Chapter 5
Standardized Measurement and Assessment

(For the concept map that goes with this chapter, click here.)

Defining Measurement

When we measure, we attempt to identify the dimensions, quantity, capacity, or degree of something.

• Measurement is formally defined as the act of measuring by assigning symbols or numbers to something according to a specific set of rules.

Measurement can be categorized by the type of information that is communicated by the symbols or numbers assigned to the variables of interest. In particular, there are four levels or types of information are discussed next in the chapter. They are called the four "scales of measurement."

Scales of Measurement

1.  Nominal Scale.
This is a nonquantitative measurement scale.

• It is used to categorize, label, classify, name, or identify variables. It classifies groups or types.
• Numbers can be used to label the categories of a nominal variable but the numbers serve only as markers, not as indicators of amount or quantity (e.g., if you wanted to, you could mark the categories of the variable called "gender" with 1=female and 2=male).
• Some examples of nominal level variables are the country you were born in, college major, personality type, experimental group (e.g., experimental group or control group).

2.  Ordinal Scale.

This level of measurement enables one to make ordinal judgments (i.e., judgments about rank order).

• Any variable where the levels can be ranked (but you don't know if the distance between the levels is the same) is an ordinal variable.
• Some examples are order of finish position in a marathon, billboard top 40, rank in class.

3.  Interval Scale.

• This scale or level of measurement has the characteristics of rank order and equal intervals (i.e., the distance between adjacent points is the same).
It does not possess an absolute zero point.
• Some examples are Celsius temperature, Fahrenheit temperature, IQ scores.
• Here is the idea of the lack of a true zero point: zero degrees Celsius does not mean no temperature at all; in a Fahrenheit scale, it is equal to the freezing point or 32 degrees. Zero degrees in these scales does not mean zero or no temperature.

4.  Ratio Scale.
This is a scale with a true zero point.

• It also has all of the "lower level" characteristics (i.e., the key characteristic of each of the lower level scales) of equal intervals (interval scale), rank order (ordinal scale), and ability to mark a value with a name (nominal scale).
• Some examples of ratio level scales are number correct, weight, height, response time, Kelvin temperature, and annual income.
• Here is an example of the presence of a true zero point: If your annual income is exactly zero dollars then you earned no annual income at all. (You can buy absolutely nothing with zero dollars.) Zero means zero.

Assumptions Underlying Testing and Measurement

Before I list the assumptions, note the difference between testing and assessment. According to the definitions that we use:

• Testing is the process of measuring variables by means of devices or procedures designed to obtain a sample of behavior and
• Assessment is the gathering and integration of data for the purpose of making an educational evaluation, accomplished through the use of tools such as tests, interviews, case studies, behavioral observation, and specially designed apparatus and measurement procedures.

In this section of the text, we also list the twelve assumptions that Cohen, et al. Consider basic to testing and assessment:

1. Psychological traits and states exist.

• A trait is a relatively enduring (i.e., long lasting) characteristic on which people differ; a state is a less enduring or more transient characteristic on which people differ.
• Traits and states are actually social constructions, but they are real in the sense that they are useful for classifying and organizing the world, they can be used to understand and predict behavior, and they refer to something in the world that we can measure.

2.  Psychological traits and states can be quantified and measured.

• For nominal scales, the number is used as a marker. For the other scales, the numbers become more and more quantitative as you move from ordinal scales (shows ranking only) to interval scales (shows amount, but lacks a true zero point) to ratio scales (shows amount or quantity as we usually understand this concept in mathematics or everyday use of the term).
• Most traits and states measured in education are taken to be at the interval level of measurement.

3.  Various approaches to measuring aspects of the same thing can be useful.

• For example, different tests of intelligence tap into somewhat different aspects of the construct of intelligence.

4.  Assessment can provide answers to some of life's most momentous questions.

• It is important that the users of assessment tools know when these tools will provide answers to their questions.

5.  Assessment can pinpoint phenomena that require further attention or study.

• For example, assessment may identify someone as having dyslexia or low self-esteem or at-risk for drug use.

6.  Various sources of data enrich and are part of the assessment process.

• Information from several sources usually should be obtained in order to make an accurate and informed decision. For example, the idea of portfolio assessment is useful.

7.  Various sources of error are always part of the assessment process.

• There is no such thing as perfect measurement. All measurement has some error.
• We defined error as the difference between a person’s true score and that person’s observed score.
• The two main types of error are random error (e.g., error due to transient factors such as being sick or tired) and systematic error (e.g., error present every time the measurement instrument is used such as an essay exam being graded by an overly easy grader). (Later when we discuss reliability and validity, you might note that unreliability is due to random error and lack of validity is due to systematic error.)

