Percentiles and Z-Scores

Question 1

Inter-Quartile Range (IQR)

Answer 1

A measure of variability based on dividing a data set into quartiles.

Question 2

Percentiles

Answer 2

The value of observation such that p percent are less than or equal to it and 100-p percent or less are greater than it.
A method of describing the standing of an individual in relation to a group.
Can be used to calculate raw score and vice versa.
Percentile = ordinal rank of a given value / number of values in dataset * 100

Question 3

Percentile Score

Answer 3

The percentage of people in the group who have the same raw score or a lower raw score than the one in question.

Question 4

Z scores

Answer 4

The transformation of a raw score to SD units on another scale with equal intervals (interval scale). Based on standard deviation as a metric, and used to compare an individual with respect to a group.
Uses assumption that the distribution is normal.
Used to calculate percentiles or % of case falling in certain score ranges
A Z score of 1 is 1 SD above the mean.

Question 5

Three uses of Z-scores

Answer 5

1. Compare an individual relative to the group OR calculate % of people falling within certain score range.
2. Compare score units which are different
3. Calculate probabilities under the normal curve (i.e. used for confidence intervals and statistics tests).

Question 6

T - scores

Answer 6

A way of converting Z scores to an understandable form.
A T of 60 is 1 SD above the mean.