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## Test Validity: What it is, and why we care.

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Validity

- What is validity?
- What is a construct?: Meehl’s nomological net
- Types of validity
- Content validity
- Criterion-related validity
- Construct Validity
- Incremental Validity
- The multi-trait multi-method matrix

What is validity?

- The validity of a test is the extent to which it measures the construct that it is designed to measure
- As we shall see, there are many ways for a test to fail or succeed, and therefore: validity is not a single measure

Paul Meehl: What is a construct?

- Meehl’s definition of a construct has 6 main elements, as follows:

1.) To say what a construct is means to say what laws it is subject to.

- This is a definition = you can refuse to work with it or say why you think it is bad, but you can’t disprove it

- The sum of all laws is called a construct’s nomological network.

What does ‘nomological’ mean?

I had always believed it came from:

ad. L. nomin meaning ‘name’

I was wrong. In fact it comes from:

ad. Gr. nom combining form of a word meaning ‘law’

So ‘psychonomics’ is the study of the laws of the psyche, and ‘nomological network’ refers to a network of psychological components whose relations can be described by laws or rules

The nomological network consists of:

Adapted from: http://trochim.human.cornell.edu/kb/nomonet.htmi.) Representations of the concepts of interest (constructs)

CONSTRUCT

CONSTRUCT

CONSTRUCT

CONSTRUCT

CONSTRUCT

OBS

OBS

OBS

OBS

OBS

OBS

OBS

OBS

OBS

OBS

ii.) Their observable manifestations &

iii.) The relationships within and between i.) and ii.)

Adapted from: http://trochim.human.cornell.edu/kb/nomonet.htm

Theoretical propositions

CONSTRUCT

CONSTRUCT

CONSTRUCT

CONSTRUCT

CONSTRUCT

Operationalized theoretical constructs

OBS

OBS

OBS

OBS

OBS

OBS

OBS

OBS

OBS

OBS

Correspondence rules

Empirical observations

Paul Meehl: What is a construct?

2.) Laws may relate observable and theoretical elements

- The relations must be ‘lawful’, but they may be either causal or statistical (what’s the relation between causal and statistical?)

- What are the ‘theoretical elements’? Constructs!

Paul Meehl: What is a construct?

- What are the ‘theoretical elements’? Constructs!

- To escape from circularity and pure speculation about the properties of constructs, we need to anchor the nomological net concretely in some objective reality, hence:

3.) A construct is only admissable if at least some of the laws to which it is subject involve observables

- If not, we could define a self-consistent network of ideas that had no relevance to the real world (and many such networks have been defined! Such as?)
- You should be able to relate this idea of observables to our earlier discussion of information: what counts as observable is what counts as information (a detectable difference that makes a difference)

Paul Meehl: What is a construct?

4.) Elaboration of a construct’s nomological net = learning more about that construct

- We elaborate a construct by drawing new relations, either between elements already in the network, or between those elements and new elements outside of the network

- This elaboration is precisely the work of psychometrics, as well as the work of science in general

Paul Meehl: What is a construct?

5.) Ockham’s razor + Einstein’s addendum

- That is: make things as simple as possible, but no simpler

6.) Identity means ‘playing the same role in the same network’

- If it looks like a duck, walks like a duck, and quacks like a duck: then it is a duck!*

- Or (in the spirit of Gregory Bateson): If it makes no difference, then it makes no difference.

* at least pending further investigation

How to measure validity

- Analyze the content of the test
- Relate test scores to specific criteria
- Examine the psychological constructs measured by the test

Construct validity

- Construct validity = the extent to which a test measures the construct it claims to measure
- Does an intelligence test measure intelligence? Does a neuroticism test measure neuroticism? What is latent hostility since it is latent?
- As Meehl notes, construct validity is very general and often very difficult to determine in a definitive manner
- If it looks like a measure of the skill or knowledge it is supposed to measure, we say it has face validity
- How can we determine construct validity? (How will you know if you get given a good exam in this class?)

Construct validity

- There are two kinds of construct validity: convergent validity or discriminant validity
- Convergent validity(sometimes called empirical validity) means that the measure under consideration agrees with other measures that are alleged (or theoretically supposed to) to measure the same things
- Divergent validity means that the measure under consideration is distinct from other measures that are alleged (or theoretically supposed to) to measure different things

Content validity

- Content validity = the extent to which the test elicits a range of responses over the range of of skills, understanding, or behavior the test measures; the extent to which it reflects the specific intended domain of content
- In abstract and/or complex domains, it may be quite difficult to ensure content validity
- Could a test have construct validity but not content validity?

- Criterion-related validity depends upon relating test scores to performance on some relevant criterion or set of criteria
- i.e. Validate tests against school marks, supervisor ratings, or dollar value of productive work
- There are two kinds of criterion-related validity: concurrent and predictive

- Concurrent validity = the validity criterion are available at the time of testing
- i.e. give the test to subjects who have been selected for their economic background or diagnostic group
- the validity of the MMPI was determined in this manner

- Predictive validity = the criterion are not available at the time of testing
- concerned with how well test scores predict future performance
- For example, IQ tests should correlate with academic ratings, grades, problem-solving skills etc.
- A good r-value for most psychological questions would be .60

What affects validity?

i.) Moderator variables: Those characteristics that define groups, such as sex, age, personality type etc.