8.  Tests and other measurement techniques have strengths and weaknesses.

• It is essential that users of tests understand this so that they can use them appropriately and intelligently.
• In this chapter, we will be talking about the two major characteristics: reliability and validity.

9.  Test-related behavior predicts non-test-related behavior.

• The goal of testing usually is to predict behavior other than the exact behaviors required while the exam is being taken.
• For example, paper-and-pencil achievement tests given to children are used to say something about their level of achievement.
• Another paper-and-pencil test (also called a self-report test) that is popular in counseling is the MMPI (i.e., the Minnesota Multiphasic Personality Inventory). Clients' scores on this test are used as indicators of the presence or absence of various mental disorders.
• The point here is that the actual mechanics of measurement (e.g., self-reports, behavioral performance, projective) can vary widely and still provide good measurement of educational, psychological, and other types of variables.

10.  Present-day behavior sampling predicts future behavior.

• Perhaps the most important reason for giving tests is to predict future behavior.
• Tests provide a sample of present-day behavior. However, this "sample" is used to predict future behavior.
• For example, an employment test given by someone in a Personnel Office may be used as a predictor of future work behavior.
• Another example: the Beck Depression Inventory is used to measure depression and, importantly, to predict test taker’s future behavior (e.g., are they a risk to themselves?).

11.  Testing and assessment can be conducted in a fair and unbiased manner.

• This requires careful construction of test items and testing of the items on different types of people.
• Test makers always have to be on the alert to make sure tests are fair and unbiased.
• This assumption also requires that the test be administered to those types of people for whom it has been shown to operate properly.

12.  Testing and assessment benefit society.

• Many critical decisions are made on the basis of tests (e.g., teacher competency, employability, presence of a psychological disorder, degree of teacher satisfactions, degree of student satisfaction, etc.).
• Without tests, the world would be much more unpredictable.

Identifying A Good Test or Assessment Procedure

As mentioned earlier in the chapter, good measurement us fundamental for research. If we do not have good measurement then we cannot have good research. That’s why it’s so important to use testing and assessment procedures that are characterized by high reliability and high validity.

Overview of Reliability and Validity

As an introduction to reliability and validity and how they are related, note the following:

• Reliability refers to the consistency or stability of test scores
• Validity refers to the accuracy of the inferences or interpretations we make from test scores
• Reliability is a necessary but not sufficient condition for validity (i.e., if you are going to have validity, you must have reliability but reliability in and of itself is not enough to ensure validity.
• Assume you weigh 125 pounds. If you weigh yourself five times and get 135, 134, 134, 135, 136 then your scales are reliable but not valid. The scores were consistent but wrong! Again, you want your scales to be both reliable and valid.

Reliability

Reliability refers to consistency or stability. In psychological and educational testing, it refers to the consistency or stability of the scores that we get from a test or assessment procedure.

• Reliability is usually determined using a correlation coefficient (it is called a reliability coefficient in this context).
• Remember (from chapter two) that a correlation coefficient is a measure of relationship that varies from -1 to 0 to 1 and the farther the number is from zero, the stronger the correlation. For example, minus one (-1.00) indicates a perfect negative correlation, zero indicates no correlation at all, and positive one (+1.00) indicates a perfect positive correlation. Regarding strength, -.85 is stronger than +.55, and +.75 is stronger than +.35. When you have a negative correlation, the variables move in opposite directions (e.g., poor diet and life expectancy); when you have a positive correlation, the variables move in the same direction (e.g., education and income).
• When looking at reliability coefficients we are interested in the values ranging from 0 to 1; that is, we are only interested in positive correlations. Note that zero means no reliability, and +1.00 means perfect reliability.
• Reliability coefficients of .70 or higher are generally considered to be acceptable for research purposes. Reliability coefficients of .90 or higher are needed to make decisions that have impacts on people's lives (e.g., the clinical uses of tests).
• Reliability is empirically determined; that is, we must check the reliability of test scores with specific sets of people. That is, we must obtain the reliability coefficients of interest to us.

There are four primary ways to measure reliability.

1.      The first type of reliability is called test-retest reliability.

·        This refers to the consistency of test scores over time.

·        It is measured by correlating the test scores obtained at one point in time with the test scores obtained at a later point in time for a group of people.

