PSYC3302 - Complete terms

Psychometrics

The science concerned with evaluating the attributes of psychological tests and the procedures used to estimate and evaluate the attributes of tests. Involves reliabilty and validity.

Psychological construct 

An unobservable hypothetical entity that is used to represent a pattern of psychologically related phenomena. Nature is abstract.

Tests or indicators used to represent a construct 

Should be __linked theoretically__ to the definition of the construct.

Psychological test

A systematic procedure for comparing the behavior of two or more people.

Criteria of tests

1) Tests involve behavioural samples of some kind.

2) The behavioural samples must be collected in some systematic way.

3) The purpose of tests is to compare behaviours of two ore more people.

Inter-individual differences

__Comparing__ the cognition/behaviour of different people.

Intra-individual differences

Measure changes in the behaviour of the same people across time.

Types of tests

1: Content (e.g., skill, personality, attitudes)

2: Types of responses (e.g., multiple-choice, open-ended)

3: Administration procedure (e.g., individual vs. group)

4: Intended purpose (criterion vs. norm referenced)

5: Time constraints (speed vs. power)

Criterion referenced tests

Involve a __cut-off score__ that specifies whether someone has achieved a sufficient level of the skill or capacity. Used in contexts where a decision must be made about someone’s __skill level__.

Norm referenced test

Involve comparing a person’s score with that of a __reference sample__. Reference sample is considered to be __representative__ of the population of interest. Compared against the average score.

Scaling

The way in which numerical values are assigned to psychological attributes.

Properties of Identity

Differentiate categories of people who share a psychological feature (do and don’t). Numbers may be used to __label the categories__ - do __not have any inherent meaning__ or true mathematical value.


1. Categories must be mutually __exclusive__.
2. Categories should be exhaustive.
3. All people classified within a given category must be identical with respect to the attribute of interest.

Properities of Order

More informative - Give the person with the highest level of an attribute a rank of 1, or alternatively, a rank of N (i.e., where N equals the total sample size). 

Properties of Quantity

Reflects the ability of numerals to provide information about the magnitude of differences between people. Numerals used in measurment are real numbers that indicate the amount of something. Can compare cases with each other in a meaningful way.

The number zero

Some are absolute, whereas others are relative (or arbitrary).

Additivity

Implies that the unit size of a measurement does not change as the units are being counted. When perfectly satisified is known as __conjoint measurement__.

Rarely satisfied in psychology.

Counting

Is a necessary but not sufficient condition for measurement.

Measurement

The assignment of numerals to objects or events according to rules. Numbers can be __assigned__ to __represent__ the quantities of psychological attributes.

Includes Steven’s four levels.

Nominal scales

Symbols or numerals that have a property of identity are used to label observations in which behaviors have been sorted into categories according to some psychological attribute.

Has identity.

Ordinal scales

Links observations of behaviour thought to reflect qualitative differences in amounts of an attribute to symbols or numerals that have the __property of order.__

Has identity and order.

Interval scales 

A constant distance between each of the units. However, there is no meaningful zero point.

Has identity, order and quantity.

Ratio scales

Same properites as interval but can say that a case has, say, 37% more of the attribute of interest than another case.

Has identity, order, quantity and absolute zero.

Dispersion

Represents the amount of variability in the data. Includes range, SD and variance.

Correlation

Standardized representation of the __association__ between two variables

Can range from -1.0 to 1.0

Composite Variables

Test __scores__ based on the __sum__ of __two__ or more items. Also called sum scores.

The variance of a composite score is a function of

1. The variance associated with the individual items.

2. The correlations amongst the items.

Composite variables - Variance

Binary Items

Dichotomous items - correct or incorrect answer.

Responses are scored 0 or 1.

Binary items - Variance

The variance of a dichotomously scored item is maximized when half of the people score 1 and the other half score 0.

Relative interpretations

Based on the __analysis of data__.

1: Knowing the mean of the distribution of scores

2: Knowing the standard deviation of the distribution of scores

Abstract interpretations

Based on the __theoretically relevant characteristics__ of the body of research which supports the test scores as valid indicators of a psychological construct.

Limitations of raw scores

Need to be __converted__ into standardized scores which incorporate information about the mean and standard deviation. More precise method.

*Z* scores

Have a mean of zero and a *SD* of one.

__Useful__ for the purposes of rendering inherently meaningless raw scores into easily __interpretable relative scores__.

T scores

Involves rescaling z scores so that the converted scores have a different mean and standard deviation.

