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| {{Refimprove|date=July 2007}}
| | In this article you will be at our very own truthful Learn Photo Editing Overview. If you happen to believe that Learn Photo Editing is usually fraud this assessment can help you. In terms of this critique everyone meticulously did our examination and promote our decision. If you feel of creating an investment on this strategy, you will need to manage reading through.<br><br>Truly does Learn Photo Editing works or could it be rip-away from?<br><br>Learn Photo Editing lasts in lots of strategies. It progressively worked inside of a less hazardous and a lot quicker way. If you want to invest in it, you can expect to hardly ever remorse your today’s preference! You could unquestionably advantage a lot inevitably! It really is a Guarantee! You have to be absolutely content with your class, or otherwise you may receive a total reimbursement - each and every penny as a result !!<br><br>Is Learn Photo Editing a Scam?<br><br>Learn Photo Editing is to use without doubt the favorite and powerful process on the planet! Lots of you have to have formulated an understanding this system is often a rip-off but trust me it really is not a trick rather. It gives every piece of information you need. It could possibly perform instantly and you will definitely unquestionably keep a lot of time!<br><br>Learn Photo Editing Pdf file Subscription Review:<br><br>I actually have acquired been cheated by other internet products like Learn Photo Editing, and so i did not think it at the start. We have considered it basically lured clients to take to pointless points. Lots of website managed that kind of point. On the other hand, it may be a unique product which it offers you genuine providers. It is really not hoax. It is usually [http://www.google.com/search?q=intricate&btnI=lucky intricate] to acquire a right electronic provider on the internet and Learn Photo Editing is right for that you select.<br><br>I joined Learn Photo Editing web page a long time before. Shortly after about times of myself personally mastering and comprehending all the guidelines I made my preliminary success about my very first moment, with little work necessary. Now I had obtained obtained those things i needed from that. Learning to be a actual user employing this style of web page, I am going to quickly responsibly notify you that it really just isn’t a gimmick and it is also definitely helped me to the best value. I might advise Learn Photo Editing for your needs.<br><br>This obtained me to decided to produce a proceed by myself to make a technique to cause me to acquire. Just after almost a few months of difficult hard work, I acknowledged some things i are actually experiencing ambitions about for years. All these stats obviously signifies that Learn Photo Editing is working effectively which is simply not scam.<br><br>A terrific resource which changes per se routinely, [https://www.rebelmouse.com/learnphotoediting2/learn-photo-editing-review-how-673580762.html editing software] Learn Photo Editing will most likely function as the most liked of anyone who wants to have terrific benefits. Even though it really is informative that practical experience is very important to make use of Learn Photo Editing.<br><br>Learn Photo Editing Pdf file Advantages:<br><br>1.The special design of this gadget helps you take it as well as you wherever you aspire to go. Very suitable for luggage, bagpacks and powerful for days on end travels.<br><br>2.It is vital of, Learn Photo Editing has completely income back again warranties should you be not happy with Learn Photo Editing. So, looking over this system could well be RISKFREE¡<br><br>3.You can begin your online business with minor expense.<br><br>4.Instant shipment possibility really helps to create the product very special to name a few similar.<br><br>Risk-free popularity kind of Learn Photo Editing. And, needless to say you can find a completely funds-back make sure:<br><br>The goods are in existence for the major though after all this and has been get to utilize and authorized by many shoppers. Thus we should really signify that Learn Photo Editing is utterly not much of a hoax. If you are unhappy as a result you may get a income back again reimbursement, the property owner give 100% entire cash-back again assure consequently. Despite the fact that I suppose you might at any time request a return as Learn Photo Editing is authentic absolutely. |
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| '''Classical test theory''' is a body of related [[psychometric]] theory that predicts outcomes of psychological [[Test (assessment)|test]]ing such as the difficulty of items or the ability of test-takers. Generally speaking, the aim of classical test theory is to understand and improve the [[Reliability (psychometric)|reliability]] of psychological tests.
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| ''Classical test theory'' may be regarded as roughly synonymous with ''true score theory''. The term "classical" refers not only to the chronology of these models but also contrasts with the more recent psychometric theories, generally referred to collectively as [[item response theory]], which sometimes bear the appellation "modern" as in "modern latent trait theory".
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| Classical test theory as we know it today was codified by Novick (1966) and described in classic texts such as Lord & Novick (1968) and Allen & Yen (1979/2002). The description of classical test theory below follows these seminal publications.
