Corrections for attenuation and corrections for range restriction

Corrections for attenuation and corrections for range restriction One of the most pervasive methodological problems in the educational and psychological field entails determination of the techniques which are to be used in assessing the nature and strength of the relationship between various measures. Of course, the correlation coefficient has provided the field with a viable statistical tool for solving this problem. Unfortunately, in some instances the appropriateness of correlational techniques may be limited by the operation of certain statistical biases in actual data bases. Thorndike (1949) has noted that two of these biases, termed range restriction and attenuation effects, can exert a powerful diminishing influence on the magnitude of observed correlation coefficients. Range restriction occurs when a researcher wants to estimate the correlation between two variables (x and y) in a population, but subjects are selected on x, and data for y are only available for a selected sample (Raju Brand, 2003). This occurs for example when scores from admission tests are used to predict academic success in higher education or are compared with grades in the program they were admitted to (Gulliksen, 1950; Thorndike, 1949). Because selection is made on the basis of scores from these kinds of instruments, the range of scores is restricted in the sample. Although the correlation between test scores and academic success can be obtained for the restricted sample, the correlation for the population of applicants remains unknown. Due to the range restriction in test scores, the correlation obtained is expected to be an underestimate of the correlation in the population (Hunter Schmidt, 1990; Henriksson Wolming, 1998). Attenuation effects refer to the fact that an observed correlation coefficient will tend to underestimate the true magnitude of the relationship between two variables to the extent that these measures are not an accurate reflection of true variation, i.e., to the extent that they are unreliable. In some applied studies, the operation of these biases may be acceptable. Yet when an investigation centers on determining the true strength of the relationship between two sets of measures, the operation of these biases in the experimental data base constitutes a serious, often unavoidable, confound (Crocker Algina, 1986; Worthen, White, Fan, Sudweeks, 1999). Psychometrics has long been aware of the implications of range restriction and attenuation effects with respect to the inferences drawn by researchers concerning the magnitude of relationships. Consequently, a variety of formulas have been derived which permit the researcher to correct data based estimates of the magnitude of a correlation coefficient for the operation of these influences (Guilford, 1954; Stanley, 1971). The aim of this review is to discuss the importance of correcting for range restriction and correcting for attenuation in predictive validity studies and review two methods to correction for range restriction (Thorndikes case II and ML estimates obtained from the EM algorithm) and two methods to correction for attenuation (traditional approach and latent variable modeling approach). Results from research evaluating the use of these methods will also be discussed. Importance of corrections for range restriction and attenuation effects As early as the beginning of the last century, Pearson (1903), in developing the Pearson product-moment correlation coefficient, noticed problems due to range restriction and attenuation and discussed possible solutions. Since then, a great number of studies have examined the biasing effect of these statistical artifacts (e.g., Alexander, 1988; Dunbar Linn, 1991; Lawley, 1943; Linn, Harnisch, Dunbar, 1981; Schmidt, Hunter, Urry, 1976; Thorndike, 1949; Sackett Yang, 2000). It is evident from literature that both range restriction and attenuation can create serious inaccuracies in empirical research, especially in the fields of employment and educational selection. The need for correcting validity coefficients for statistical artifacts is becoming more recognized. Validity generalization research has demonstrated that artifacts like range restriction and attenuation account for large percentages of the variance in distributions of validity coefficients. Although the Society for Industrial and Organizational Psychologys (SIOP) Principles (1987) recommend correcting validity coefficients for both range restriction and criterion unreliability, researchers rarely do so. Ree et al. (1994) discussed the application of range restriction corrections in validation research. They reviewed validity articles published in Educational and Psychological Measurement, Journal of Applied Psychology, and Personnel Psychology between 1988 and 1992. Ree et al. (1994) concluded that only 4% of the articles dealing with validation topics applied range restriction corrections. Researchers may be reluctant to apply corrections for range restriction and attenuation for several reasons. Seymour (1988) referred to statistical corrections as hydraulic, implying that researchers can achieve a desired result by pumping up the corrections. Another reason for reluctance in applying corrections may be because the APA Standards (1974) stated that correlations should not be doubly corrected for attenuation and range restriction. The more current Standards (1985), however, endorse