3.3 - Raw Scores

meaningless

A simple raw score on a test without any type of comparative information, is a _______ number

derived

To make sense of the scores, a score will need to be converted to a ______ score or compared against some criterion

• Norm-referenced

• Criterion-referenced

• Self-referenced

Interpretation of Scores (3)

Norm-referenced

Compares an individual’s score with scores of others

Norm-referenced

A student scores in the 80th percentile on an IQ test

Criterion-referenced

Compares an individual’s score to a fixed standard or benchmark (established by authority)

Criterion-referenced

Passing a driving test requires 80% correct answers

Self-referenced

Compares an individual’s score with their own previous scores

Self-referenced

A client improves from 50% to 70% on repeated stress assessments

• Frequency Distribution

• Histogram

• Frequency Polygon

• Bar Graph

Ways to ORGANIZE Raw Data (4)

Frequency Distribution

Tabulates how many times each score or response occurs

Frequency Distribution

Histogram

a graph of bars that presents the data from a frequency distribution in a more visual format

• used with quantitative variable

Histogram

Frequency Polygon

A line graph of a frequency distribution

• Connects points at the peak of each value

• Higher peaks = greater frequency

Frequency Polygon

Bar Graph

Visual representation of nominal data

• Bars represent categories, not continuous data

• Bars can be in any order

Bar Graph

Measures of Central Tendency

Refers to typical score indicators, or the average score for a distribution of scores.

Measures of Central Tendency

Single value that attempts to describe a set of data by identifying the central position within that set of data

Measures of Central Tendency

Also called MEASURES OF CENTRAL LOCATION

• Mean

• Median

• Mode

Measures of CENTRAL Tendency (3)

Mean

arithmetic average

Mean

susceptible to the influence of outliers

• Arithmetic

• Population

• Sample

Mean: (3)

Arithmetic Mean

the sum of the scores divided by the number of scores in the collection

Population Mean

Mean computed from ALL members of the population.

Population Mean

✅ Symbol

\mu (mu)

Sample Mean

Mean computed from only a subset (sample) of the population.

👉 Used when studying part of the group only

Median

the middle score for a set of data that has been arranged in order

average

If there are 2 medians, get their ____

5

Data: 2, 4, 6, 8

• Mean?

Mode

values that occur most often

Measures of Variability

indicate the extent of individual differences

around a measure of central tendency

Measures of Variability

“How far apart are the scores?”

Measure of Variability

“Describe the amount of variation”

• Shows how much scores deviate from the average

Example:

Class A: 85, 86, 87

Class B: 60, 85, 100

Both have mean = 86

BUT Class B has bigger spread → more variable

variability

“Large spread = large differences”

• More distance between scores = greater ____

• Range

• Standard Deviation

• Variance

Measures of Variability (3)

Range

the difference between the highest and the lowest scores

Standard Deviation

The average distance of scores from the mean

👉 Shows how much scores go above or below the mean.

Variance

the average squared deviation around the mean

Variance

the standard deviation squared