Test Theory | All the Chapters
Chapter 1 | The world of Psychological Testing ecture I
5 ways to introduce the field
1) Categories of tests.
2) Uses and users of tests.
3) Issues: assumptions and questions.
4) Historical periods and forces (not focused on).
5) By definition.
Categories of tests
- Mental ability tests are subdivided into individually administered intelligence tests.
group administered intelligence tests and other ability tests.
- Achievement tests attempt to test a person's level of knowledge or skill in a particular
domain.
- Objective personality tests test personality objectively, based on items answered in
e.g., a true/false format.
- Projective techniques are tests such as the Rorschach Inkblot Test.
- Neuropsychological tests are designed to yield information about the functioning of
the central nervous system, especially the brain.
Additional ways to categorise tests:
- Paper-and-pencil vs performance → using paper and pencil to answer a set of
questions vs completing actions (e.g., leading a group).
- Speed vs power → how fast vs testing the limit of an ability.
- Individual vs Group.
- Maximum performance vs Typical performance → achievement and ability tests vs
personality, interest and attitude tests.
- Norm-referenced interpretation vs criterion-referenced interpretation → tests norms
based on performance of cases in a standardisation program vs reference to clearly
defined criterion rather than on reference to a set of norms.
Major contexts for the use of tests
The fields of clinical psychology, counselling, school psychology, and neuropsychology
use tests for clinical use. In educational settings, tests such as group-administered tests of
ability and achievement are used. Tests are then also used to predict success in academic
work. Personnel/employment testing is used in business and military settings. Research also
uses tests. There are three subcategories:
1) Tests serve as the operational definition of the dependent variable.
2) Describing samples.
3) Research on the tests themselves.
Four crucial assumptions
1) People differ in important traits. Examples of traits are memory, extroversion, and
depression.
2) We can quantify those traits. This means arranging cases along a continuum.
3) These traits are reasonably stable.
4) Measures of the traits relate to actual behaviour.
,Reliability refers to the stability of test scores. Validity refers to what the test is actually
measuring. Included within validity is the concept of fairness. Fairness is the flip side of bias.
Interpretation of tests usually depends on norms. Norms are based on the test scores of large
groups of individuals who have taken the test in the past.
The differential perspective assumes that the answer to a question may differ for
different people. We are more interested in how people differ than in how they are the same.
We think about differences in terms of syndromes or dimensions. Syndromes describe a
specific condition; you either have it or you don't. The dimensional approach describes a
continuum from less to more, etc.
There are six common elements that make a test a test:
1) A test is some form of procedure or device.
2) A test yields information.
3) The procedure or device yields information about behaviour land cognitive processes).
4) A test yields information only about a sample of behaviour.
5) A test is a systematic, standardised procedure.
6) There is some reference to quantification or measurement.
There are three uses of the term standardised:
1) A uniform procedure for administering and scoring.
2) The test has norms (lecturer doesn't necessarily agree).
3) Group-admin is tired, machine - scored. multiple choice tests of ability and
achievement.
, Chapter 3 | Test Norms ecture I
Purpose of norms
The raw score is the more or less immediate result of an individual's responses to a
test. In the normed score system, the individual's raw score is compared with scores of
individuals in the norm group. Normed scores are also known as derived scores or scale
scores.
Variables
Variables are objects we study that vary from less to more. At the most general level,
a variable is a construct. We then give verbal descriptions and definitions of the variable. The
operational definition of the variable is how we measure it. Statistics operate on raw data, the
most specific level for a variable. There are two divisions of statistics:
1) Descriptive statistics summarise or describe the raw data to aid our understanding of
it.
2) Inferential statistics draw conclusions - inferences- about what is probably true in the
population based on what we discovered about the sample.
Types of scales
- Nominal scale: distinguishes objects from one another by tagging each object with a
number.
- Ordinal scale: objects are assigned numerals that indicate an ordering, such as more or
less of a trait, without specifying anything about the distances between objects on the
scale.
- Interval scale: places objects in order and does so with equal intervals.
- Ratio scale: places objects in order, does so with equal intervals, and has a true zero
point which indicates the complete absence of something.
Most of our psychological measurements are on an ordinal or interval scale.
Organising raw data
A frequency distribution organises raw data into groups of adjacent scores. It is
usually converted to a graphic form frequency histogram or a frequency polygon.
Central tendency
An index for the complete set of data is called a measure of central tendency – the
centre around which the raw data tend to cluster. There are three commonly used measures:
∑"
1) Mean; the arithmetic average. ! = #
2) Median; the middle score.
3) Mode; the most frequently occurring score.
The measure of central tendency is easy to use but robs any sense of variability. Therefore, we
provide an index of variability:
- The range is the distance from the lowest to the highest score.
∑(%&%'())!
- The standard deviation: #$ = % #
where & = & − &()*.