Mean is __always 50__ and the standard deviation is __always 10__.

Used in MMPI.


1. Convert the raw scores into *z*-scores
2. Convert the *z*-scores using the following formula: T = z(10)+50

Percentile ranks 

Indicate the __percentage__ of scores that are __equal to__ or __below a specific test score__.

Assumes that the distribution of raw scores is perfectly normal.

Probability samples

Use procedures that ensure a representative sample.

Random sampling

Type of probability sample, as you would expect a random sample from the population to be representative of the population.

Rarely happens in practice.

Closed-ended

Questions ask respondents to choose from a fixed set of alternatives. For example, yes/no questions.

Open-ended questions

Do not provide respondents with any response alternatives. Given space to respond in their own words.

This may take a narrative form (i.e., long-answer) or short-answer

Rating Scales

The most widely used response format such as the Likert scale. Likert scales use words to ‘anchor’ the numerical ratings. Most surveys use between 4 and 7 points.

Respondents are not capable of making the distinctions between adjacent points in a rating scale with 11 or more points.

6-7 points is best → 5 points is the bare mimimum for a continously measured variable.

Reliability

Pertinent to the __consistency__ of measurement.

The degree of correspondence between __observed scores__ and __true scores__. Theoretically, the correlation between observed scores and true scores.

A __necessary but not sufficient condition for validity__.

The __discrepancy__ between observed scores and true scores is considered to be due to __measurement error__.

Opposite to measurement error.

A property of test scores (from samples), not tests, per se.

Classical Test Theory 

A measurement theory that __defines the conceptual basis of reliability__.

Specifies procedures for estimating the reliability of scores derived from a psychological test or instrument.

True scores

A __hypothetical score__ devoid of measurement error.

Conceived in the context of a particular test or instrument – not a construct. Not “construct scores”.

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May be “perfect”, but this is __only true in the context of measurement error__ associated with data derived from a particular test or instrument. We assume they are devoid of measurement error.

Observed scores

The scores we obtain __from tests__ or instruments.

We want the ______ scores to be as close to their corresponding true scores as possible.

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Want a __large (positive) correlation__ between observed scores and true scores 

Want observed scores and error scores to be __uncorrelated__.

If observed scores and error scores are correlated highly, it means they are measuring the same process: error.

An observed score is

True score + measurment error.

Error scores

Should have a __mean of zero__ - Should be just as many people that should have an observed score that is too large as too small (and the magnitudes should be the same).

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Error scores should be a __random process__ - should not correlate with anything (except possibly their corresponding observed scores).

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Error scores should be __uncorrelated with true scores__ - “extraneous” error related factors should affect people equally.

1. Reliablity is the ratio of true score variance to observed variance

The ratio of SS Effect to SS Total

Conceptually, in the reliability case, it is the ratio of SS True to SS Observed

2. Reliability is the (squared) correlation between observed scores and true scores

When you __square the reliability index__, you get a conceptual estimation of reliability.

Conceptual - it is not possible to know what the true scores are, so we’ll never be able to estimate the actual correlation.

3. Reliability is the lack of error variance

Subtract the ratio of error variance to observed variance by 1 to place in the same context of reliability (rather than error).

4. Reliability is the lack of correlation between observed scores and error scores.

If reliability is the correlation between true scores and observed scores, then it is necessarily the case that it is the absence of a correlation between observed scores and error scores.

Parallel tests

Two tests are considered ____ if they are __identical__ to each other __psychometrically__, but __differ__ in the actual __items__ that make up each test.

Tau equivalence - a person’s true score on one test would be expected to be __identical__ on the other test. Assumes equal error variances between the two tests.

Reliability guidelines

According to Nunnally.

Exploratory Research = .70 or higher

Basic Research = .80 or higher

Applied Cases = .90 or even .95 or higher

Validity

Represents the degree to which the observed scores from a test __actually represent__ the attribute (or construct) of interest.

Alternative forms reliability

Same as parallel forms.

Carry-over effects of concern - would have to wipe the memory of test taker

Test-retest reliability

Create only __one test__, but administer it on __two different occasions__.

The same items are presented on both occasions, so the true scores should represent the same construct. Assume the construct of interest to be a stable one.

All other assumptions associated with parallel forms apply.

Equal error variances

If you had people sit the test under the same conditions (e.g., same room, same time of day), you might be able to assume that responses are affected by error to the same degree.

