Week 6 (Test Administration, Norms & Standardised Scores)

What does the property of magnitude refer to in measurement scales?

The concept of "moreness" — the ability to compare instances as having more, less, or equal amounts of a trait.

What does the equal intervals property mean in a scale?

The difference between any two adjacent points on the scale is the same across the entire scale.

Do most psychological tests have equal intervals?

No, most do not — equal score differences may not reflect equal differences in the trait.

What is meant by an absolute zero on a measurement scale?

Indicates a complete absence of the trait being measured (e.g., 0 heart rate = no heartbeat).

What is a nominal scale?

A scale that categorizes data without magnitude, equal intervals, or absolute zero (e.g., gender, ethnic codes). Only classification is possible.

What mathematical operations are valid for nominal scales?

None; only categorization is valid.

What is an ordinal scale?

A scale with magnitude only; it ranks data but does not have equal intervals (e.g., race positions, IQ ranks).

Can you perform arithmetic on ordinal scale data?

No; the intervals between ranks are not known, so averages and differences are not meaningful.

What is an interval scale?

A scale with magnitude and equal intervals but no absolute zero (e.g., temperature in Celsius/Fahrenheit).

Can ratio comparisons be made with interval scales?

No; without a true zero, statements like “twice as much” are invalid.

What is a ratio scale?

A scale with magnitude, equal intervals, and an absolute zero (e.g., weight, height, speed).

What operations are valid on a ratio scale?

All arithmetic operations, including meaningful ratios (e.g., 60 kg is twice 30 kg).

What does a frequency distribution show?

How often each score occurs within a dataset—provides context for individual scores.

How are scores arranged in a frequency distribution?

Scores on the X-axis (low to high), frequency on the Y-axis.

What is the typical shape of test score distributions?

Bell-shaped (normal distribution), with most scores clustering around the center.

What does a positively skewed distribution indicate?

A tail that extends to the right

What does a negatively skewed distribution indicate?

A tail that extends to the left

What does percentile rank indicate?

The percentage of scores that fall below a given score.

What is the formula for calculating percentile rank?

Pr = (B / N) × 100

What does ‘B’ mean in Pr = (B / N) × 100

Number of scores below the score of interest

What does ‘N’ Pr = (B / N) × 100

Total number of scores

Is the percentile rank the same as the percentage score?

Percentile rank reflects relative position, not raw performance.

What does a percentile indicate?

A position in the distribution that corresponds with a specific raw score.
E.g., P25 = 25% of scores are below this value.

In relation to percentiles what is P25?

First Quartile = 1 quarter of scores are below this value 

How do you calculate a percentile position?

Pi = (n × desired percentile)/100 + 0.5
Arrange the data from smallest to largest 

Decide which percentile you want to calculate

• Then, find the raw score at that rank.

What does ‘pi’ mean in Pi = (n*pi)/100 + 0.5?

Percentile you are interested in

What does ‘n’ mean in Pi = (n*pi)/100 + 0.5?

Total number of scores in the sample

In relation to percentiles what is P50?

Second Quartile = 2 quarter of scores are below this value

In relation to percentiles what is P75?

Third Quartile = 3 quarter of scores are below this value

What are advantages of using percentiles & percentile ranks?

• Easy to calculate

• Intuitively understandable

What are limitations of percentile ranks?

• Distort scale properties

• Not equal-interval

• Same raw score gap ≠ same percentile gap

• Less useful for detailed data analysis

Why is percentile transformation considered non-linear?

It compresses differences at the distribution ends and exaggerates them in the middle.

What is the Mean in a distribution?

The arithmetic average: sum of all scores divided by the number of cases.

What does Standard Deviation (SD) tell us?

It estimates how much scores vary around the mean — indicates spread or variability.

What does a small SD indicate?

Most scores are close to the mean (low variability).

What does a large SD indicate?

Scores are spread out more widely from the mean (high variability).

What are Standard Scores?

Scores that show how far a raw score is from the mean in SD units.

What is a Z score and how is it calculated?

Z = (Xi − Mean) / SD

What do Z-scores do?

Standardizes raw scores to indicate distance from the mean in SDs.

What does a Z score of 0 mean?

The score is exactly at the mean.

What do positive Z scores indicate?

Z > 0: Above the mean

What do negative Z scores indicate?

Z < 0: Below the mean

Why are Z scores useful?

They allow comparison of scores across different scales or distributions.

What is the Standard Normal Distribution?