·        A primary issue is identifying the appropriate time interval between the two testing occasions.

·        The longer the time interval between the two testing occasions, the lower the reliability coefficient tends to be.

2.      The second type of reliability is called equivalent forms reliability.

• This refers to the consistency of test scores obtained on two equivalent forms of a test designed to measure the same thing.
• It is measured by correlating the scores obtained by giving two forms of the same test to a group of people.
• The success of this method hinges on the equivalence of the two forms of the test.

3.      The third type of reliability is called internal consistency reliability

• It refers to the consistency with which the items on a test measure a single construct.
• Internal consistency reliability only requires one administration of the test, which makes it a very convenient form of reliability.
• One type of internal consistency reliability is split-half reliability, which involves splitting a test into two equivalent halves and checking the consistency of the scores obtained from the two halves.
• The measure of internal consistency that we emphasize in the chapter is coefficient alpha. (It is also sometimes called Cronbach’s alpha.) The beauty of coefficient alpha is that it is readily provided by statistical analysis packages and it can be used when test items are quantitative and when they are dichotomous (as in right or wrong).
• Researchers use coefficient alpha when they want an estimate of the reliability of a homogeneous test (i.e., a test that measures only one construct or trait) or an estimate of the reliability of each dimension on a multidimensional test. You will see it commonly reported in empirical research articles.
• Coefficient alpha will be high (e.g., greater than .70) when the items on a test are correlated with one another. But note that the number of items also affects the strength of coefficient alpha (i.e., the more items you have on a test, the higher coefficient alpha will be). This latter point is important because it shows that it is possible to get a large alpha coefficient even when the items are not very homogeneous or internally consistent.

4.      The fourth and last major type of reliability is called inter-scorer reliability.

• Inter-Scorer Reliability refers to the consistency or degree of agreement between two or more scorers, judges, or raters.
• You could have two judges rate one set of papers. Then you would just correlate their two sets of ratings to obtain the inter-scorer reliability coefficient, showing the consistency of the two judges’ ratings.

Validity

Validity refers to the accuracy of the inferences, interpretations, or actions made on the basis of test scores.

• Technically speaking, it is incorrect to say that a test is valid or invalid. It is the interpretations and actions taken based on the test scores that are valid or invalid.
• All of the ways of collecting validity evidence are really forms of what used to be called construct validity. All that means is that in testing and assessment, we are always measuring something (e.g., IQ, gender, age, depression, self-efficacy).

Validation refers to gathering evidence supporting some inference made on the basis of test scores.

There are three main methods of collecting validity evidence.

1.  Evidence Based on Content

Content-related evidence is based on a judgment of the degree to which the items, tasks, or questions on a test adequately represent the domain of interest. Expert judgment is used to provide evidence of content validity.

To make a decision about content-related evidence, you should try to answer these three questions:

• Do the items appear to represent the thing you are trying to measure?
• Does the set of items underrepresent the construct’s content (i.e., have you excluded any important content areas or topics)?
• Do any of the items represent something other than what you are trying to measure (i.e., have you included any irrelevant items)?

2.  Evidence Based on Internal Structure

Some tests are designed to measure one general construct, but other tests are designed to measure several components or dimensions of a construct. For example, the Rosenberg Self-Esteem Scale is a 10 item scale designed to measure the construct of global self-esteem. In contrast, the Harter Self-Esteem Scale is designed to measure global self-esteem as well as several separate dimensions of self-esteem.

• The use of the statistical technique called factor analysis tells you the number of dimensions (i.e., factors) that are present. That is, it tells you whether a test is unidimensional (just measures one factor) or multidimensional (i.e., measures two or more dimensions).
• When you examine the internal structure of a test, you can also obtain a measure of test homogeneity (i.e., how well the different items measure the construct or trait).
• The two primary indices of homogeneity are the item-to-total correlation (i.e., correlate each item with the total test score) and coefficient alpha (discussed earlier under reliability).

3.  Evidence Based on Relations to Other Variables

This form of evidence is obtained by relating your test scores with one or more relevant criteria. A criterion is the standard or benchmark that you want to predict accurately on the basis of the test scores. Note that when using correlation coefficients for validity evidence we call them validity coefficients.

There are several different kinds of relevant validity evidence based on relations to other variables.

The first is called criterion-related evidence which is validity evidence based on the extent to which scores from a test can be used to predict or infer performance on some criterion such as a test or future performance. Here are the two types of criterion-related evidence:

• Concurrent evidence—validity evidence based on the relationship between test scores and criterion scores obtained at the same time.
• Predictive evidence—validity evidence based on the relationship between test scores collected at one point in time and criterion scores obtained at a later time.