such corrections. A third reason for not using the corrections is that knowledge of unrestricted standard deviations is often lacking (Ree et al., 1994). Finally, researchers may be concerned that in applying corrections to correlation coefficients, they may inadvertently overcorrect. Linn et al. (1981) stated that, procedures for correcting correlations for range restriction are desperately needed in highly selective situations (i.e., where selection ratios are low) (p. 661). They continued, The results also clearly support the conclusion that corrections for range restriction that treat the predictor as the sole explicit selection variable are too small. Because of this undercorrection, the resulting estimates still provide a conservative indication of the predictive value of the predictor (p. 661). Linn et al. stated that ignoring range restriction and/or attenuation corrections because they may be too large is overly cautious. They suggested the routine reporting of both observed and corrected correlations. Both observed and corrected correlations should be reported because there is no significance test for corrected correlations (Ree et al., 1994). Based on the logic and suggestions from literature, there appear to be a number of reasons to correct for restriction of range and attenuation in predictive validity studies. These corrections could be used to adjust the observed correlations for biases, and thus yield more accurate results. Correction Methods for Range Restriction There are several methods for correcting correlations for range restriction. This review is meant to examine two approaches to correction for range restriction; Thorndikes 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. Thorndikes case II Thorndikes (1949) Case II is the most commonly used range restriction correction formula in an explicit selection scenario. Explicit selection 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 (e.g., no one with a test score below a specified cutoff on x is selected into the organization) (Mendoza, 1993). Thorndikes Case II equation can be written as follows 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. The use of this formula requires that the unrestricted, or population, variance of x be known. Although often this is known, as in the case of a predictive study where all applicants are tested and test data on all applicants are retained, it is not uncommon to encounter the situation in which test data on applicants who were not selected are discarded and thus are not available to the researcher who later wishes to correct the sample validity coefficient for range restriction (Sackett and Yang, 2000). Issues with Thorndikes case II method Thorndikes Case II is by far the most widely used correction method. It is appropriate under the condition of direct range restriction (a situation where applicants are selected directly on test scores). Researchers used it and proved its appropriateness. For example, Chernyshenko and Ones (1999) and Wiberg and Sundstrà ¶m (2009) showed that this formula produced close estimates of correlation in a population. Although the use of Thorndikes Case II formula is straightforward, this formula imposes some requirements. First, it requires that the unrestricted, or population, 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. In this example, if education level (z) and test score (x) are known for all applicants, a method for solving the problem exists (Aitken, 1934). Third, the correction formula requires two assumptions: that the x-y relationship is linear throughout the range of scores (i.e., the assumption of linearity) and that the error term is the same in the restricted sample and in the population (i.e., the assumption of homoscedasticity). Note that no normality assumption is required for the formula (Lawley, 1943). Another issue that was found in literature with this method arises when it is applied for indirect restriction of range (a case where the applicants are selected on another variable that is correlated with the test scores) even though it has been shown to underestimate validity coefficients (Hunter Schmidt, 2004, Ch. 5; Hunter et al., 2006; Linn et al., 1981; Schmidt, Hunter, Pearlman, Hirsh, 1985, p. 751). Maximum Likelihood estimates obtained from the Expectation Maximization algorithm Using this approach, the selection mechanism is viewed as a missing data mechanism, i.e. the selection mechanism is viewed as missing, and the missing values are estimated before estimating the correlation. By viewing it as a special case of missing data, we can borrow from a rich body of statistical methods; for an overview see e.g. Little Rubin (2002), Little (1992) or Schafer Graham (2002). 