Transcript Goldenrod Gall Lab - Part II

Date
Group Project Task
Details
Feb 8, 9
Article Analysis
Due at start of class.
See pgs. 139-141
Feb 15, 16 In-class work day
Discuss scientific writing, statistics,
proposals
Feb 22, 23 Proposal
Due at start of class
Intro & methods for topic
See pgs. 144-156
Mar 1, 2
Start data collection
Receive TA approval
March
Collect data, analyze
data, write draft of paper
See pgs. 157-161
for details on paper
Mar 29, 30 In-class work day
Peer edit papers
Apr 5, 6
Due at start of class
Final paper
Apr 12, 13 In-class work day
Discuss presentations
Apr 26, 27 In-class presentations
Present work to class
See pgs. 164-166
Today we will
– Perform & understand basic descriptive statistics
– Understand ideas of inferential statistics
(hypothesis testing)
– Become familiar with three statistical tests:
• T-test, Chi-square, Regression
– Select & perform appropriate statistical test for
your group’s question
– Communicate your findings in writing and in an
oral presentation to your peers
What do they have in
common?
Descriptive Statistics
What are the characteristics of my data set?
What does my sample suggest about the
population?
•
Center of data
–
•
mean, median, mode
Spread of data
–
Variance, standard deviation, standard error
Later we’ll discuss, Inferential Statistics
- Using data to test hypotheses
Center of Data
“central tendency”
Spread of Data
small variance
large variance
Spread of Data
standard deviation
From Wikipedia
Spread of Data
standard deviation
From Wikipedia
Standard Deviation vs. Standard Error
Both estimate spread of data around mean
• Standard Deviation
- Estimates variability of population
around the mean
• Standard Error
- Measures precision of sample mean
standard error = standard deviation
√sample size
Data Analysis
For your group’s variables, calculate:
1) Sum
2) Mean
3) Median
4) Mode
5) Standard Deviation
6) Standard Error
7) Variance
(use Data Analysis ToolPak)
A) Record these measures on handout
B) Write 1-2 sentences on
- What do these measures tell you about your data?
C) Plot data in excel, sketch on pg 88
For guidance, see p. 172-173 (stats); 191-193 (excel)
(demo use of Data Analysis ToolPak)
Types of Data
• Count
– Number of events
– (only whole #s, no fractions)
Ex: # galls with evidence of predation
• Continuous
– Includes fractions/decimals
Ex: Length of gallfly larvae
• Categorical
– Data fall into groups
Ex: Parasitoid/Predator/None
(other exs: Male/Female,
Juvenile/Adult, Red/Blue)
In ecology (as in science, in general),
you need to use your data to
test hypotheses.
To test your hypotheses &
to interpret your data
you use inferential statistics
Three types of Tests
• Student’s t-test
– Determine if means of two
populations are considered different
– For continuous data
• Chi-Square
– Determine if means of two
populations are considered different
– For count or frequency data
• Correlation/Regression
– Indicates how closely two things are
related to each other
Success Failure
Treatment 1
15
35
Treatment 2
14
85
Question: What affects rates
of play in meerkats
1) Available energy
2) Size of individual
3) Sex of pups
Types of Data
Count, Continuous or Categorical?
Question 1:
Does rate of play differ for
provisioned & unprovisioned
pups?
Rate of play
Continuous
Provisioned vs. unprovisioned pups
Categorical
Results
Unprovisioned
(Control)
Provisioned
(Treatment)
Mean = 7.3
Mean = 13.5
So these are different, Right?
Maybe, let’s look at the spread of the data
Consider Means & Variance
• Declaring two
populations different
depends on both:
• Means
• Variation
• For the same means,
more variation =
less likely means can
be declared as
different
Use the t-test!
How do you calculate the t statistic?
Is the difference statistically significant?
•Calculate t-value from your data tcalc
•Compare to “critical t-value”
tcritical
T-value needed for significant differences
•If tcalc > tcritical,
then your group means differ significantly
• When tcalc > tcritical,
your p-value (significance value) is very small
• P-values ≤ 0.05 indicate significant differences
What is the p-value?
• The probability that the findings from
study are due to chance.
– For example, a p-value of .01 (p = .01)
means there is a 1 in 100 chance the result
occurred by chance.
– The standard accepted value is 0.05 or less.
Provisioned pups play more
*
Treatment
p < 0.05
Control
Types of Data
Count, Continuous or Categorical?
Question 2:
Does size of individuals affect
rate of play?
Rate of play
Continuous
Size of individuals
Continuous
The Data
Weight (kg)
Rate (min/hr)
1.5
14.4
1.0
15.6
2.0
30.5
2.0
33.7
1.7
10.1
3.5
36.6
Larger pups play more
40
35
Rate of play (min/hr)
30
25
20
15
r = 0.8
10
5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Body weight (kg)
There is a positive relationship between rates of play and
body weight
Correlation/Regression
• Correlations tell you if there is a relationship
between 2 variables
(but provide no information on causation)
• Correlation coefficient ranges between -1
and 1
• Regression implies that one variable predicts
the other
Correlation/Regression
Types of Data
Count, Continuous or Categorical?
Question 3:
Does sex of individuals affect
the number of play events?
# of play events
Sex of individuals
Count
Categorical
3) Sex of the pup
Study Description:
Observe the frequency of play of male
and female pups
If sex does not determine play we
would expect the probability to be
50%
Data
Sex
Observed
Expected
Male
11
15
Female
19
15
Data
Sex
Male
(Observed - Expected)2 Degrees of
/ Expected
Freedom
(11-15)2 /15= 1.07
1
Female
(19-15)2 /15= 1.07
Total
2.14
Table pg. 189
For 1 df the critical value is 3.84
2.14< 3.84 so neither sex plays more than
expected by chance
Play by Sex
60
Play Frequency
50
40
Observed
30
Expected
20
10
0
Male
Female
Sex
Data Analysis & Conclusions
1) Write your hypotheses (null & alternative)
i.e., null: no difference A = B, alternative: A > B
2) Determine which test is best for testing your hypothesis
t-test, Chi-square, correlation/regression
3) Perform test in Excel (see pgs. 191-193)
4) Record degrees of freedom (df) and appropriate stat output
(T-value, Chi-square value, P-value, R2)
5) On pg 89, write
-
Statistical conclusion – Significant difference or not?
How do you know?
Biological conclusion – What does the statistical conclusion mean
for your hypothesis? Explain.
Reference graph in conclusion
6) Prepare a few PPT slides (<5) to explain findings to class
Announcements
-
Read Adaptation Lab (pgs. 29-40)
-
We’ll meet here & then go to greenhouse
-
Complete Article Analysis for group project
-
1 article per person
Different article than group members
1 article from primary literature (scientific journals)
I suggest you avoid journals Science and Nature