1. A protocol for data exploration to avoid common statistical problems
Zuur et al Methods in Ecology and Evolution 2010, 1, 3–14
doi: /j X x
Presented by Han Y. H. Chen

2. Selecting the appropriate inferential statistics
Generalized Linear Model (GLM) as a dominant method in statistics

3. Simple statistics
One-way ANOVA, followed by post-hoc comparison (example)
Simple regression (by example)
ANCOVA
MANOVA

5. Step 1. Are there outliners in Y and X?
An observation that has a relatively large or small value compared to the majority of observations
boxplot as the tool of detection
Simple command in R: boxplot(y) and dotplot

6. Multi‐panel Cleveland dotplot for all of the morphometric variables measured

7. Step 2: Do we have homogeneity of variance?
Homogeneity of variance is an important assumption in analysis of variance (ANOVA), other regression‐related models and in multivariate techniques like discriminant analysis
The solution: transformation of the response variable to stabilize the variance, or applying statistical techniques that do not require homogeneity (generalized least squares)

8. Step 3: Are the data normally distributed?
ANOVA and regression assume normality, but PCA does not

9. In linear regression, we actually assume normality of all the replicate observations at a particular covariate value
But cannot be verified unless one has many replicates at each sampled covariate value

10. Normality assumption applies to model residuals, not raw data
hist(resid(model))
qqnorm(resid(model)); qqline(resid(model))
shapiro.test(resid(model))
Remedies: bootstrapping if parametric is desired
Non-parametric, Rfit package or similar

11. Step 4: Are there lots of zeros in the data?
The effects of straw management on waterbird abundance in flooded rice fields
One possible statistical analysis is to model the number of birds as a function of time, water depth, farm, field management method, temperature
Because this analysis involves modelling a count, GLM (Poisson or negative binomial) is the appropriate analysis, but there are many zeros

12. The frequency of double zeros is very high
All the blue circles correspond to species that have more than 80% of their observations jointly zero
Remedies:
zero inflated GLMs
multivariate techniques

13. Step 5: Is there collinearity among the covariates?
Which covariates are driving the response variable(s)? The biggest problem to overcome is often collinearity
Collinearity = confusing statistical analysis
Nothing is significant
Dropping one covariate can make the others significant or even change the sign of estimated parameters. 

15. Strategy for addressing collinearity
Sequentially drop the covariate with the highest VIF, recalculate the VIFs and repeat this process until all VIFs are smaller than a pre‐selected threshold = 3

16. Step 6: What are the relationships between Y and X variables?

17. What are the assumptions for general linear model (lm)
Both for regression and ANOVA
Independence of observations (can not be met in almost all situations!)
Normality –the distributions of the residuals are normal
Equality (homogeneity) of variances – the variance of data in groups (or along the x gradients) is the same
Additional for regression: Linearity
Verifications are done on model residuals, not raw data

18. Scatterplots are also useful to detect observations that do not comply with the general pattern between two variables
measurement errors, typing mistakes

19. Step 7: Should we consider interactions?
see R demonstration for interaction effects

20. Step 8: Are observations of the response variable independent?
A crucial assumption of most statistical techniques is that observations are independent of one another
Pseudoreplications
Spatial autocorrelation:
Observations at locations close to each other have more similar characteristics than those far away
Temporal autocorrelation
Repeated observations on the same objects are more similar

21. Plot auto‐correlation functions (ACF) for regularly spaced time series
Auto-correlated
Not auto-correlated

22. Remedies for independence
Know your experimental or sampling design
Linear model assumes completely randomized design by default
Completely randomized block design
Split-plot design (nested)
Repeated measures
Apply correct statistical model
Linear mixed effect models (packages “lme4” or “nlme”)

23. Take home message
Simple statistical analysis is the best if it meets all assumption, but ecological reality is more complex
Simple questions have been studied for so long, no niche for novelty/discovery
Statistics without verifying assumptions are not reliable and do not serve the purpose

24. A good starting place to learn R graphics