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. MCAR means that the data is Missing Completely At Random, i.e. the missing data distribution does not depend on the observed or missing values. In other words, the probability of missingness in data Y is unrelated to X and Y. MAR means that the data is Missing At Random, i.e. the conditional distribution of data being missing given the observed and missing values depends only on the observed values and not on the missing values. In other words, the probability of missingness in data Y is related to X, but not to Y. MNAR means that data is Missing Not At Random. In other words, the probability of missingness on Y is related to the unobserved values of Y (Little Rubin, 2002; Schafer Graham, 2002). If the data is either MCAR or MAR, we can use imputation methods to replace missing data with estimates. In predictive studies, the selection mechanism that is based solely on X, the data is considered to be MAR (Mendoza, 1993). Using this approach, we can use information on some of the other variables to impute new values. Herzog Rubin (1983) stated that by using imputation one can apply existing analysis tools to any dataset with missing observations and use the same structure and output. There are several different techniques that use imputation to replace missing values. The most commonly applied techniques are mean imputation, hot-deck imputation, cold-deck imputation, regression imputation and multiple imputations (Madow, Olkin, Rubin, 1983; Sà ¤rndal, Swensson, Wretman, 1992). In general, imputation may cause distortions in the distribution of a study variable or in the relationship between two or more variables. This disadvantage can be diminished when e.g. multiple regression imputation is used (Sà ¤rndal et al., 1992). For example, Gustafsson Reuterberg (2000) used regression to impute missing values in order to get a more realistic view of the relationship between grades in upper secondary schools in Sweden and the Swedish Scholastic Achievement Test. Note that regression imputation is questionable to use, because all imputed values fall directly on the regression line, the imputed data lack variability that would be present had both X and Y been collect ed. In other words the correlation would be 1.0 if only computed with imputed values (Little Rubin, 2002). Therefore literature suggest using imputed Maximum Likelihood (ML) estimates for the missing values that are obtained using the Expectation Maximization (EM) algorithm (Dempster, Laird, Rubin, 1977). Maximum likelihood (ML) estimates obtained from the Expectation Maximization (EM) algorithm is imputed for the criterion variable for examinees who failed the selection test for example (Dempster et al., 1977; Little, 1992). The complete and incomplete cases were used together as the EM algorithm reestimates means, variances and covariances until the process converges. The base of EM missing values is an iterative regression imputation. The final estimated moments are the EM estimates including estimates for the correlation. For an extensive description see SPSS (2002). The idea is that the missing Y values are imputed using the following equation where and are the estimates obtained from the final iteration of the EM algorithm. Schaffer and Graham (2002) suggested that using EM imputation is valid when examining missing data. Issues with ML estimates obtained from the EM algorithm method This approach is seldom used with range restriction problems, although it has been mentioned as a possibility (Mendoza, 1993). In a more recent study, Mendoza, Bard, Mumford, Ang, (2004) concluded that the ML estimates obtained from the EM algorithm procedure produced far more accurate results. Wiberg and Sundstrà ¶m (2009) evaluated this approach in an empirical study and their results indicated that ML estimates obtained from the EM algorithm seem to be a very effective method of estimating the population correlation. Since there is not much work in 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  [1]  at the same time as we obtain a good estimate of the population correlation. 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 (e.g., Crocker Algina, 1986; Worthen, White, Fan, Sudweeks, 1999). In this review, two approaches for correcting attenuation effects caused by measurement error; traditional approach and latent variable modeling approach, will be described and results from research evaluating their use will be discussed. 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). When Spearman first proposed the correction for attenuation, he advocated correcting for both the predictor and the criterion variables for unreliability. His equation, rTx,Ty = , is known as double correction. The double correction performed on the obtained validity coefficient reveals what the relationship would be between two variables if both were measured with perfect reliability. Because measurement error truncates, or reduces, the size of the obtained validity coefficient, the effect of the correction is to elevate the magnitude of the corrected validity coefficient above the magnitude of the obtained validity coefficient. The lower the reliability of the predictor and/or criterion variables, the greater will be the elevation of the correction. If both the test and the criterion exhibit very high reliability, the denominator of the equation will be close to unity, thus rTx,Ty à ¢Ã¢â‚¬ °Ã‹â€  . The double correction formula was followed by the single correction formula as researchers began to shift the emphasis from test construction to issues of using tests to predict criteria. As the name implies, the formula involves correcting for unreliability in only one of the two variables. The formula would be either rTx,Ty = (correcting for unreliability in the criterion variable only) or rTx,Ty = (correcting for unreliability in the predictor variable only). The rationale for the single correction of the criterion unreliability was best stated by Guilford (1954): In predicting criterion measures from test scores, one should not make a complete [double] correction for attenuation. Corrections should be made in the criterion only. On