Statistics:
Descriptive
Individuals
Relationships
Test
Items 
A Guide to Test Statistics
Edward P. Asmus, Ph.D.
University of Miami
Descriptive Statistics
Maximum

The biggest number in a set of scores.
Minimum

The smallest number in a set of scores.
Range

Range = Maximum  Minimum
Mean

The arithmetic average of a group of scores.
Mean =
where,
x 
= 
sum of all scores, and 
n 
= 
the number of scores. 
Median

The midpoint of a range of scores.
Median =
where,
l 
= 
exact lower limit of the interval
containing the median, 

= 
number of people below l 

= 
number of people in the interval
containing the median, and 
i 
= 
size of the interval. 
Standard Deviation

Provides a reference of a group of scores to the normal curve or, it describes
the variability in a group of scores.
SD =
where,
x 
= 
a score, 

= 
mean, 
n 
= 
number of scores, and 

= 
sum of. 
Test Statistics for Individuals
zscore

Indicates where a person places on the normal curve.
z =
where,
x 
= 
individuals score, 

= 
mean of all scores, and 
SD 
= 
standard deviation 
T score

Indicates a persons score such that an average score is 50 and for every
10 points above or below 50 indicates 1 standard deviation above or below
the average of the group.

T = 10z + 50 where,
Stanine

The stanine, or standard nine, indicates a persons score such than an average
score is 5 and for every 2 points above or below 5 indicates 1 standard
deviation above or below the average of the group.
Stanine = 2z + 5 where,
Statistic of Relationship
Pearson Product Moment Correlation

A number ranging from 1.00 to +1.00 that indicates how well two groups
of numbers relate to each other. +1.00 equals a perfect positive relationship,
1.00 equals a perfect negative relationship, and 0.00 indicates no relationship.
r =
where,

= 
mean of the group of x scores, 

= 
mean of the group of y scores, 
n 
= 
number of xy pairs, 

= 
sum of all pairs of x score
multiplied by y score, 

= 
standard deviation of x scores, 

= 
standard deviation of y scores. 
Statistics About a Test
Reliability

Indicates the consistency with which a test measures. That is, it indicates
how consistent the scores are in two different administrations of the same
test.
SplitHalf Reliability

Compute the Pearson Product Momment Correlation between the scores obtained
for each person on the odd items and the scores obtained on the even items.

Correct the scores using the SpearmanBrown Prophecy Formula.
SpearmanBrown Prophecy Formula

where,
K 
= 
ratio to increase to desired length
of a test (usually 2), and 
r 
= 
odd even correlation of scores. 
Cronbach's Coefficient alpha Reliability

where,
k 
= 
number of items in test, 

= 
standard deviation of item, and 

= 
standard deviation of test. 
Statistics About Test Items
Item Difficulty
Indicates how difficult an item is. Ranges between zero, no one got
the item correct, to one, everyone got the item correct.
where,
n 
= 
number of people who took the
test, and 

= 
number of people who got the
item correct. 
Item Discrimination

Indicates how well the item distinguished between those who did well on
the test and those who did not.

Correlate the peoples' responses on the item and the peoples' score on
the test.
Ed.Asmus@miami.edu
Last Update: June 21, 2000
