Reliability and Validity

 Reliability and Validity Chong Ho Yu, Ph.D. Conventional views of reliability (AERA et al., 1985) •

Temporal stability: the same form of a test on two or more separate occasions to

the same group of examinees (Test-retest). On many occasions this approach is not practical because repeated measurements are likely to change the examinees. For example, the examinees will adapt the test format and thus tend to score higher in later tests. Hence, careful implementation of the test-retest approach is strongly recommendation (Yu, 2005). •

Form equivalence: two different forms of test, based on the same c ontent, on one

occasion to the same examinees (Alternate form). After alternate forms have been developed, it can be used for different examinees. It is very common in high-stake examination for pre-empting cheating. A examinee who took Form A earlier  could not share the test items with another student who might take Form B later,  because the two forms have different items. •

Internal consistency: the coefficient of test scores obtained from a single test or 

survey (Cronbach (Cronbach Alpha, Alpha, KR20, Spilt-half). For instance, let's say respondents are asked to rate statements in an attitude survey about computer anxiety. One statement is "I feel very negative about computers in general." Another statement is "I enjoy using computers." People who strongly agree w ith the first statement should be strongly disagree with the second statement, and vice versa. If the rating of both statements is high or low among several respondents, the responses are said to be inconsistent and patternless. The same principle can be applied to a test. When no pattern is found in the students' responses, probably the test is too difficult and students just guess the answers randomly.

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Reliability is a necessary but not sufficient condition for validity. For  instance, if the needle of the scale is five pounds away from zero, I always over-report my weight by five pounds. Is the measurement consistent? Yes, but it is consistently wrong! Is the measurement valid? No! (But if it under-reports my weight by five pounds, I will consider it a valid measurement) •

Performance, portfolio, and responsive evaluations, where the tasks vary substantially from student to student and where multiple tasks may be evaluated simultaneously, are attacked for lacking reliability. One of the difficulties is that there are more than one source of measurement errors in performance assessment. For example, the reliability of writing skill test score is affected by the raters, the mode of discourse, and several other factors (Parkes, 2000).

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Replications as unification: Users may be confused by the diversity of reliability

indices. Nevertheless, different types of reliability measures share a common thread: What constitutes a replication of a measurement procedure? (Brennan, 2001) Take internal consistency as an example. This measure is used because it is convenient to compute the reliability index based upon data collected from one occasion. However, the ultimate inference should go beyond one single testing occasion to others (Yu, 2005). In other words, any procedures for estimating reliability should attempt to mirror a result based upon full-length replications.

Conventional views of validity (Cronbach, 1971) •

Face validity: Face validity simply means the validity at face value. As a check 

on face validity, test/survey items are sent to teachers to obtain suggestions for  modification. Because of its vagueness and subjectivity, psychometricians have abandoned this concept for a long time. However, outside the measurement arena,

face validity has come back in another form. While discussing the validity of a theory, Lacity and Jansen (1994) defines validity as making common sense, and  being persuasive and seeming right to the reader. For Polkinghorne (1988), validity of a theory refers to results that have the appearance of truth or reality. The internal structure of things may not concur with the appearance. Many times  professional knowledge is counter-common sense. The criteria of v alidity in research should go beyond "face," "appearance," and "common sense." •

Content validity: draw an inference

from test scores to a large domain of  items similar to those on the test. Content validity is concerned with sample-population representativeness. i.e. the

knowledge and skills covered by the test items should be representative to the larger domain of knowledge and skills. For example, computer literacy includes skills in operating system, word  processing, spreadsheet, database, graphics, internet, and many others. However, it is difficult, if not impossible, to administer a test covering all aspects of  computing. Therefore, only several tasks are sampled from the population of  computer skills. Content validity is usually established by content experts. Take computer  literacy as an example again. A test of computer literacy should be written or  reviewed by computer science professors because it is assumed that computer  scientists should know what are important in his discipline. By the first glance, this approach looks similar to the validation process of face validity, but yet there is a difference. In content validity, evidence is obtained by looking for agreement

in judgments by judges. In short, face validity can be established by one person  but content validity should be checked by a panel. However, this approach has some drawbacks. Usually experts tend to take their  knowledge for granted and forget how little other people know. It is not uncommon that some tests written by content experts are extremely difficult. Second, very often content experts fail to identify the learning objectives of a subject. Take the following question in a philosophy test as an example:

What is the time period of the philosopher Epicurus?

a. 341-270 BC  b. 331-232 BC c. 280-207 BC d. None of the above This type of question tests the ability of memorizing historical facts, but not  philosophizing. The content expert may argue that "historical facts" are important for a student to further understand philosophy. Let's change the subject to computer science and statistics. Look at the following two questions:

When was the founder and CEO of Microsoft, William Gates III born?

a. 1949  b. 1953 c. 1957 d. None of the above

Which of the following statement is true about ANOVA

a. It was invented by R. A. Fisher in 1914  b. It was invented by R. A. Fisher in 1920 c. It was invented by Karl Pearson in 1920 d. None of the above It would be hard pressed for any computer scientist or statistician to accept that the above questions fulfill content validity. As a matter of fact, the memorization approach is a common practice among instructors. Further, sampling knowledge from a larger domain of k nowledge involves subjective values. For example, a test regarding art history may include many questions on oil paintings, but less questions on watercolor paintings and  photography because of the perceived importance of oil paintings in art history. Content validity is sample-oriented rather than sign-oriented. A behavior is viewed as a sample when it is a subgroup of the same kind of behaviors. On the other hand, a behavior is considered a sign when it is an indictor or a proxy of a construct. (Goodenough, 1949). Construct validity and criterion validity, which will be discussed later, are sign-oriented because both of them indicate behaviors different from those of the test.

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Criterion: draw an inference from test scores to performance. A high score of a

valid test indicates that the tester has met the performance criteria. Regression analysis can be applied to establish criterion validity. An independent

variable could be used as a predictor variable and a dependent variable, the

criterion variable. The correlation coefficient between them is called validity coefficients.

For instance, scores of the driving test by simulation is the predictor variable while scores of the road test is the criterion variable. It is hypothesized that if the tester passes the simulation test, he/she should meet the criterion of being a safe driver. In other words, if the simulation test scores could predict the road test scores in a regression model, the simulation test is claimed to have a high degree of criterion validity. In short, criterion validity is about prediction rather than explanation. Predication is concerned with non-casual or mathematical dependence where as explanation is pertaining to causal or logical dependence. For example, one can  predict the weather based on the height of mercury inside a thermometer. Thus, the height of mercury could satisfy the criterion validity as a predictor. However, one cannot explain why the weather changes by the change of mercury height. Because of this limitation of criterion validity, an evaluator has to conduct construct validation.

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Construct: draw an inference form

test scores to a psychological construct. Because it is concerned with abstract and theoretical construct, construct validity is also known as theoretical construct. According to Hunter and Schmidt (1990), construct validity is a quantitative question rather than a qualitative distinction such as "valid" or "invalid"; it is a matter of degree. Construct validity can be measured

 by the correlation between the intended independent variable (construct) and the proxy independent variable (indicator, sign) that is actually used.

For example, an evaluator wants to study the relationship between general cognitive ability and job performance. However, the evaluator may not be able to administer a cognitive test to every subject. In this case, he can use a proxy variable such as "amount of education" as an indirect indicator of cognitive ability. After he administered a cognitive test to a po rtion of all subjects and found a strong correlation between general cognitive ability and amount of  education, the latter can be used to the larger group because its construct validity is established. Other authors (e.g. Angoff,1988; Cronbach & Quirk, 1976) argue that construct validity cannot be expressed in a single coefficient; there is no mathematical index of construct validity. Rather the nature o f construct validity is qualitative. There are two types of indictors:

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Reflective indictor: the effect of the construct.

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Formative indictor: the cause of the construct.

When an indictor is expressed in terms of multiple items of an instrument, factor analysis is used for construct validation. Test bias is a major threat against construct validity, and therefore test bias

analyses should be employed to examine the test items (Osterlind, 1983). The presence of test bias definitely affects the measurement of the psychological construct. However, the absence of test bias does not guarantee that the test  possesses construct validity. In other words, the absence of test bias is a necessary, but isn't a sufficient condition.

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Construct validation as unification: The criterion and the content models tends

to be empirical-oriented while the construct model is inclined to be theoretical.  Nevertheless, all models of validity requires some form of interpretation: What is the test measuring? Can it measure what it intends to measure? In standard scientific inquiries, it is important to formulate an interpretative (theoretical) framework clearly and then to subject it to empirical ch allenges. In this sense, theoretical construct validation is considered functioning as a un ified framework  for validity (Kane, 2001).

A modified view of reliability (Moss, 1994) •

There can be validity without reliability if reliability is defined as consistency among independent measures.

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Reliability is an aspect of construct validity. As assessment becomes less standardized, distinctions between reliability and validity blur.

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In many situations such as searching faculty candidate and conferring graduate degree, committee members are not trained to agree on a common set of criteria and standards

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Inconsistency in students' performance across tasks does not invalidate the assessment. Rather it becomes an empirical puzzle to be solved by searching for a more comprehensive interpretation.