the one hand it is not a fallible criterion that we should aim to predict, including all its errors; it is a true criterion or the true component of the obtained criterion. On the other hand, we should not correct for errors in the test, because it is the fallible scores from which we must make predictions. We never know the true scores from which to predict. (p. 401) Although most researchers have adopted Guilfords position on correcting only for criterion unreliability, there have been cases where correcting only for unreliability in the predictor was used. However, these occasions appear to be special cases of double correction, where either the reliability of the criterion was unknown or where the criterion was assumed to be measured with perfect reliability. The former situation was not unusual. We often know more about the reliability of tests than the reliability of criteria. The later situation is more unusual in that variables are rarely assessed with perfect reliability. Issues with traditional approach The correction for attenuation due to measurement error is one of the earliest applications of true-score theory (Spearman, 1904) and has been the subject of numerous debates, spurring criticisms from its very inception (e.g., Pearson, 1904). Despite this, no real consensus on correction for attenuation 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  [2]  would exceed obtained variance (error variance). Psychometricians have offered various explanations for this phenomenon. Before the year ended, Karl Pearson (1904, in his appendix) had declared that any formula that produced correlation coefficients greater than one must have been improperly derived; however, no errors were subsequently found in Spearmans formula. This led to debate over both how correction for attenuation could result in a correlation greater than one and whether a procedure that often resulted in a correlation greater than one was valid. Many explanations for correction for attenuations supposed flaw have been suggested. Error in estimating reliability. Many statistics used to estimate reliability are known to regularly underestimate reliability (i.e., overestimate the amount of error; Johnson, 1944; Osburn, 2000). Whereas this bias is tolerated as being in the preferred direction for some applications (as when a researcher wants to guarantee a minimum reliability), the result of correction for attenuation is inflated if the denominator entered into the equation is less than the accurate value (Winne Belfry, 1982). Other researchers have shown that some reliability estimates can overestimate reliability when transient errors are present; however, it has been argued that this effect is probably small in practice (Schmidt Hunter, 1996, 1999). Normal effects of sampling process. Others, including Spearman (1910), have attempted to explain corrected correlations greater than one as the normal result of sampling error. Worded more explicitly, this asserts that a corrected correlation of 1.03 should fall within the sampling distribution of corrected correlations produced by a population with a true-score correlation less than or equal to one. Despite this, it was some time before researchers first began to examine the sampling distributions of corrected correlations. However, some early studies that have examined the accuracy of correction for attenuation are of note  [3]  . Misunderstanding of random error. Thorndike (1907) applied multiple simulated error sets to a single set of true-score values and concluded that the equation for correction for attenuation worked reasonably well. Johnson (1944) extended this study and demonstrated that random errors would occasionally raise the level of observed correlations above the true-score correlation. In those cases, the equation to correct for attenuation corrects in the wrong direction. Johnsons conclusion that Corrected coefficients greater than one are caused by fluctuations in observed coefficients due to errors of measurement and not by fluctuations caused by errors of sampling, as suggested by Spearman (Johnson, 1944, p. 536). Garside (1958) referenced the various bases of error variance in the coefficients as function fluctuations. Latent variable modeling approach Latent variable approach is considered when a multifactorial test is used in the admission of students to various schools. Most often a composite measure related to the total test score or subtests are used in such prediction. The use of a multiple factor latent variable model for the observed variables comprising the test can make more efficient use of the test information. Correctly assessing the predictive validity in traditional selection studies, without latent variables, is a difficult task involving adjustments to circumvent the selective nature of the sample to be used for the validation. Latent variable modeling of the components of a test in relation to a criterion variable provides more precise predictor variables, and may include factors which have a small number of measurements. For many ability and aptitude tests it is relevant to postulate a model with both a general factor influencing all components of the test, and specific factors influencing more narrow subsets (Fan, 2003). In confirmatory factor analysis where each latent factor has multiple indicators, measurement errors are explicitly modeled in the process. The relationship between such latent factors can be considered as