS' menu that gives
you 'point and click' convenience to run some of the more basic procedures. You then
use a series of dialog boxes to set up the analysis you want and SAS will put the
code together for you. You can then recall the program SAS created to the PROGRAM EDITOR
window to see what the code should look like. This provides for a good learning
environment where you can be productive quickly, and yet learn the basic
programming techniques needed for the more compex analyses sure to come later.
We will provide a SAS demonstration by working through the first exercise above. You can copy the SAS files that perform these analyses to your own directory from this Zip file.
When learning a new statistical
package, it's helpful to have some completed analyses to compare.
- How do your results compare with your previous results?
- What is important in the SAS output to answer the research question?
- How much of the rest of the output do you understand?
You can save any program or output to a file by making the appropriate window active,
and then selecting 'SAVE AS' from the 'FILE' menu.
Return to Mercury Home Page
