Week 2B: Dispersion in a distribution
range (at least ordinal)
difference between largest and smallest score
affected by extreme scores and outliers
IQR (at least ordinal
quartiles
3 values that split data into 4 equal parts
upper quartile - lower quartile
deviance (at least interval)
how far a point is spread from the center of a distribution (mean)
normal distribution
total devaince= add up deviance for each data point
sample score- mean score
sum of squared errors (or squared deviances)
when total deviance equals 0
indicator of total dispersion/deviance of the scores from the mean
variance (at least interval)
average dispersion
when total dispersion is too big to compare to other samples that differ in size
sum of squares divided by number of observations
answer is in unit squared
standard deviation
bc variance is in units squared, we square root the variance
average error between mean and the observations made
small standard deviation= data points are close to the mean
standard deviation is zero= all data points are the same
z-score (at least interval)
implies that majority of scores lies around centre of the distribution
as we get further from the centers, numbers become less frequent
skew
kurtosis
no symmetry
pointyness
standardizing scores
used to convert a data set to a mean of zero an SD of 1
using formula, find z-value and find it on the table; then look for smaller and larger portion (probabilities)
smaller portion= area above the value
probability of overhang "how special": if we want to know a specific percentage in the middle of the normal distribution graph, we subtract is from 100%, then the we divide the remainder by 2 because the graph is symmetrical and we want to cut off a total of that remaining percentage. We do this by locating the final remaining percentage (decimal form) on the z-score table,