- The variance, which is simply sd2.
- The inter quartile range (IQR): the distance between the first and third quartiles.
Z-score
"&"+,-
A z-score is defined as + = ./
. The distribution is ~ N (0. 1) .
, Shapes of distributions
- Normal curve/Normal distribution: symmetrical.
- Kurtosis: describes the "peakedness" of a distribution: leptokurtic distribution (sharp).
vs platykurtic distribution (flat).
- Skewness: the degree of symmetry for the left and right sides of the curve: positive
skewness (peak on the left) vs negative skewness (peak on the right).
The raw score
Consider theta (q).
The major categories of test norms
1) Percentile ranks: PR tells the percentage of cases in the norm group falling below a
given raw score.
0
↳ -. = 1 × 011 in which B is the amount of scores below x and n the total amount of
scores. formula is
given .
↳ A percentile (% ile) is a point on a scale below which a specified percentage of
cases falls. Note that you have to order the scores first !
↳ see table 3.2 (pdf pg. 105) for some widely used standard score systems.
2) Standard scores are conversions of z-scores into a new system with an arbitrarily
chosen mean (m) and standard deviation (sd).
23.
↳ to convert a raw score into a standard score: 33 = × (& − 5*) + 5# formula is given .
23-
• SS = desired standard score
• SDs = sd in the standard score system
• SDr = sd in the raw score system
• Mr = mean in the raw score system
• Ms = mean in the standard score system
• X= raw score
→ When the score (X) is translated into z-score form, the formula is: SS= z (SDs) +
5#
3) Developmental norms (see next page).
T-scores are standard scores with M = 50 and SD = 10.
The SAT is a standard scores system with M = 500 and SD = 100.
Deviation IQ's
45
Normally, <= = 65 × 100. This is also called a ratio IQ because it represents the ratio
of MA to CA. The IQ's obtained from modern intelligence tests are not ratio IQ's. They
are standard scores with M = too and SD = is or 16. These standard scores are often called
deviation IQ's.
Stanines
Stanines are a standard score system with M = 5 and SD ≈ 2. Stanines were
constructed to a) divide the normal distribution into g units and b) have the units cover equal
distances on the base of the normal curve, except for units 1 and 9.
The normal curve equivalent (NCE) is a standard scores system developed so that the
NCE's are equal to percentile ranks at points 1, 50 and 99.
Scaled scores are raw scores obtained from different levels on tests. Often linked by a
Chapter 1 | The world of Psychological Testing ecture I
5 ways to introduce the field
1) Categories of tests.
2) Uses and users of tests.
3) Issues: assumptions and questions.
4) Historical periods and forces (not focused on).
5) By definition.
Categories of tests
- Mental ability tests are subdivided into individually administered intelligence tests.
group administered intelligence tests and other ability tests.
- Achievement tests attempt to test a person's level of knowledge or skill in a particular
domain.
- Objective personality tests test personality objectively, based on items answered in
e.g., a true/false format.
- Projective techniques are tests such as the Rorschach Inkblot Test.
- Neuropsychological tests are designed to yield information about the functioning of
the central nervous system, especially the brain.
Additional ways to categorise tests:
- Paper-and-pencil vs performance → using paper and pencil to answer a set of
questions vs completing actions (e.g., leading a group).
- Speed vs power → how fast vs testing the limit of an ability.
- Individual vs Group.
- Maximum performance vs Typical performance → achievement and ability tests vs
personality, interest and attitude tests.
- Norm-referenced interpretation vs criterion-referenced interpretation → tests norms
based on performance of cases in a standardisation program vs reference to clearly
defined criterion rather than on reference to a set of norms.
Major contexts for the use of tests
The fields of clinical psychology, counselling, school psychology, and neuropsychology
use tests for clinical use. In educational settings, tests such as group-administered tests of
ability and achievement are used. Tests are then also used to predict success in academic
work. Personnel/employment testing is used in business and military settings. Research also
uses tests. There are three subcategories:
1) Tests serve as the operational definition of the dependent variable.
2) Describing samples.
3) Research on the tests themselves.
Four crucial assumptions
1) People differ in important traits. Examples of traits are memory, extroversion, and
depression.
2) We can quantify those traits. This means arranging cases along a continuum.
3) These traits are reasonably stable.
4) Measures of the traits relate to actual behaviour.
,Reliability refers to the stability of test scores. Validity refers to what the test is actually
measuring. Included within validity is the concept of fairness. Fairness is the flip side of bias.
Interpretation of tests usually depends on norms. Norms are based on the test scores of large
groups of individuals who have taken the test in the past.
The differential perspective assumes that the answer to a question may differ for
different people. We are more interested in how people differ than in how they are the same.
We think about differences in terms of syndromes or dimensions. Syndromes describe a
specific condition; you either have it or you don't. The dimensional approach describes a
continuum from less to more, etc.
