**Correction for Range Restriction and Attenuation Effect Essay For Singaporean**

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**Essay Title- Correction for Range Restriction and Attenuation Effect **

Students studying psychology often need to obtain an approximation of the relationship between the conditions and the predictor deciding them. There is always an error faced in estimation through Correlation Coefficient. Correlation depicts the relationship between two variables. The challenge is the delineation of the factors that influence the joint impact of range restriction and attenuation on the magnitude of the correlation coefficient. The concept of predictor reliability changes in selection situations because of the correlation between error and true scores.

**The Problem related to Range Restriction –**

It is a general research problem that is the estimation of the population correlation between x and y from a sample xy which has been controlled by some selection process. An extended arrangement system for range-restriction scenarios is developed that conceptualizes range-restriction situations from several groupings of the following facets: (a) the variable(s) on which selection occurs (x, y and/or a 3rd variable z), (b) whether unobstructed variances for the applicable variables are known, and (c) whether a 3rd variable, if involved, is measured or unmeasured.

As a result, predictor-criterion relationships obtained from such samples are usually underestimated because of restriction in range. This is problematic when, due to selection, a relatively homogenous sample that is not representative of the population of interest It examines the statistical correction for attenuation and the controversies surrounding the procedure.

**Attenuation effect –**

Attenuation effects mention the detail that an observed correlation coefficient will incline to underrate the true scale of the construction between two variables to the degree that these measures are not an accurate reflection of true variation, i.e., to the extent that they are unreliable. Generally, the operation of these prejudices may be acceptable.

**Importance of corrections for range restriction and attenuation effects –**** **

The need for revising validity coefficients for statistical objects is fetching due recognition. Validity generalization research has demonstrated that artifacts like range restriction and attenuation account for large percentages of the variance in distributions of validity coefficients. Though, the Society for Industrial and Organizational Psychology’s (SIOP) Principles (1987) endorse modifying the validity coefficients for both range restriction and criterion unreliability. Students and researchers may be reluctant to apply corrections for range restriction and attenuation for several reasons.

**Correction Methods for Range Restriction** –

There are several methods for correcting correlations for range restriction. Thorndike’s case II and ML estimates obtained from the EM algorithm. These methods will be described first, and then results from research evaluating their use will be discussed.

**Thorndike’s case II** –

Thorndike’s (1949) Case II is the most commonly used range restriction correction formula in an explicit selection scenario. It is a process, based on the predictor x, that restricts the availability of the criterion y. The criterion is only available (measured) for the selected individuals. For example, consider the seemingly straightforward case where there is direct selection on x. Equation is

Rxy =

where Rxy = the validity corrected for range restriction; rxy = the observed validity in the restricted group; and ux = sx/Sx, where sx and Sx are the restricted and unrestricted SDs of x, respectively. Both the restricted and unrestricted SDs of x are available at hand.

**Issues with Thorndike’s case II method – **

Even the use of Thorndike’s Case II formula is straightforward, this formula imposes some requirements. First, it requires that the unrestricted, or population, the variance of x be known. Second, the formula requires that there is no additional range restriction on additional variables. If the organization also imposes an additional cutoff, such as a minimum education requirement, applying the Case II formula produces a biased result

**Maximum Likelihood estimates obtained from the Expectation-Maximization algorithm** –

There are three general missing data situations; MCAR, MAR, and MNAR. Assume X is a variable that is known for all examinees and Y is the variable of interest with missing values for some examinees. In this approach, the selection mechanism is observed as a missing data mechanism, i.e. the selection mechanism is viewed as missing, and the missing values are estimated before estimating the correlation. MCAR means that the data is Missing Completely. At Random, MNAR means that data is Missing Not At Random. In other words, the probability of missing Y is related to the unobserved values of Y. Using this approach, we can use the information on some of the other variables to impute new values**. Maximum likelihood (ML)** estimates obtained from the Expectation-Maximization (EM) algorithm are imputed for the criterion variable for examinees who failed the selection test for example.

**Issues with ML estimates obtained from the EM algorithm method – **

Since there is not much work in the literature examining the appropriateness and effectiveness of this approach, many questions need to be answered when using ML estimates obtained from the EM algorithm for correction for range restriction. Many researches need to evaluate the use of this approach in areas that are of special interest include simulations of different population correlations and different selection proportions when using the missing data approach. Regarding the EM imputation approach, one important research question is how many cases can be imputed at the same time as we obtain a good estimate of the population correlation.

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**Correction Methods for Attenuation –**

In educational and psychological research, it is well known that measurement unreliability, that is, measurement error, attenuates the statistical relationship between two composites Two approaches for correcting attenuation effects caused by measurement error; traditional approach and latent variable modeling approach areas such

**Traditional approach –**

In classical test theory, the issue of attenuation of correlation between two composites caused by measurement unreliability is usually discussed within the context of score reliability and validity. More specifically, if there are two measured variables x and y, their correlation is estimated by the Pearson correlation coefficient rxy from a sample. Because the measured variables x and y contain random measurement error, this correlation coefficient rxy is typically lower than the correlation coefficient between the true scores of the variables Tx and Ty (rTx,Ty) (Fan, 2003).

The equation,

rTx,Ty = ,is known as double correction.

**Issues with the traditional approach **

There is no real consensus on correction for attenuation that has emerged in the literature, and many ambiguities regarding its application remain. One of the early criticisms is corrected validity coefficients greater than one. Although it is theoretically impossible to have a validity coefficient in excess of 1.00, it is empirically possible to compute such a coefficient using Spearman correction formula. For example, if = .65, = .81, and = .49,

rTx,Ty = 1.03

The value of 1.03 is theoretically impossible because valid variance would exceed obtained variance (error variance).

**Conclusion –**

There are several methods that can be used to correct correlations for attenuation and range restriction, and some have been more frequently used than others. For correction for attenuation, the traditional method for correcting for attenuation is the best known and is easy to use.

However, in more complex modeling situations it is probably easier to adopt an SEM approach to assessing relationships between variables with measurement errors ‘removed’ than to try to apply the traditional formula on many relationships simultaneously.

However, because the ML estimates obtained from the EM algorithm approach is not commonly used in range restriction studies, the usefulness and accuracy of this method should be further examined.

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