quantile-quantile plots (QQ plot)
- plots the observed sample values against quantiles of a theoretical distribution
- if the data actually comes from that type of distribution, then points will fall roughly on a straight line
- normal quantile-quantile plot (normal QQ plot)
- checking the normality assumption
- data roughly on the line data is approximately normally distributed
- normally compare against the standard normal distribution (see middle is 0)
- if skewed = skewness is on the opposite side of the original distribution's skewness
- different distributions
- right-skewed
- normally its a hard cap on the left side (think logs with 0)
- normal would have it going outliers->middle->outliers
- skewness makes it start at the "middle"
- left-skewed
- hard cap on the right side
- under-dispersed
- less outliers
- everything tends to the z-score 0
- when the percentile that the outliers normally are starts, everything is still close to the mean
- over-dispersed
- more outliers
- the percentile where it should be getting close to the mean still has outliers (more concentration)