There are six common elements that make a test a test:
1) A test is some form of procedure or device.
2) A test yields information.
3) The procedure or device yields information about behaviour land cognitive processes).
4) A test yields information only about a sample of behaviour.
5) A test is a systematic, standardised procedure.
6) There is some reference to quantification or measurement.
There are three uses of the term standardised:
1) A uniform procedure for administering and scoring.
2) The test has norms (lecturer doesn't necessarily agree).
3) Group-admin is tired, machine - scored. multiple choice tests of ability and
achievement.
, Chapter 3 | Test Norms ecture I
Purpose of norms
The raw score is the more or less immediate result of an individual's responses to a
test. In the normed score system, the individual's raw score is compared with scores of
individuals in the norm group. Normed scores are also known as derived scores or scale
scores.
Variables
Variables are objects we study that vary from less to more. At the most general level,
a variable is a construct. We then give verbal descriptions and definitions of the variable. The
operational definition of the variable is how we measure it. Statistics operate on raw data, the
most specific level for a variable. There are two divisions of statistics:
1) Descriptive statistics summarise or describe the raw data to aid our understanding of
it.
2) Inferential statistics draw conclusions - inferences- about what is probably true in the
population based on what we discovered about the sample.
Types of scales
- Nominal scale: distinguishes objects from one another by tagging each object with a
number.
- Ordinal scale: objects are assigned numerals that indicate an ordering, such as more or
less of a trait, without specifying anything about the distances between objects on the
scale.
- Interval scale: places objects in order and does so with equal intervals.
- Ratio scale: places objects in order, does so with equal intervals, and has a true zero
point which indicates the complete absence of something.
Most of our psychological measurements are on an ordinal or interval scale.
Organising raw data
A frequency distribution organises raw data into groups of adjacent scores. It is
usually converted to a graphic form frequency histogram or a frequency polygon.
Central tendency
An index for the complete set of data is called a measure of central tendency – the
centre around which the raw data tend to cluster. There are three commonly used measures:
∑"
1) Mean; the arithmetic average. ! = #
2) Median; the middle score.
3) Mode; the most frequently occurring score.
The measure of central tendency is easy to use but robs any sense of variability. Therefore, we
provide an index of variability:
- The range is the distance from the lowest to the highest score.
∑(%&%'())!
- The standard deviation: #$ = % #
where & = & − &()*.
- The variance, which is simply sd2.
- The inter quartile range (IQR): the distance between the first and third quartiles.
Z-score
"&"+,-
A z-score is defined as + = ./
. The distribution is ~ N (0. 1) .
, Shapes of distributions
- Normal curve/Normal distribution: symmetrical.
- Kurtosis: describes the "peakedness" of a distribution: leptokurtic distribution (sharp).
vs platykurtic distribution (flat).
- Skewness: the degree of symmetry for the left and right sides of the curve: positive
skewness (peak on the left) vs negative skewness (peak on the right).
The raw score
Consider theta (q).
The major categories of test norms
1) Percentile ranks: PR tells the percentage of cases in the norm group falling below a
given raw score.
0
↳ -. = 1 × 011 in which B is the amount of scores below x and n the total amount of
scores. formula is
given .
↳ A percentile (% ile) is a point on a scale below which a specified percentage of
cases falls. Note that you have to order the scores first !
↳ see table 3.2 (pdf pg. 105) for some widely used standard score systems.
2) Standard scores are conversions of z-scores into a new system with an arbitrarily
chosen mean (m) and standard deviation (sd).
23.
↳ to convert a raw score into a standard score: 33 = × (& − 5*) + 5# formula is given .
23-
• SS = desired standard score
• SDs = sd in the standard score system
• SDr = sd in the raw score system
• Mr = mean in the raw score system
• Ms = mean in the standard score system
• X= raw score
→ When the score (X) is translated into z-score form, the formula is: SS= z (SDs) +
5#
3) Developmental norms (see next page).
T-scores are standard scores with M = 50 and SD = 10.
The SAT is a standard scores system with M = 500 and SD = 100.
Deviation IQ's
45
Normally, <= = 65 × 100. This is also called a ratio IQ because it represents the ratio
of MA to CA. The IQ's obtained from modern intelligence tests are not ratio IQ's. They
are standard scores with M = too and SD = is or 16. These standard scores are often called
deviation IQ's.
Stanines
Stanines are a standard score system with M = 5 and SD ≈ 2. Stanines were
constructed to a) divide the normal distribution into g units and b) have the units cover equal
distances on the base of the normal curve, except for units 1 and 9.
The normal curve equivalent (NCE) is a standard scores system developed so that the
NCE's are equal to percentile ranks at points 1, 50 and 99.
Scaled scores are raw scores obtained from different levels on tests. Often linked by a