- A test that is well-validated on one group may be less good with another

- Validity is usually better with more heterogeneous groups, because the range of behaviors and test scores is larger

And therefore:

ii.) Base rates: Tests are less effective when base rates are very high or very low (that is, whenever they are skewed from 50/50)

What affects validity?

iii.) Test length

- For similar reasons of the size of the domain sampled (think of the binomial rabbits or trying to decide how biased a coin is), longer tests tend to be more reliably related to the criterion than shorter tests

Test length

- Informally, we can see that the same size changes (such as being 1 flip away from fair) make more difference to the size of area under the curve when N is low
- Next class we consider how to think about this for other values in a more formal manner

What affects validity?

iii.) Test length

- For similar reasons of the size of the domain sampled (think of the binomial rabbits or trying to decide how biased a coin is), longer tests tend to be more reliably related to the criterion than shorter tests

- Note that this depends on the questions being independent (= every question increasing information)

- When it is not, longer tests are not more reliable

- eg. short forms of WAIS

- However, note that independence need only be partial (|r| < 1, but not necessarily r = 0)

What affects validity?

iv.) The nature of the validity criterion

- Criterion can be contaminated, especially if the interpretation of test responses is not well-specified, allowing for results to ‘feed back’ to criterion

- In such cases, there is confusion between the validation criteria and the test results = the circularity of self-fulfilling prophecy (a ‘dormitive principle’)

- In essence we are then stuck at the theoretical level of the nomological net, with no way for empirical study (= no information) to tell us we are wrong

How to measure construct validity

i.) Get expert judgments of the content

ii.) Analyze the internal consistency of the test (Tune in next class for how to do this, and why it is not strictly validity, though it informs validity)

iii.) Study the relationships between test scores and other non-test variables which are known/presumed to relate the same construct

- eg. Meehl mentions Binet’s vindication by teachers

iv.) Question your subjects about their responses in order to elicit underlying reasons for their responses.

v.) Demonstrate expected changes over time

How to measure construct validity

vi.) Study the relationships between test scores and other test scores which are known/presumed to relate to (or depart from) the construct (Convergent versus discriminant validity)

- Multitrait-multimethod approach: Correlations of the same trait measured by the same and different measures > correlations of a different trait measured by the same and different measures [ We will look at this in more detail in a minute.]

What if correlations of measures of different traits using the same method > correlations of measures of the same trait using different methods?

- Incremental validity refers to the amount of gain in predictive value obtained by using a particular test (or test subset)
- If we give N tests and are 90% sure of the diagnosis after that, and the N+1th test will make us 91% sure, is it worth ‘buying’ that gain in validity?
- Cost/benefit analysis is required.

Validity coefficient

- Validity coefficient = correlation (r) between test score and a criterion
- There is no general answer to the questions: how high should a validity coefficient be? Or: What shall we use for a criterion?

Measuring validation error

- Coefficient of determination =r2

= the percent of variation explained

- Coefficient of alienation = k = (1 - r2)0.5
- k is the inverse to correlation: a measure of nonassociation between two variables
- If k = 1.0, you have 100% of the error you’d have had if you just guessed (since this means your r was 0)
- If k = 0, you have achieved perfection = your r was 1, and there was no error at all*
- If k = 0.6, you have 60% of the error you’d have had if you guessed

* N.B. This never happens.

Example

- The correlation between SAT scores and college performance is 0.40. How much of the variation in college performance is explained by SAT Scores?
- r2 = 0.16, so 16% of the variance is explained (and so 84% is not explained).
- What is the coefficient of alienation?
- Sqrt(1- 0.16) = Sqrt(0.84) = 0.92

Why should we care?

- k is useful in reporting accuracy of a test in a way which is unit free BUT notice that it tells you nothing you didn’t already know from being told r
- It has some other uses in statistics [beyond the scope of this class]

Multitrait-multimethod matrix

- The multi-trait, multi-method matrix is a way of representing the relations between several traits (constructs) and several methods for measuring those constructs, in a systematic and organized fashion
- The organization allows one to display and understand a great deal of information about both reliability (which we will discuss in detail next class) and validity in a compact form

Multitrait-multimethod matrix

Image from: http://trochim.cornell.edu/kb/mtmmmat.htm

Multitrait-multimethod matrix

Image from: http://trochim.cornell.edu/kb/mtmmmat.htm

- Validity diagonals: Tell you how well you can measure the same construct using different methods (monotrait-heteromethod diagonals)
- Each entry shows the correlation between two different methods used to measure the same construct
- We hope these will be highly correlated = convergent validity

Multitrait-multimethod matrix

Image from: http://trochim.cornell.edu/kb/mtmmmat.htm

- Heterotrait monomethod triangles: These show different constructs measured by the same method
- Correlations of the same trait measured by the same and different measures (Validity diagonals) should be greater than correlations of a different trait measured by the same and different measures (Heterotrait monomethod triangles)
- If not, what is going on?

Multitrait-multimethod matrix

Image from: http://trochim.cornell.edu/kb/mtmmmat.htm

- Heterotrait heteromethod triangles: These show different constructs measured by different methods
- Because they share neither trait nor method, they should be expected to be low

Multitrait-multimethod matrix

Image from: http://trochim.cornell.edu/kb/mtmmmat.htm

- Reliability diagonal: Test-Retest or internal consistency reliabilities
- These tell you how reliably you can measure each construct (A,B,C) with each method ( = mono-trait, mono-method correlations)
- Next class we discuss reliability in detail

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