free from the attenuation caused by the measurement error. For example, The  GMAT exam is a standardized assessment that helps business schools assess the qualifications of applicants for advanced study in business and management. The GMAT exam measures three areas; Verbal, Quantitative Reasoning, and Analytical Writing Skills. To illustrate the point, lets look at the verbal exam. The verbal exam measures three related latent variables (Critical Reasoning (), Reading Comprehension (), Grammar and Sentence Structure ()). Each of these variables has many indicators. In such model, is considered to represent the true relationship between the three latent variables (, ,, respectively) that is not attenuated by the measurement error ( to ). This approach for obtaining measurement-err or-free relationship between factors is well-known in the area of structural equation modeling but is rarely discussed within the context of measurement reliability and validity. Using this approach, once the interitem correlation is obtained, the population reliability in the form of Cronbachs coefficient alpha  [4]  could be obtained. Cronbachs coefficient alpha takes the form  Ã‚ ¡ = ) where k is the number of items within a composite, is the sum of item variances, and is the variance of the composite score. The variance of the compositeis simply the sum of item variances ( ) and the sum of item covariances (2). = + 2. The population intervariable correlation is obtained from the two-factor model in the Figure above based on the following (Jà ¶reskog Sà ¶rbom, 1989): ÃŽÂ £ = ΆºÃƒÅ½Ã‚ ¦ÃƒÅ½Ã¢â‚¬ ºÃƒ ¢Ã¢â€š ¬Ã‚ ² + ÃŽËÅ" where ÃŽÂ £ is the population covariance matrix (correlation matrix for our standardized variables), Άº is the matrix of population pattern coefficients, ÃŽÂ ¦ is the population correlation matrix for the two factors, and ÃŽËÅ" is the covariance matrix of population residuals for the items. Issues with latent variable modeling approach This approach for obtaining measurement-error-free correlation coefficients is well known in the area of structural modeling, but it is rarely discussed within the context of measurement reliability and validity. Fan (2003) used this approach to correct for attenuation and showed that this approach provided not only near identical and unbiased means but also near identical confidence intervals for the sampling distribution of the corrected correlation coefficients. It is pointed out, however, that the latent variable modeling approach may be less applicable in research practice due to more difficult data conditions at the item level in research practice. DeShon (1998) stated that latent variable modeling approach provides a mathematically rigorous method for correcting relationships among latent variables for measurement error in the indicators of the latent variables. However, this approach can only use the information provided to correct for attenuation in a relationship. It is not an all-powerful technique that corrects for all sources of measurement error. Conclusion It has long been recognized that insufficient variability in a sample will restrict the observed magnitude of a Pearson product moment coefficient. Since R. L. Thorndikes days, researchers have been correcting correlation coefficients for attenuation and/or restriction in range. The topic has received considerable attention (Bobko, 1983; Callender Osborn, 1980; Lee, Miller, Graham, 1982; Schmidt Hunter, 1977) and today correlation coefficients are corrected for attenuation and range restriction in a variety of situations. These include test validation, selection, and validity generalization studies (meta-analysis; Hedges Olkin, 1985), such as those conducted by Hunter, Schmidt, and Jackson (1982). For example, Pearlman, Schmidt, and Hunter (1980) corrected the mean correlation coefficient in their validity generalization study of job proficiency in clerical occupations for predictor and criterion unreliability as well as for range restriction on the predictor. 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. Fan (2003) shows that the SEM approach (at least in the CFA context) produces equivalent results to the application of the traditional method. For correction for range restriction, the Thorndike case II method has been shown to produce close estimates of the correlation in a population (Hunter Schmidt, 1990). Wiberg and Sundstrà ¶m (2009) show that ML estimates obtained from the EM algorithm approach provides a very good estimate of the correlation in the u nrestricted sample as well. 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. Using an appropriate method for correcting for attenuation and range restriction is most important when conducting predictive validity studies of instruments used, for example, for selection to higher education or employment selection. The use of inappropriate methods for statistical artifacts correction or no correction method at all could result in invalid conclusions about test quality. Thus, carefully considering methods for correcting for attenuation and range restriction in correlation studies is an important validity issue. The literature reviewed here clearly suggests that practitioners should apply attenuation and range restriction corrections whenever possible, even if the study does not focus on measurement issues (American Educational Research Association, American Psychological Association, National Council on Measurement in Education, 1999).