A theoretical, symmetrical, bell-shaped curve based on probability theory, central to statistics and psych testing.

What is the mean of the standard normal distribution?

0

What is the standard deviation of the standard normal distribution?

1 (Z scores on X-axis).

68% of scores are within

±1 SDs

95% of scores are within

±2 SDs

99.7% of scores are within

±3 SDs

What percentile is a score 1 SD above the mean?

84th percentile.

What percentile is a score 1 SD below the mean?

16th percentile.

Why is the standard normal distribution important?

• It supports many inferential statistics

• Allows precise probability calculations

• Reflects natural distribution of many human traits

What makes the standard normal distribution mathematically useful?

We can compute exact areas under the curve to determine percentages of cases within score ranges.

Why does the standard normal distribution frequently occur in nature?

Many human characteristics (physical & psychological) naturally follow a normal distribution.

What is a standardised score system?

A method to convert z-scores into a new scale with a defined mean and SD.

What is the formula to convert a z-score into another system?

y=SZ+M

• y= converted score

• S = SD of new system

• Z = z-score

• M = mean of new system

What is McCall’s T-score system?

A standard score with a mean of 50 and SD of 10.

How does McCall’s T-score differ from z-scores?

T-scores shift and scale z-scores to keep values positive and more interpretable.

What is the formula to convert a z-score to a T-score?

T=10Z+50

How do you convert a z-score to an IQ score?

IQ = 15Z + 100, where mean = 100 and SD = 15.

Why are standardised scores useful?

They enable score comparisons across different tests/scales by aligning distributions.

What are quartiles in a distribution?

Values that divide the data into 4 equal parts:

• Q1 = 25th percentile

• Q2 = 50th percentile (median)

• Q3 = 75th percentile

What are deciles in a distribution?

Values that divide the data into 10 equal parts (e.g., D9 = 90th percentile, D8 = 80th percentile).

What are 3 advantages of using standard scores?

• Allow comparison within/across tests

• Align with normally distributed traits

• Preserve magnitude of raw score differences

What are 2 disadvantages of standard scores?

• Require understanding of z-scores and normal curve

• Different systems use varying means and SDs, which can be confusing

What are norms in psychological testing?

Score distributions from defined groups used to interpret individual test performance relative to peers.

What is the norm group?

A representative sample of the target population for whom the test is intended.

Why is test standardisation important?

It establishes score distributions in the norm group, allowing future examinees to be compared to that distribution.

What are the 5 steps in norms development?

• Develop the test: define, create, analyze, and validate items

• Sampling: select a representative group

• Testing and scoring: administer and collect raw scores

• Describe scores: calculate central tendency, reliability, and distribution

• Standardising: convert raw scores into a standardised score system

What are age-related norms?

Norms developed separately for different age ranges to reflect developmental differences.

Why are different norm groups used?

Different populations may have varying score distributions; separate norms are used for different test purposes (e.g., selection, training, development).

What are examples of norm types?

National, international, convenience, subgroup, local, and institutional norms.

What are developmental norms?

Norms created for traits that change systematically with age or grade.

What is Age Equivalence (AE)?

Indicates average test performance for each age group.

What is Grade Equivalence (GE)?

Indicates average test performance for each grade level.

What is random sampling in norm development?

Every member of the population has an equal chance of being selected.

What is stratified random sampling?

The population is divided into subgroups (strata) based on key variables; participants are randomly selected from each stratum proportionally.

What does "good faith" sampling involve?

Selecting a diverse, representative sample and comparing it to census data to ensure representativeness.

What are Norm-Referenced Scores?

Scores compared to a reference group to determine relative standing (e.g., WAIS-IV, personality tests).

What are Criterion-Referenced Scores?

Scores compared to a fixed benchmark or standard, not other people (e.g., pass mark of 50/100).

What type of test score is used to assess adaptive behaviour?

Criterion-referenced scores.

What are key features of norm-referenced tests?

• Used to classify across a continuum

• Broad, indirectly relevant domains

• Scores: standard score, percentile, grade equivalent

• E.g., creativity, personality, attitudes

What are key features of criterion-referenced tests?

• Assesses if a standard is met

• Narrow, directly relevant domains

• Scores: percentage with pass/fail cutoff

• E.g., reading, algebra, typing, diagnostic skills

What domains are best assessed with norm-referenced tests?

Broad traits or attributes like intelligence, personality, and creativity.

What domains are best assessed with criterion-referenced tests?

Specific skill mastery or competency like math skills, reading levels, and clinical competencies.