1. Nasty data… When killer data can ruin your analyses
JENA GRADUATE ACADEMY Dr. Friedrich Funke

2. Learning Objectives What will you have learnt today?
Why to inspect your data
Why data become nasty
How to inspect your data
Coping strategies

3. Why to inspect your data?
Assumptions of parametric tests (e.g. ANOVA)
The error terms are…
randomly, independently, and normally distributed,
with a mean of zero and
a common variance (homoscedasticity)

4. Why to inspect your data?
Basic statistical method – Ordinary least squares (OLS)

5. Where are we? Why to inspect your data  violation of assumptions
Why data become nasty
How to inspect your data
Coping strategies

6. Where are we? Why to inspect your data  violation of assumptions
Why data become nasty
How to inspect your data
Coping strategies
Input errors (55 instead of 5)
dropout/non-response
human nature keeps the game interesting

7. Am I allowed to alter my data?
29%
67% 4%
It is unethical to alter data for any reason. Or
Data points should be removed if they are outliers and there is a identifiable reason for invalidity.
Data points should be removed if they are outliers. Extremity is reason enough.

8. Am I allowed to alter my data?
It is unethical to alter data for any reason
A good model for most data is better than a poor model for all of your data.

9. Where are we? Why to inspect your data  violation of assumptions
Why data become nasty
How to inspect your data
Coping strategies

10. Graphical data screening

11. Normal q-q plot

12. Test on normality
Access e.g. via EXPLORE

13. My data are skewed – what shall i do?
Transformed variables are difficult to interpret
Scales are often arbitrary  no problem of interpretation
Find a transformation that produces the prettiest picture and skewness and kurtosis near 0 (iterative)

14. Common data transformations
Before/after
COMPUTE after = sqrt(before). or
COMPUTE after = lg10(before+constant).
COMPUTE after = 1/(before+constant).

15. Common data transformations
Add a constant to make the smallest value > 1
For left-skewed variables reverse the variables (reversed = max+1-old_var)

16. To be completed with residual Analysis

17. Rules of thumb
Studentized deleted residuals with an absolute value greater than 2 deserve a look (greater than 4, alarm bells)
Cook's D problematic if D. One recommendation is to consider values to be large which exceed 4/PAn.
Another suggested rule is to consider any value greater than 1 or 2 as indicating that an observation requires a careful look.
Finally, some researchers look for gaps between the D values.

18. Checklist For Screening Data
Inspect univariate descriptive statistics for accuracy of input
out-of-range values, be aware of measurement scales
plausible means and standard deviations
coefficient of variation
Evaluate amount and distribution of missing data: deal with problem
Independence of variables
Identify and deal with nonnormal variables
check skewness and kurtosis, probability plots
transform variables (if desirable)
check results of transformations
Identify and deal with outliers
univariate outliers
multivariate outliers
Check pairwise plots for nonlinearity and heteroscedasticity
Evaluate variables for multicollinearity and singularity
Check for spatial autocorrelation
Adapted from Tabachnick & Fidell

19. Best practice flow chart
Plausible range, missing, normality, outliers, homoscedascity
Pairwise linearity (differential skewness?)
Studentized deleted residuals, leverage, Cooks‘s D …
e.g. squareroot, lg10, arcsin

20. Understanding WHY they are there is most important
Take home message
Detecting nasty data is important
Knowing how to handle them is better
Understanding WHY they are there is most important

21. Francis Bacon in Novum Organum:
» For whoever knows the ways of Nature will more easily notice her deviations; and, on the other hand, whoever knows her deviations will more accurately describe her ways «