Test-retest interval

All other things equal, the __magnitude of the interval__ between the two testing sessions will affect the magnitude of the correlation between the scores.

Also known as ‘__stability coefficient__’.

Internal-Consistency Reliability

P__ractical alternative__ to the alternative forms procedure and the test-retest procedure. Respondents complete __one form of the test__ → diff items = diff forms.

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1\. The __length__ of the test - A longer test (more items) will be found to yield more reliable scores than a shorter test.

2\. The degree of __consistency__ between the parts/items in the test.

Spearman-Brown formula

Makes an __adjustment__ to the internal consistency reliability estimate to reflect the actual length of the test.

Split-half issues

You get a different reliability estimate depending on how you specify the two halves of the test.

Very unlikely to __get the same correlation__ as in the first split-half example.

Cronbach’s alpha

A reliability formula that represents the reliability of __all possible split-halves__.

The ratio of true score variance to total variance, which is how reliability has been defined at the theoretical level.

Cronbach’s Alpha Assumptions

1. Indicators (items) are essentially tau-equivalent - each item is an equally strong indicator of the true score scores (may differ by constant).
2. Each item’s error term is uncorrelated with every other item’s error term - For items that are more alike, a positive correl exists (Cronbach can’t deal with this so it pretends it doesn’t exist).
3. Error scores are uncorrelated with the true scores.
4. Items used to generate a composite score measure only one attribute or construct - unidimensionality.

Standardized Coefficient Alpha

Should be applied to scores that have been converted from raw scores to standardized scores.

Kuder-Richardson 20 formula

Introduced to estimate the internal consistency reliability associated with composite scores based on dichotomously scored items.

Cronbach’s alpha formula works just fine on dichotomously scored items.

Parallel assumptions

Equal true score variance, equal means, equal error variance.

Most strict.

Tau-Equivalent

Equal true score variance, equal means, unequal error variances.

Essentially Tau-Equivalent

Equal true score variance, unequal means, unequal error variances.

Congeneric

Unequal true score variance (but all greater than zero), unequal means, unequal error variances.

Least strict.

Cronbach’s alpha is a lower-bound estimate

If the assumption of essential tau-equivalence is not satisfied, then Cronbach’s alpha will tend to __underestimate reliability__.

Substantial in smaller scales.

The larger the sample size, the greater the confidence.

* 0.7 = Sample of 400.
* 0.9 = Sample of 100.

Relationship between number of items and reliability

When the mean inter-item correlation is .30, it can be observed that the level of Cronbach’s alpha rises relatively rapidly from 2 items to about 8 items. 

After about 15 items, the increase is much more gradual and arguably not sufficiently beneficial in most cases.

Sample Homogeneity

A __more homogenous__ sample will yield lower reliability estimates than a __heterogeneous__ sample.

This is because greater homogeneity implies less variance. Less variance implies smaller inter-item correlations, all other things equal.

Coefficient omega (*ω*) 

A modern approach to estimating internal consistency reliability. Introduced by McDonald (1999)

Sometimes referred to as McDonald’s omega. Unlike coefficient alpha, it does not assume essential tau-equivalence.

A lower-bound estimate of reliability.

Standard error of measurement

Represents the amount of error “around” a __point estimate__ in standard deviation form.

A point-estimate is one’s “best guess” of what a person’s score is on the test.

A __confidence interval__ can be estimated around a point-estimate - reflects a range of values that is often interpreted as a range in which the true score is likely to fall.

Is high internal consistency all we want?

While high levels of reliability are desired, they are __not the only consideration__.

Tests with extremely high levels of internal consistency may be __extremely narrow__ in breadth.

Observed score correlation

The correlation you get based on the data you have. Will be compromised to the degree to which there is measurement error in your data.

“Compromised” (or __attenuated__) to the degree that the scores are associated with __less than perfect reliability__.

True score correlation

A hypothetical correlation you can estimate, if you know the reliabilities associated with the scores. Not compromised by measurement error.

R max

The maximum possible correlation between two variables is equal to the square root of the product of their respective reliabilities.

Correction for Attenuation Formula

What the correlation would have been had the measures provided perfectly reliable scores?

The ratio of the observed correlation to the square root of the product of the reliabilities (i.e., *r*max).

Validity

The degree to which a test measures __what it is supposed to measure__. M__ost important__ issue in psychological measurement

Or the degree to which evidence and theory support the interpretations of test scores entailed by the proposed uses of a test.

Related to the __proposed uses__ of the scores.

