Descriptive statistics:

Question 1

Arithmetic mean

Answer 1

Arithmetic mean 𝑥ҧ („x bar“)is the sum of all values divided by the number of values

• Caution: sensitive towards outliers and skewed distributions

Question 2

Median

Answer 2

divides the observations into two equal parts such that 50% of the values are greater than or equal to the median and 50% are less than or equal to the median

• Sort values in increasing order
• If n is odd, then median is the middle ordered value
• If n is even, then median is the arithmetic mean of the two middle ordered values

Mean vs. Median: for skewed distributions or in the presence of outliers, the median is more robust than the mean

Question 3

Residuals

Answer 3

difference between values and mean: 𝑥𝑖 − 𝑥ҧ(x-strich)

Question 4

Standard deviation:

Answer 4

to make variance comparable to the mean (i.e.same unit), we take the square root

SO without the square root it is s^2 the Variance

Question 5

standard error of the mean, SE

Answer 5

describes the unreliability of the arithmetic mean estimate

• SE increases with variance
• SE decreases with sample size
  (meaning, larger samples increase
  reliability of our estimates !!) * SEisintheunitofthedata

Question 6

Confidence interval

Answer 6

The confidence interval shows the likely range in which the mean would fall and is calculated from the standard error of the mean SE estimate and a constant c

Question 7

What does conditional and marginal r2 mean?

Answer 7

In Linear mixed effect models:
r^2 marginal: describes variance explained by fixed effects

r^2 conditional: describes variance explained by random and fixed effects together

Question 8

What are odds?

Answer 8

Odds express the chance that an event occurs.

𝑜𝑑𝑑𝑠 =𝑝/1 − 𝑝 =𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛 𝑜𝑓 𝑠𝑢𝑐𝑐𝑒𝑠𝑠𝑒𝑠/ 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛 𝑜𝑓 𝑓𝑎𝑖𝑙𝑢𝑟𝑒𝑠

Advice: only interpret direction of Odds

• Odds < 1 .. Success is less likely
• Odds > 1 .. Success is more likely

Question 9

AIC for what?

Answer 9

If AIC smaller, model is a better fit.
(smaller BIC Bayesian Information criterion, log(likelihood) auch besser)

Simpler model preferred to more complex ones, because of Parsimony principle.
From most complex to simplest model by removing variables which do not have a highly significant effect on the unexplained variance.