Literacy, Love, Loss and Arda Essay

Literacy is important in keeping the history of the Middle-earth. This is to ensure that the future generations could get a grasp on what has happened to the different races; ie Man, Elves, Dwarves, Orcs, Hobbits, Trolls, Goblin-men, Uruk-hai, among others. History and recorded accounts of significant events is especially important to the wizards. This is shown in the part when Gandalf the Grey desired to know more about the ring in Bilbo’s possession. He immediately took the initiative to set out for the right thing to do. He asked Bilbo to leave it, and transfer to Frodo, the one who would be tasked to carry the ring to Rivendell, and later on, to the Crack of Mount Doom. He went to research for records. Fortunately, he found accounts from Isildur. â€Å"It has come to me†¦ the One Ring. It shall be an heirloom of my kingdom. All those who follow my bloodline shall be bound to its fate for I will risk no hurt to the Ring. It is precious to me, though I buy it with great pain. The markings upon the band begin to fade. The writing, which at first as clear as the red flame, has all but disappeared. A secret now that only fire can tell. † (Tolkien) With the history kept intact in that library, he was able to think of the best thing to do – to destroy it. In the mines of Moria, they had to pass a tunnel but there was a door with inscriptures above it. Frodo was able to read what was written there, and asked Gandalf what was the Elvish word for â€Å"friend. † When Gandalf uttered Mellon, the door opened (Tolkien). This showed that being able to read and write got the Fellowship moving. This also reflects that if nobody was educated, it could have been that they were not able to enter that door. This goes down to the truth that the earlier people had educated themselves also as evident in that password, which was made by them. Inside the mine was the kingdom ruled by dwarves. However, they found him already dead, as what was carved on the surface of his tomb. The language of the dwarves – Dwarvish – was helpful in this stage, because Gimli would not have known that Balin was already dead if it was not for the writings. Reading and writing is important to all the creatures of the Middle-earth. It is the most powerful tool to drive back to history of a village, or to a well-known person. It is also used to conceal secrets to treasured places. It is significant also to inform relatives and the society that a respectable lord has died. Most important of it could be its usefulness in terms of transmitting message from day-to-day activities. 2. What is the role of romantic love in the Lord of the Rings? How big a part does it play, and just what is this part? Give examples. The most famous romantic love story exposed in the Lord of the Rings could be that of Aragorn and Arwen. This was exaggerated in the adaptation of the novel into movie. â€Å"I would rather share one lifetime with you than face all the ages of this world alone†¦ I choose a mortal life†¦ It is mine to give whom I will†¦ like my heart. † These lines of Arwen, possibly coming from the deepest portion of her heart reflected the utmost devotion and truest affection in her heart for Aragorn. This love for Aragorn influenced her to make the biggest and most daring decision ever – to give up immortality, which has been a precious gift to the race where she belonged. She opted to be mortal and loved Aragorn, who also loved her so much. Their love for each other was so powerful that gave them inspiration to head on with their lives. Later near the end of their journey, they had a child, who was seen by Arwen when she was walking towards a life that never ends. This made them strong against the dark force enwrapping Middle-earth and the loneliness that kept on haunting them (Tolkien). Smeagol also had this passionate affection with the One Ring. He stayed in the dark Misty Mountains all by himself, but never thought of leaving the ring to somebody. He felt in love with the beauty and power the ring was giving him – unnatural long life. When he lost it, he tried to recover it. He followed the trails of the Fellowship tasked to bring his â€Å"precious† to Mount Doom. He succeeded in getting it from Frodo’s hands, but unfortunately, he ended falling into the fire of the mountain, where the ring was forged. At the end of the Return of the King, Sam was seen with his own family. He married Rosie, and had children afterwards. Even after Frodo had fled to the Undying Lands, Sam remained loyal to him by taking care of the book given to him by his friend. No one could blame him for that because they had gone to a perilous journey that truly tested their friendship.

