Assesing normality and QQ plots -

Question 1

Model distribution - 3

Answer 1

• Theoretical probability distribution
• Describes unknown true population distribution
• Example: t-dist, chi square district, exponential dist

Question 2

Model distribution - 3

Answer 2

• Theoretical probability distribution
• Describes unknown true population distribution
• Example: t-dist, chi square district, exponential dist

Question 3

Assessing normality - 1 + 3

Answer 3

• When to assume normal distribution as model distribution?
• • Shape of histogram, if it deviates too much from bell then not likely.
• • If QQ plot points follow approximately a straight line
• • If QQ is straight line y = a + bx then mean is intercept of line and sd is b

Question 4

Sample size in assessing normality - 1

Answer 4

• For small n there is more variation, so histograms and QQ plots are more reliable for large n

Question 5

QQ plot - 4

Answer 5

• Quantile plot
• Sorts data in ascending order
• Plots data against quantiles calculated from theoretical distribution
• Zai is value to which (2i - 1) / 2n of the area is to the left.

Question 6

Location-scale family - 4

Answer 6

• Family of probability distributions
• Each member of family can be obtained by changes in location or scale
• Changes are linear transformations Y = a+ bX
• Normal distributions form a location scale family

Question 7

Empirical assess QQ plot - 3

Answer 7

• X axis: Theoretical quantiles
• Y axis: sample quantiles of data set
• Used to assess if distribution can be used as model distribution

Question 8

Theoretical QQ plot - 5

Answer 8

• X axis: Theoretical quantiles of probability distribution
• Y axis: Theoretical quantiles of another probability distribution
• Used to compare shape of two probability distributions
• Verifies whether they belong to same location-scale family

Question 9

Empirical Comparison QQ - 4

Answer 9

• X axis: Sample quantiles of data set
• Y axis: Sample quantiles of another data set
• Compare shapes of data distributions
• Assesses whether they could originate from model distribution belonging to same location-scale family

Question 10

How to interpret QQ p-lots - 1 + 4

Answer 10

• By drawing imaginary straight line through the middle of QQ plot
• • If left part of plot is below straight line –> left tail of sample heavier than left tail of snd
• • Left part is above straight line –> left tail of snd heavier than left tail of sample
• • If right part of plot is above straight line –> right tail of sample is heavier than right tail of snd
• • If right part of plot is below straight line –> right tail of snd heavier than right tail of sample

Question 11

Hoe to assess normality of data with QQ plot - 4

Answer 11

• Make normal qq plot, qqnorm()
• If points follow approx straight line y = a + bx (b > 0), then N(a,bˆ2) is reasonable distribution
• If points don’t follow straight line then most likely not from normal distribution
• If points don’t follow straight line probably they come from location scale family, with lighter or heavier tails