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You have data! What’s next?
Data Analysis, Your Research Questions, and
Proposal Writing
Zoo 511
Spring 2014
Part 1:
Research Questions
Part 1:
Research Questions
Write down > 2 things you thought were interesting
or engaging during the field trip (can be a species,
a habitat feature, a relationship, etc). You can
phrase these as questions, but you don’t have to
yet.
Part 1:
Research Questions
What makes a good question?
Your questions should be specific
and answerable
NOT SO USEFUL
USEFUL
What habitat do fish
prefer?
Does sculpin CPUE differ
among geomorphic
units?
In what kind of stream
are brown trout most
likely to be found?
Is brown trout density
related to flow velocity?
…and statistically testable
Does sculpin CPUE differ among
geomorphic units?
Is brown trout density related to
flow velocity?
Brown Trout/m2
Sculpin
Sculpin per CPUE
minute
6
5
4
3
2
1
0
RIFFLE
RUN
POOL
Current Velocity (m/s)
Part 2: Statistics
How do we find the answer to our
question?
Why use statistics?
Are there more green sunfish in pools or
runs?
Run
5
4
1
Pool
2
7
3
12
??
10
•Statistics help us find patterns in the face of variation, and draw
inferences beyond our sample sites
•Statistics help us tell our story; they are not the story in themselves!
Statistics Vocab
(take notes on your worksheet)
Categorical Variable: Discrete groups, such as Type
of Reach (Riffle, Run, Pool)
Continuous Variable: Measurements along a
continuum, such as Flow Velocity
What type of variable is “Mottled Sculpin /meter2”?
What type of variable is “Substrate Type”?
Statistics Vocab
Explanatory/Predictor Variable: Independent
variable. On x-axis. The variable you use to predict
another variable.
Response Variable: Dependent variable. On y-axis.
The variable that is hypothesized to depend on/be
predicted by the explanatory variable.
Statistics Vocab
Mean: The most likely value of a random variable or set
of observations if data are normally distributed (the
average)
Variance: A measure of how far the observed values
differ from the expected variables (Standard deviation is
the square root of variance).
Normal distribution: a symmetrical probability distribution
described by a mean and variance. An assumption of
many standard statistical tests.
N~(μ1,σ1)
N~(μ1,σ2)
N~(μ2,σ2)
Statistics Vocab
Hypothesis Testing: In statistics, we are always
testing a Null Hypothesis (Ho) against an alternate
hypothesis (Ha).
p-value: The probability of observing our data or
more extreme data assuming the null hypothesis
is correct
Statistical Significance: We reject the null
hypothesis if the p-value is below a set value (α),
usually 0.05.
What test do you need?
For our data, the response variable will probably
be continuous.
T-test: A categorical explanatory variable with only
2 options.
ANOVA: A categorical explanatory variable with >2
options.
Regression: A continuous explanatory variable
Student’s T-Test
Tests the statistical significance of the
difference between means from two
independent samples
Null hypothesis: No difference between means.
Compares the means of 2 samples of a categorical
variable
p = 0.09
Mottled
Sculpin/m2
Cross Plains Salmo Pond
Analysis of Variance (ANOVA)
Tests the statistical significance of the
difference between means from two or
more independent groups
Mottled Sculpin/m2
p = 0.03
Riffle Pool
Run
Null hypothesis: No difference between means
Precautions and Limitations
• Meet Assumptions
•Samples are independent
• Assumed equal variance (this assumption
can be relaxed)
Variance
not equal
sculpin density in pools
sculpin density in runs
Precautions and Limitations
• Meet Assumptions
•Samples are independent
• Assumed equal variance (this assumption
can be relaxed)
• Observations from data with a normal
distribution (test with histogram)
Precautions and Limitations
• Meet Assumptions
•Samples are independent
• Assumed equal variance (this assumption
can be relaxed)
• Observations from data with a normal
distribution (test with histogram)
• No other sample biases
Simple Linear Regression
• Analyzes relationship between two
continuous variables: predictor and response
•Null hypothesis: there is no relationship
(slope=0)
Least squared line
(regression line:
y=mx+b)
Residuals
Residuals
Residuals are the distances from observed points
to the best-fit line
Residuals always sum to zero
Regression chooses the best-fit line to minimize
the sum of square-residuals. It is called the Least
Squares Line.
Precautions and Limitations
• Meet Assumptions
• Relationship is linear (not exponential,
quadratic, etc)
• X is measured without error
• Y values are measured independently
• Normal distribution of residuals
Have we violated any assumptions?
Residual Plots Can Help Test Assumptions
0
0
“Normal”
Scatter
Fan Shape:
Unequal
Variance
0
Curve
(linearity)
if assumptions are violated
• Try transforming data (log transformation, square
root transformation)
• Most of these tests are robust to violations of
assumptions of normality and equal variance (only
be concerned if obvious problems exist)
• Diagnostics (residual plots, histograms) should
NOT be reported in your paper. Stating that
assumptions were tested is sufficient.
Precautions and Limitations
• Meet Assumptions
• Relationship is linear (not exponential,
quadratic, etc)
• X is measured without error
• Y values are measured independently
• Normal distribution of residuals
•Interpret the p-value and R-squared value
Residuals
P-value: probability of observing your data (or
more extreme data) if no relationship existed
- Indicates the strength of the relationship,
tells you if your slope (i.e. relationship) is nonzero (i.e. real)
R-Squared: indicates how much variance in the
response variable is explained by the
explanatory variable
-Does not indicate significance
R-Squared and P-value
High R-Squared
Low p-value (significant relationship)
R-Squared and P-value
Low R-Squared
Low p-value (significant relationship)
R-Squared and P-value
High R-Squared
High p-value (NO significant relationship)
R-Squared and P-value
Low R-Squared
High p-value (No significant relationship)
We just talked about:
• Types of variables
• 3 statistical tests: t-test, ANOVA, linear
regression
• When to use these tests
• How to interpret the test statistics
• How to be sure you’re meeting assumptions of
the tests
Part 3: Proposal
Writing a Proposal
• What is the function of a proposal?
– To get money
Writing a Proposal
• What is the function of a proposal?
• What information should go in a proposal?
– Research goals/objectives/hypotheses/questions
– Why does this matter? (Rationale)
– Procedure / Methods
– Future directions / implications
– Budget/cost analysis
– Expected results
Other data you can use
Previous years’ data on website: all of the same
information was collected from the same place,
around the same time of year. Replication!
USGS: http://waterdata.usgs.gov/nwis/uv?05435943
Background info: from the Upper Sugar River
Watershed Association
Think about these data sources as you generate
your questions.