Here are three more types of validity evidence researchers should provide:

• Convergent evidence—validity evidence based on the relationship between the focal test scores and independent measures of the same construct. The idea is that you want your test (that your are trying to validate) to strongly correlate with other measures of the same thing.
• Divergent evidence—evidence that the scores on your focal test are not highly related to the scores from other tests that are designed to measure theoretically different constructs. This kind of evidence shows that your test is not a measure of those other things (i.e., other constructs).
• Putting the ideas of convergent and divergent evidence together, the point is that to show that a new test measures what it is supposed to measure, you want it to correlate with other measures of that construct (convergent evidence) but you also want it NOT to correlate strongly with measures of other things (divergent evidence). You want your test to overlap with similar tests and to diverge from tests of different things. In short, both convergent and divergent evidence are desirable.
• Known groups evidence is also useful in demonstrating validity. This is evidence that groups that are known to differ on the construct do differ on the test in the hypothesized direction. For example, if you develop a test of gender roles, you would hypothesize that females will score higher on femininity and males will score higher on masculinity. Then you would test this hypothesis to see if you have evidence of validity.

Now, to summarize these three major methods for obtaining evidence of validity, look again at Table 5.6 (also shown below).

Please note that, if you think we have spent a lot of time on validity and measurement, the reason is because validity is so important in empirical research. Remember, without good measurement we end up with GIGO (garbage in, garbage out).

Using Reliability and Validity Information

You must be careful when interpreting the reliability and validity evidence provided with standardized tests and in empirical research journal articles.

• With standardized tests, the reported validity and reliability data are typically based on a norming group (which is an actual group of people). If the people with which you intend to use a test are very different from those in the norming group, then the validity and reliability evidence provided with the test become  questionable. Remember that what you need to know is whether a test will work with the people in your classroom or in your research study.
• When reading journal articles, you should view an article positively to the degree that the researchers provide reliability and validity evidence for the measures that they use. Two related questions to ask when reading and evaluating an empirical research article are  “It this research study based on good measurement?” and “Do I believe that these researchers used good measures?” If the answers are yes, then give the article high marks for measurement. If the answers are no, then you should invoke the GIGO principle (garbage in, garbage out).

Educational and Psychological Tests

Three primary types of educational and psychological tests are discussed in your textbook: intelligence tests, personality tests, and educational assessment tests.

1)  Intelligence Tests

Intelligence has many definitions because a single prototype does not exist. Although far from being a perfect definition, here is our definition: intelligence is the ability to think abstractly and to learn readily from experience.

• Although the construct of intelligence is hard to define, it still has utility because it can be measured and it is related to many other constructs.

For some examples of intelligence tests, click here.

2)   Personality Tests.

Personality is a construct similar to intelligence in that a single prototype does not exist. Here is our definition: personality is the relatively permanent patterns that characterize and can be use to classify individuals.

• Most personality tests are self-report measures. A self-report measure is a test-taking method in which the participants check or rate the degree to which various characteristics are descriptive of themselves.
• Performance measures of personality are also used. A performance measure is a test-taking method in which the participants perform some real-life behavior that is observed by the researcher.
• Personality has also been measured with projective tests. A projective test is a test-taking method in which the participants provide responses to ambiguous stimuli. The test administrator searches for patterns on participants’ responses. Projective tests tend to be quite difficult to interpret and are not commonly used in quantitative research.

For some examples of personality tests, click here.

3)   Educational Assessment Tests.

There are four subtypes of educational assessment tests:

• Preschool Assessment Tests.

--These are typically screening tests because the predictive validity of many of these tests is weak.

• Achievement Tests.

--These are designed to measure the degree of learning that has taken place after a

person has been exposed to a specific learning experience. They can be teacher

constructed or standardized tests.

For some examples of achievement tests, click here.

• Aptitude Tests.

--These focus on information acquired through the informal learning that goes

on in life.
--They are often used to predict future performance whereas achievement tests are used to measure current performance.

• Diagnostic Tests.
--
These tests are used to identify the locus of academic difficulties in students.

Sources of Information about Tests

The two most important main sources of information about tests are the Mental Measurements Yearbook (MMY) and Tests in Print (TIP). Some additional sources are provided in Table 5.7. Also, here are some useful internet links (from Table 5.8):