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Initial disagreement (e.g., among students, teachers, and parents in responsive evaluation) would not invalidate the assessment. Rather it would provide an impetus for dialog.

Li (2003) argued that the preceding view is incorrect: •

The definition of reliability should be defined in terms of the classical test theory: the squared correlation between observed and true scores or the proportion of true variance in obtained test scores.

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Reliability is a unitless measure and thus it is already model-free or standard-free.

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It has been a tradition that multiple factors are introduced into a test to improve validity but decrease internal-consistent reliability.

An extended view of Moss's reliability (Mislevy, 2004) •

Being inspired by Moss, Mislevy went further to ask whether there can be reliability without reliability (indices).

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By blending psychometrics and Hermeneutics, in which a holistic and integrative approach to understand the whole in light of its parts is used, Mislevy demanded  psychometricians to think about what they intend to make inferences about.

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In many cases we don't present just one argument; rather problem solving involves arguments or chains of reasoning with massive evidence.

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Off-the-shelf inferential machinary (e.g. compute reliability indices) may fail if  we quantify things or tasks that we don't know much about.

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Probability-based reasoning to more complex assessments based upon cognitive  psychology is needed.

A radical view of reliability (Thompson et al, 2003) •

Reliability is not a property of the test; rather it is attached to the property of the data. Thus, psychomterics is datammetrics.

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Tests are not reliable. It is important to explore reliability in virtually all studies.

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Reliability generalization, which can be used in a meta-analysis application

similar to validity generalization, should be implemented to assess variance in measurement error across studies.

An updated perspective of reliability (Cronbach, 2004) In a 2004's article, Lee Cronbach, the inventor of Cronbach Alpha as a way of measuring reliability, reviewed the historical development of Cronbach Alpha. He asserted, "I no

longer regard the formula (of Cronbach Alpha) as the most appropriate way to examine most data. Over the years, my associates and I developed the complex generaliability (G) theory" (p. 403). Discussion of the G theory is beyond the scope of this document.  Nevertheless, Cronbach did not object use of Cronbach Alpha but he recommended that researchers should take the following into consideration while employing this approach: •

Standard error of measurement: It is the most important piece of information to

report regarding the instrument, not a coefficient. •

Independence of sampling

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Heterogeneity of content

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How the measurement will be used: Decide whether future uses of the

instrument are likely to be exclusively for absolute decisions, for differential decisions, or both. •

Number of conditions for the test

A critical view of validity (Pedhazur & Schmelkin,1991) •

Content validity is not a type of validity at all because validity refers to inferences made about scores, not to an assessment of the content of an instrument.

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The very definition of a construct implies a domain of content. There is no sharp distinction between test content and test construct.

A modified view of validity (Messick, 1995) The conventional view (content, criterion, construct) is fragmented and incomplete, especially because it fails to take into account both evidence of the value implications of  score meaning as a basis for action and the social consequences of score use. Validity is not a property of the test or assessment, but rather of the meaning of the test scores. •

Content: evidence of content relevance, representativeness, and technical quality

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Substantive: theoretical rationale

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Structural: the fidelity of the scoring structure

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Generalizability: generalization to the population and across populations

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External: applications to multitrait-multimethod comparison

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Consequential: bias, fairness, and justice; the social consequence of the

assessment to the society Critics argued that consequences should not be a component of validity because test developers should not be held responsible for the consequences of misuse; accountab ility should lie with the misuser. Messick (1998) counter-argued that social consequences of  score interpretation include the value implications of the construct label, which may or  may not commensurate with the construct's trait implications and need to be addressed in appraising score meaning. While test developers should not be accountable to misuse of  tests, they should still pay attention to the unanticipated consequences of legitimate score interpretation.

A different view of reliability and validity (Salvucci, Walter, Conley, Fink, & Saba (1997) Some scholars argue that the traditional view that "reliability is a necessary but not a sufficient condition of validity" is incorrect. This school of thought conceptualizes reliability as invariance and validity as unbiasedness. A sample statistic may have an expected value over samples equal to the population parameter (unbiasedness), but have very high variance from a small sample size. Conversely, a sample statistic can have very low sampling variance but have an expected value far departed from the population  parameter (high bias). In this view, a measure can be unreliable (high variance) but still valid (unbiased).

