Important take-home messages

• Population vs sample:
  • What is the population?
  • Is the entire population known – is statistics at all needed?
• Sampling
  • Sampling strategy must ensure random sampling
    • Difficult to investigate it afterwards
  • Convenience sampling often used, dangerous!
  • Be honest with yourself, describe problems: Is the sample representative for the target group/population/market segment/…?
• Badly chosen big sample is much worse than a well-chosen small sample
• Watch out for biases
  • Sample/selection bias
  • Response bias
  • Non-response bias
  • (Survivorship bias)
• Data collection
  • Privacy vs necessary information (< 50 or >= 50, age in years, birth date)

Controlling (for)

• Multivariate analysis: “Controlled (for)” means that it’s influence is removed
  • Size of effect often not of interest
  • Module 4: Cadmium exposure’s effect on vital capacity, controlled for age
• Randomized experiments vs observational studies
• Example [A] 10.1

Confounders

• Which variables to control for?
• Effect on response variable cannot be distinguished from another (or more) of the explanatory variables
• Variables affecting the association studied, but not measured are sometimes called lurky
• Example: correlation between college GPA and income later in life
  • Potential lurking variables: IQ, tendency to work (hard), …
• Example:
  • Plant cucumbers in a garden, some in sun some in shade.
  • Add fertilizer to those in sun.
  • Wait…
  • More cucumbers on those in sun: due to sun light or fertilizer?
  • Effect of fertilizer confounded with effect of sun light.
• Example:
  • Ice cream sale increases with number of shark attacks
  • Weather probably (!) has an impact?
• Analyze effect of explanatory variable: not observe a confounder explaining major part of effect
  • Omitted variable bias

Multicolinearity

• If one or more explanatory variables are linearly dependent (or close to)

Simpsons “paradox”

mylm <- lm(SleepHrs ~ Age, data = DF)
summary(mylm)

## 
## Call:
## lm(formula = SleepHrs ~ Age, data = DF)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -3.728 -0.917 -0.102  1.338  3.505 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -15.0791     3.4825   -4.33  3.6e-05 ***
## Age           0.4644     0.0661    7.02  2.9e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.7 on 98 degrees of freedom
## Multiple R-squared:  0.335,  Adjusted R-squared:  0.328 
## F-statistic: 49.3 on 1 and 98 DF,  p-value: 2.86e-10

Simpsons “paradox”

Simpsons “paradox”

Summary

• Some terms introduced, a lot more to it – but gives some ideas of potential problems

Data wrangling

Read data:

• rio: A Swiss-Army Knife for Data I/O
  • rio: A Swiss-Army Knife for Data I/O
  • Excel: readxl (part of rio)
• R for Data Science

Case: Questionnaire about biking habits in Region Sjælland

• Questionnaire:
  • Shared in approx 30 different Facebook groups
• Questions:
  • Representative for the entire region?
    • Each municipality represented in sample proportional to its population size?
    • Disabled people?
    • People biking (municipalities’ age distribution may vary)
• Important take-home messages:
  • Sampling strategy must ensure random sampling
    • Difficult to investigate it afterwards
  • Convenience sampling often used, dangerous!

Analysis

Demo