Drunk Drivers And Drunk Driving - 946 Words

While I have never personally been involved in a crash caused by drunk driving, as a firefighter I have approached the aftermath of many. The worst drunk driving accident I have witnessed was a car that had rolled three times. The guy flew out the front window, leaving deep cuts all over his head. Because he was intoxicated, he tried to get up and move around, oblivious to his injuries or pain. He didn’t even realize he had gotten into an accident. As I watched the scene unfold, it made me angry. I didn’t understand how people could out themselves and others into dangerous or even fatal risks! Sadly, 50 to 70 percent of convicted drunk drivers continue to drive on a suspended license. On average, two in three people will be involved in a drunk driving crash in their lifetime (11 Facts). Drunk driving is an issue that can be overcome by putting a Breath Alcohol Ignition Interlock Device in a car and always assigning a designated driver. The substantial problem with drunk driving is that every death it causes could be prevented. While drivers with a low BAC (blood alcohol concentration) are involved in fewer fatal crashes, those with a higher BAC of .15 are often the ones that cause the fatal crashes. In addition, people with high BAC drivers tend to be male between the ages of 25 to 35 with a history of DWI’s (â€Å"Drinking and Driving†). By definition, alcohol is a depressant that slows down the functions of the central nervous system. This causes the normal brain functionShow MoreRelatedDrunk Driving And Drunk Drivers2145 Words   |  9 Pageskilled in drunk driving incidents. Out of those people, 65% (6,515) were drivers, 27% (2,724) were passengers, and 8% (837) were non-passengers (â€Å"Drunk Driving Statistics†). Over half of those fatalities (67.1%) involved blood alcohol levels over .15% (â€Å"Drunk Driving Statistics†). The legal blood-alcohol content is .08%. 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The crime of driving a vehicle or operating a motorized machine while under the influence of alcohol is totally against the law of the land, but some people still won’t stop. Is there any gain in drunk-driving than loss of lives, loss of driving privileges, and property—vehicles? One-third of traffic deaths invo lve alcohol-impaired driving (MADD). Therefore, a behavior that involves a tiny proportion of drivers is oneRead MoreDrunk Drivers Should Not Be Banned1279 Words   |  6 Pagesa large amount of drunk driving accidents almost every year there are drunk drivers getting away and not having any harsh consequences.Drunk driving has killed over hundreds of citizens due to the mistakes by over intoxicated drivers. States all across the country have lowered the blood alcohol limit to keep drunk drivers off the road from hitting a pedestrian. Some citizens believe that drunk drivers should not be punished more harshly due to be over intoxicated while driving. If there is no harmRead MoreAlcohol Related Accidents Essay874 Words   |  4 Pageschance of being in an accident with a drunk driver. Drunk driving is a serious problem that the United States, as well as the world, is trying to deal with, because it does not only effect a select few, it effects everyone. Drunk driving amongst hig h school students is an enormous problem that the United States is trying to cope with. Many programs have come to surface over the past few years, that educate students on this situation. MADD, mothers against drunk driving, is a non profit organization thatRead MoreDrunk Drivers Essay1097 Words   |  5 PagesDriving a vehicle is a huge responsibility, and can be dangerous for anyone who is careless on the road. That danger increases as drivers attempt to drive either intoxicated or drunk. Blood alcohol concentration, also known as BAC, is the amount of alcohol in the blood of one’s system, and is used as a measure of degree of intoxication in an individual (answers.com). In the United States it is illegal per se, to drive with a BAC of .08 for all drivers who are 21 and older (nhtsa.gov). As the bloodRead MoreDrunk Driver And Drunk Drivers923 Words   |  4 PagesIn 2013, 10,076 people died because of drunk drivers. One every 52 minutes. 290,000 were injured because of the accidents (MADD). In 2012, 3,328 people died because of car crashes due to the fact that drivers were on their phones. 421,000 were injured (Texting and Driving Statistics). Driving is not an easy task so you should always be attentive to what you’re doing. A big difference between both is being sober and being drunk. Someone that’s drunk isn’t fully aware of what’s going on. Someone whoRead MoreDrinking And Driving1335 Words   |  6 Pages Drink and Driving is and Ongoing Problem Erica Esposito Kean University Abstract This paper explores the research and find results on how drinking and driving has become a big problem in the United States. Drinking and driving effects a person’s ability to operate a vehicle and therefore drunk drivers need to be educated on the repercussions with drinking and driving. Every day drunk drivers are arrested, either for traffic violations, reckless driving, and random stops on theRead MoreDrunk Driving Essay780 Words   |  4 Pagesalcohol-impaired drivers (Wu, 2016). Many people drive while under the influence of alcohol because they do not see the risk of getting into an accident or potentially injuring someone. They only see the convenience of not leaving their car somewhere or purchasing a driving service. Driving while under the influence of alcohol has a negative impact on society. Drunk driving is detrimental to families, studies show that it takes human life, and has a legal punishment. When a drunk driver gets into anRead MoreDeath by Driving Drunk930 Words   |  4 Pagesone of the leading causes of death during driving is drunk driving. Drunk driving not only puts you in danger but everyone around you in danger. There are many ways that alcohol affects you that makes you drive very bad. To help stop this, The police have made many laws regarding drunk driving and have made many arrests regarding driving under the influence. There are also many stories out there that make us wonder about the dangers and risks of drunk driving. Theres also many laws and reforms being