Population parameter (Red line) =

Population parameter (Red line)

Sample statistic (Yellow line) --> unbiased Sample statistic (Yellow line) --> Biased High variance (Green line)

low variance (Green line)

Unreliable but valid

Invalid but reliable

Caution and advice There is a common misconception that if someone adopts a validated instrument, he/she does not need to check the reliability and validity with his/her own data. Imagine this: When I buy a drug that has been approved by FDA and my friend asks me whether it heals me, I tell him, "I am taking a drug approved by FDA and therefore I don't need to know whether it works for me or not!" A responsible evaluator should still check the instrument's reliability and validity with his/her own subjects and make any modifications if necessary. Low reliability is less detrimental to the performance pretest. In the pretest where subjects are not exposed to the treatment and thus are unfamiliar with the subject matter, a low reliability caused by random guessing is expected. One easy way to overcome this  problem is to include "I don't know" in multiple choices. In an experimental settings where students' responses would not affect their final grades, the experimenter should explicitly instruct students to choose "I don't know" instead of making a guess if they really don't know the answer. Low reliability is a signal of high measurement error,

which reflects a gap between what students actually know and what scores they receive. The choice "I don't know" can help in closing this gap. Last Updated: 2008

References American Educational Research Association, American Psychological Association, &  National Council on Measurement in Education. (1985). Standards for educational and  psychological testing. Washington, DC: Authors. Angoff, W. H. (1988). Validity: An evolving co ncept. In H. Wainer & H. I. Braun (Eds.), Test validity. Hillsdale, NJ: Lawrence Erlbaum. Brennan, R. (2001). An essay on the history and future of reliability from the perspective of replications. Journal of Educational Measurement, 38, 295-317. Cronbach, L. J. (1971). Test validation. In R. L. Thorndike (Ed.). Educational Measurement (2nd Ed.). Washington, D. C.: American Council on Education. Cronbach, L. J. (2004). My current thoughts on Coefficient Alpha and successor   procedures. Educational and Psychological Measurement, 64, 391-418. Cronbach, L. J. & Quirk, T. J. (1976). Test validity. In International Encyclopedia of  Education. New York: McGraw-Hill. Goodenough, F. L. (1949). Mental testing: Its history, principles, and applications. New York: Rinehart. Hunter, J. E.; & Schmidt, F. L. (1990). Methods of meta-analysis: Correcting error and  bias in research findings. Newsbury Park: Sage Publications.

Kane, M. (2001). Current concerns in validity theory. Journal of educational Measurement, 38, 319-342. Lacity, M.; & Jansen, M. A. (1994). Understanding qualitative data: A framework of text analysis methods. Journal of Management Information System, 11, 137-160. Li, H. (2003). The resolution of some paradoxes related to reliability and validity. Journal of Educational and Behavioral Statistics, 28, 89-95. Messick, S. (1995). Validity of psychological assessment: Validation of inferences from  persons' responses and performance as scientific inquiry into scoring meaning. American Psychologist, 9, 741-749. Messick, S. (1998). Test validity: A matter of consequence. Social Indicators Research, 45, 35-44. Mislevy, R. (2004). Can there be reliability without reliability? Journal of Educational and Behavioral Statistics, 29, 241-244. Moss, P. A. (1994). Can there be validity without reliability? Educational Researcher, 23, 5-12. Osterlind, S. J. (1983). Test item bias. Newbury Park: Sage Publications. Parkes, J. (2000). The relationship between the reliability and cost of performance assessments. Education Policy Analysis Archives, 8. [On-line] Available URL: http://epaa.asu.edu/epaa/v8n16/ Pedhazur, E. J.; & Schmelkin, L. P. (1991). Measurement, design, and analysis: An integrated approach. Hillsdale, NJ: Lawrence Erlbaum Associates, Publishers. Polkinghorne, D. E. (1988). Narrative knowing and the human sciences. Albany: State University of New York Press.

Salvucci, S.; Walter, E., Conley, V; Fink, S; & Saba, M. (1997). Measurement error  studies at the National Center for Education Statistics. Washington D. C.: U. S. Department of Education Thompson, B. (Ed.) (2003). Score reliability: Contemporary thinking on reliability issues. Thousand Oaks: Sage. Yu, C. H. (2005). Test-retest reliability. In K. Kempf-Leonard (Ed.). Encyclopedia of  Social Measurement, Vol. 3 (pp. 777-784). San Diego, CA: Academic Press.

Questions for discussion Pick one of the following cases and determine whether the test or the assessment is valid. Apply the concepts of reliability and validity to the situation. These cases may be remote to this cultural context. You may use your own example. 1. In ancient China, candidates for government officials had to take the examination regarding literature and moral philosophy, rather than public administration. 2. Before July 1, 1997 when Hong Kong was a British colony, Hong Kong doctors, including specialists, who graduated from non-Common Wealth medical schools had to take a general medical examination covering all general areas in order to be certified.