Summary
Summary Ecological Methods I
- Course
- Institution
Summary of lectures & practicals by subject
[Show more]
1 review
By: casperbraams • 3 months ago
Seller
Followmichouweimar
Reviews received
Content preview
Univariate analysis (exam 1)Group differences
Introduction
Ecological problems
Lot of sites/plots
Many variables
Lot of natural variation (noise)
solution: statistics
Sample size (N)
Larger N better estimate mean & s, value stabilizes
Larger N smaller CI
Don’t learn standard deviation (SD or s) formula
Standard deviation = s = σ
Variation = s2
SPSS: levels of measurements
Nominal => categories
- Habitat, sex, colour
- Prey species killed
Ordinal => order
- Abundant, frequent, rare
- Droppings
Scale => ratio scale
- Absolute 0 (weight, length, intake)
- Subtract, add, multiplication
- Fish size & body mass
Distribution type
Normal => symmetric & continuous
Lognormal => skewed & continuous
- Exponential growth (biomass)
Poisson & negative binomial => skewed, non continuous (discrete)
- Counts (quadrants)
Binomial => 2 outcomes
- Dead/alive, present/absent
,T-tests
Independent samples (df = N – 2)
1. Unequal variances
2. Equal variances
Dependent samples (df = N – 1)
3. Paired sample
Hypothesis => testable explanation of observation
Clear direction: larger/smaller, increase/decrease
Based on observations + what you already know to be true
If … then …
Independent variable (x) = cause
Dependent var (y) = effect
Example:
- Ho => no difference
- H1 => mean body weight larger in area B than area A
Standard error of the mean (SE) = standard deviation of X̄ = s/√ N
T-test unequal variances (1)
Difference between 2 means/SE of that difference
- If X̄ 1- X̄ 2 = 0 t = 0
- If X X̄ 1- X̄ 2 = large or S2/N decreases t increases
Threshold: p = 0.05!!
- p ≤ 0.05 reject Ho
- p ≥ 0.05 do not reject Ho
T-test for equal variances (2)
Difference between 2 means/SE of that difference
Levene’s test
- Ho: equal variances (p ≥ 0.05)
,Degrees of freedom (df)
Df < N
- Depends on test & data
Significant outcome if: calculated t > critical t from table
Reporting statistics
1. Used test
2. Statistical parameter value (e.g. t-value)
3. Df/N
4. P-value
One-sided vs two-sided
One-tailed test sooner significant
- But: only use if you know that 1 group has higher mean (e.g. more mortality in polluted
area)
Ecology: lot of noise & uncertainty often two-tailed
- Doubt always use two-tailed
- Sometimes one-tailed (F-test)
Type 1 & type 2 error
Type 1 => reject Ho while true
4. Conclude someone is pregnant who is not
Type 2 => do not reject Ho while false
T-test for paired data (3)
Example:
- Same animal measured 2x (at two moments in
time)
z̄ = average value of difference
Power & sample size
Power => likelihood of test reaching correct conclusion
- Smaller type II error larger power than visually inspected
Larger power implications for:
- Experimental design
- Sample size
- Test results
Minimum sample size calculation
, Non-parametric & transformation
Parametric test: assumes data distribution is characterized by mean, SD
- Only use (transformed) normally distributed data (black line)
- Higher power than non-parametric test
Not normally distributed (red line) transform data OR use non-parametric test
- Preferably transform, only use non-parametric test as last option
Test for normality
- Histogram
- Statistical test Shapiro Wilk test
Data transformation
Check:
- Variance (s2), mean (X̄ ) & histogram
Rules of thumb (no hard guidelines)
- S2 > X̄ log(variable) or ln(var) e.g. growth, biomass
- S2 X̄ √ var e.g. area, size
- Highly skewed √ √ var
- Binomial ln(p/(1-p)) e.g. presence/absence (binomial data)
0 values
- Use log(x+1) or ln(x+1)
- √ var + 0.5
Transform whole var check again!
- Still not normal: use non-parametric test (can also be used for normal data)
- Parametric test has higher power
Non-parametric tests
Mann Whitney U test
Wilcoxon matched pairs test
Kruskal Wallis test
Mann Whitney U test (1)
Not normal & unmatched pairs
Ho: 2 medians are equal
U value for 2 groups
- Compare smallest U value with table
- U < critical value reject Ho
- Tied data? (same value & rank) use asymptote p
Wilcoxon matched pairs test (2)
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller michouweimar. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $3.75. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
49497 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now