Construct validity 

The degree to which test scores can be interpreted as __reflecting__ a particular psychological __construct__.

Test content

Represents the match between the __actual content__ of the test and the __content that should be__ included in the test.

The __description__ of the nature of the construct should __help define__ the appropriate content of the test.

Includes construct and face validity.

Content Validity

When the items __cover the entire breadth__ of the construct. Items can __not exceed the boundaries__ of the construct.

Constructs such as personality __suffer from a lack of clear boundaries__.

Assessed by experts in field.

Domain sampling theory

If 110 questions in an exam represent a __random assortment__ of material covered across the entire unit, __the correlation__ between performance on a 110 final exam and a 1500 final exam would likely __be very high__.

Standard Error of Estimate

Allows for finding validity of a short form vs a long form of a particular test.

Face Validity

Face validity represents the degree to which the items associated with a measure __appear__ to be related to the construct of interest.

__Not crucial__ from a fundamental psychometric perspective More of a __practical consideration__.

Assessed by non-experts.

People can also respond in a way that they think is __most advantageous__ for them.

Factorial Validity 

The internal structure of a test - its design and what the test actually measures.

1\. The number of dimensions measured by a test.

2\. Whether the items of a test are related to the dimensions of interest.

3\. Whether the dimensions of interest are related to each other.

The ______ (hypothesized structure) of a test can be tested using various __quantitative techniques__, such as factor analysis.

Determining whether the scores of a measure correspond to the __number and nature of dimensions__ of theorized dimensions that underlie the construct of interest.

Can determine what factors “load” onto a dimension of interest.

Response Processes

Should be a __close match__ between the psychological processes that the respondents __actually use__ when completing a measure and the process that they __should use__.

Cheating is an example behaviour that seriously comprises a researcher’s capacity to interpret the scores as valid indicators of performance.

Convergent validity/evidence

The degree to which test scores __are correlated__ with tests of __similar__ constructs. Should be a __positive correlation__ between your self-reported scores and the rater-reported scores (convergent validity).

Discriminant validity/evidence

The degree to which test scores are __uncorrelated__ with tests of unrelated constructs.

It helps to know what a construct __is not__ in the process of its validation. Constructs should not correlate with everything under the sun.

Concurrent Validity Evidence

Observed when scores from one measure correlate in a theoretically meaningful way with the scores of another measure considered to be the “__gold standard__”.

Does not have to based on measures administered __precisely at the same time__ - but the time period __should be very close__.

N__ot particularly impressive__.

Predictive Validity Evidence

The degree to which test scores are correlated with relevant variables that are measured at a __future point in time__.

V__ery impressive__ - relatively rare.

Consequential Validity

S__ocial/personal consequences__ associated with using a particular test.

Criterion Validity

The observation of an association between a psychometric measure and a relevant outcome variable, such as different groups. 

Sometimes referred to as ‘criterion groups validity’.

The __oldest form of validity__.

For example, diagnosed with a clinical disorder versus not diagnosed with a clinical disorder

Induction-Construct Development Interplay

A measure is developed solely from an __inductive perspective__ (essentially through discovery).

Lot of refinement in the model along the way.

Eg. Dictionary example about personality.

Measurement as Theory

The primary objective of validation research is to offer a theoretical explanation of the processes that lead up to the measurement outcome.

Measurement considered a __fundamental theory development__ end in its own right.

Hope/assume that the measures we use yield scores that are valid indicators of the constructs of interest.

Constructs and __well articulated theories__ play a primary role in measurement and in psychology more generally.

Factor analysis

A data analytic technique used to help determine the number and nature of dimensions associated with the scores derived from a test.

1. Helps us clarify the number of factors within a set of items (or indicators).


2. Helps us determine the nature of the associations among the factors.
3. Helps us determine which items are linked to which factor, which facilitates the interpretation of those factors.

Unidimensional test

Consists of items which all measure one, single factor.

Each item is linked to one attribute only.

The degree to which each indicator is linked to the attribute can be estimated with __factor analysis__ or __component analysis__.

Multidimensional test (uncorrelated)

Consists of items which measure two or more dimensions which are unrelated to each other.

N__o link__ between the two dimensions (components/ factors). You would calculate a __separate score__ for each dimension

U__nacceptable__ to calculate a __total score__

Multidimensional test (correlated)

Consists of items which measure two or more dimensions which are correlated with each other (positively or negatively).

Higher-order model.

An overall (global) component is included, instead of a link between the two dimensions.