# PSYC32H3 Chapter Notes - Chapter 1: Percentile Rank, Truncated Distribution, Standard Score

by OC65075

Department

PsychologyCourse Code

PSYC32H3Professor

Zachariah CampbellChapter

1Chapter 1 Psychometrics in Neuropsychological Assessment

The Normal Curve

Basis of many commonly used statistical and psychometric models and is the assumed

distribution for many psychological variables.

Definition and Characteristics

Unimodal, symmetrical, asymptotic at the tails.

The ordinate (height of the curve at any point along the x-axis) is the proportion of

persons within the sample who obtained a given score.

Normal curve can also be referred to as a probability distribution.

Relevance for Assessment

As a frequency distribution, the area under any given segment of the normal curve

indicates the frequency of observations or cases within that interval.

•This provides psychologists with an estimate of the normality/abnormality of any

given test score or range of scores

oNormality – score falls in the center of the bell shape, where most of the

scores are located

oAbnormality – score falls at the ends of the bell shape, where there are

few scores

Z Scores and Percentiles

Percentile: the percentage of scores that fall at or below a given test score

Converting scores to percentiles – raw scores are ‘standardized’. Usually to Z scores

z = (x – X)/SD

x= measurement value (test score)

X= the mean of the test score distribution

SD= the standard deviation of the test score distribution

Resulting distribution of Z scores has a mean of 0 and a SD of 1.

Interpretation of Percentiles

The relationship between raw or Z scores and percentiles is not linear.

•A constant difference between raw or Z scores will be associated with a variable

difference in percentile scores, as a function of the distance of the two scores

from the mean.

•This is due to the fact that there are proportionally more observations (scores)

near the mean than there are farther from the mean

oOtherwise, the distribution would be rectangular or non-normal

Linear Transformations of Z Scores: T Scores and Other Standard Scores

Linear transformation can be used to produce other standardized scores.

T scores, Z scores, standard scores, and percentile equivalents are derived from

samples. They are often treated as population values, any limitations of generalizability

due to reference sample composition or testing circumstances must be taken into

consideration when standardized scores are interpreted.

The Meaning of Standardized Test Scores: Score Interpretation

When comparing scores, it should be done when the distributions for tests that are

being compared are approximately normal in the population. If standardized scores are

to be compared, they should be derived from similar samples or (more ideally) from the

same sample.

Also when comparing scores, the reliability of the two measures must be considered

and they intercorrelation before determining if a significance exists.

•Relatively large disparities between standard scores may not actually reflect

reliable differences and therefore may not be clinically meaningful.

When test scores are not normally distributed, standardized scores may not accurately

reflect actual population rank.

Comparability across tests does not imply equality in meaning and relative importance

of scores.

Interpreting Extreme Scores

In clinical practice, one may encounter standard scores that are either extremely low or

high. The meaning/comparability of the scores depends on the characteristics of the

normative sample from which they derive.

Whenever extreme scores are being interpreted, examiners should verify that an

examinee’s score falls within the range of raw scores in the normative sample.

•If the normative sample size is substantially smaller than the estimated

prevalence size and the examinee’s score falls outside the sample range, then

considerable caution may be indicated in interpreting the percentile associated

with the standardized score.

When interpreting extreme scores, it depends on the properties of the normal samples

involved.

The Normal Curve and Test Construction

A test with a normal distribution in the general population may show extreme skew or

other divergence from normality when administered to a population that differs

considerably from the average individual.

Whether a test produces a normal distribution is also an important aspect of evaluating

tests for bias across different populations.

Depending on the characteristics of the construct being measured and the purpose for

which a test is being designed, a normal distribution of scores may not be obtainable or

desirable. For example:

•The population distribution of the construct being measured may not be normally

distributed

•One may want only to identify and/or discriminate between persons at only one

end of a continuum of abilities

oThe characteristics of only one side of the sample score distribution are

critical while the characteristics on the other side of the distribution are not

considered important

oThe measure may even be deliberately designed to have floor or ceiling

effects

Non-Normality

It is not unusual for test score distributions to be markedly non-normal, even with large

samples.

The degree to which a given distribution approximates the underlying population

distribution increases as the number of observations (N) increases and becomes less

accurate as N decreases.

•Larger sample will produce a more normal distribution only if the underlying

population from which the sample is obtained is normal.

**Unlock Document**

###### Document Summary

Basis of many commonly used statistical and psychometric models and is the assumed distribution for many psychological variables. The ordinate (height of the curve at any point along the x-axis) is the proportion of persons within the sample who obtained a given score. Normal curve can also be referred to as a probability distribution. Percentile: the percentage of scores that fall at or below a given test score. Converting scores to percentiles raw scores are standardized". Usually to z scores z = (x x)/sd x= measurement value (test score) X= the mean of the test score distribution. Sd= the standard deviation of the test score distribution. Resulting distribution of z scores has a mean of 0 and a sd of 1. Linear transformations of z scores: t scores and other standard scores. Linear transformation can be used to produce other standardized scores. T scores, z scores, standard scores, and percentile equivalents are derived from samples.

## More from OC65075

###### PSYC32H3 Chapter Notes - Chapter 1: Clinical Neuropsychology, Neuropsychological Test, Neuropsychology

Textbook Note

## Similar documents like this

###### PSYC32H3 Lecture Notes - Lecture 4: Reticular Formation, Medulla Oblongata, Corticospinal Tract

Lecture Note

###### PSYC32H3 Lecture Notes - Lecture 5: Stimulant, Ephedrine, Behaviour Therapy

Lecture Note

###### PSYC32H3 Chapter Notes - Chapter 1: Neuropsychological Assessment, Neurofibrillary Tangle, Senile Plaques

Textbook Note

###### PSYC32H3 Chapter Notes -Selective Serotonin Reuptake Inhibitor, Fluoxetine

Textbook Note

###### PSYC32H3 Chapter Notes - Chapter 3: Vasoconstriction, Anaplasia, Idiopathy

Textbook Note

###### PSYC32H3 Lecture 1: PSY62H1 Lecture 1 - Introduction

Lecture Note

###### PSYC31_ Chapters 1,3,5 .docx

Textbook Note

###### PSYC32H3 Chapter Notes - Chapter 1: Evoked Potential, Telepathy, Angiography

Textbook Note

###### PSYC32H3 Lecture Notes - Lecture 2: Anterograde Amnesia, Long-Term Memory, Prospective Memory

Lecture Note

###### PSYC32H3 Chapter Notes - Chapter 4: Antibody, Sarin, Analog Science Fiction And Fact

Textbook Note

###### PSYC32H3 Chapter Notes - Chapter 1: Clinical Neuropsychology, Neuropsychological Test, Neuropsychology

Textbook Note

###### PSYC32H3 Chapter Notes - Chapter 2: Neocortex, Homeostasis, Red Nucleus

Textbook Note

###### PSYC32H3 Chapter 2: Reading 1 Notes Week 2

Textbook Note

###### PSYC32H3 Chapter 8: CHAPTER 8 PSYC31

Textbook Note

###### PSYC32H3 Study Guide - Final Guide: Knowledge Society, Data Analysis, Living Wage

Exam Note