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| ==History==
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| Classical Test Theory was born only after the following 3 achievements or ideas were conceptualized: one, a recognition of the presence of errors in measurements, two, a conception of that error as a random variable, and third, a conception of correlation and how to index it. In 1904, [[Charles Spearman]] was responsible for figuring out how to correct a correlation coefficient for attenuation due to measurement error and how to obtain the index of reliability needed in making the correction.<ref>Traub, R. (1997). Classical Test Theory in Historical Perspective. ''[[Educational Measurement: Issues and Practice]]'' 16 (4), 8-14. doi:doi:10.1111/j.1745-3992.1997.tb00603.x</ref> Spearman's finding is thought to be the beginning of Classical Test Theory by some (Traub, 1997). Others who had an influence in the Classical Test Theory's framework include: [[George Udny Yule]], [[Truman Lee Kelley]], those involved in making the [[Kuder-Richardson Formulas]], [[Louis Guttman]], and, most recently, [[Melvin Novick]], not to mention others over the next quarter century after Spearman's initial findings
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| ==Definitions==
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| Classical test theory assumes that each person has a ''true score'',''T'', that would be obtained if there were no errors in measurement. A person's true score is defined as the expected number-correct score over an infinite number of independent administrations of the test. Unfortunately, test users never observe a person's true score, only an ''observed score'', ''X''. It is assumed that ''observed score'' = ''true score'' plus some ''error'':
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| X = T + E
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| observed score true score error
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| Classical test theory is concerned with the relations between the three variables <math>X</math>, <math>T </math>, and <math> E </math> in the population. These relations are used to say something about the quality of test scores. In this regard, the most important concept is that of ''reliability''. The reliability of the observed test scores <math>X</math>, which is denoted as <math>{\rho^2_{XT}}</math>, is defined as the ratio of true score variance <math>{\sigma^2_T}</math> to the observed score variance <math>{\sigma^2_X}</math>:
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| <math>{\rho^2_{XT}} = \frac{{\sigma^2_T}}{{\sigma^2_X}}</math>
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| Because the variance of the observed scores can be shown to equal the sum of the variance of true scores and the variance of error scores, this is equivalent to
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| <math>{\rho^2_{XT}} = \frac{{\sigma^2_T}}{{\sigma^2_X}} = \frac{{\sigma^2_T}}{{\sigma^2_T}+{\sigma^2_E}}</math> | |
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| This equation, which formulates a signal-to-noise ratio, has intuitive appeal: The reliability of test scores becomes higher as the proportion of error variance in the test scores becomes lower and vice versa. The reliability is equal to the proportion of the variance in the test scores that we could explain if we knew the true scores. The square root of the reliability is the correlation between true and observed scores.
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| ==Evaluating tests and scores: Reliability==
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| Reliability cannot be estimated directly since that would require one to know the true scores, which according to classical test theory is impossible. However, estimates of reliability can be obtained by various means. One way of estimating reliability is by constructing a so-called ''[[parallel test]]''. The fundamental property of a parallel test is that it yields the same true score and the same observed score variance as the original test for every individual. If we have parallel tests x and x', then this means that
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| <math>{\varepsilon}(X_i)={\varepsilon}(X'_i)</math>
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| and | |
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| <math>{\sigma}^2_{E_i}={\sigma}^2_{E'_i}</math>
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| Under these assumptions, it follows that the correlation between parallel test scores is equal to reliability (see Lord & Novick, 1968, Ch. 2, for a proof).
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| <math> | |
| {\rho}_{XX'}=
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| \frac{{\sigma}_{XX'}}{{\sigma}_X{\sigma}_{X'}}=
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| \frac{ {\sigma}_T^2 }{ {\sigma}_X^2 }=
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| {\rho}_{XT}^2
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| </math> | |
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| Using parallel tests to estimate reliability is cumbersome because parallel tests are very hard to come by. In practice the method is rarely used. Instead, researchers use a measure of internal consistency known as [[Cronbach's alpha|Cronbach's <math>{\alpha}</math>]]. Consider a test consisting of <math>k</math> items <math>u_{j}</math>, <math>j=1,\ldots,k</math>. The total test score is defined as the sum of the individual item scores, so that for individual <math>i</math>
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| <math>X_{i}=\sum_{j=1}^{k}{U_{ij}}</math>
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| Then [[Cronbach's alpha]] equals
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| <math> \alpha =\frac{k}{k-1}\left(1-\frac{\sum_{j=1}^{k}{\sigma^{2}_{U_{j}}}}{\sigma^2_{X}}\right)</math>
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| Cronbach's <math>{\alpha}</math> can be shown to provide a lower bound for reliability under rather mild assumptions. {{citation needed|date=October 2013}} Thus, the reliability of test scores in a population is always higher than the value of Cronbach's <math>{\alpha}</math> in that population. Thus, this method is empirically feasible and, as a result, it is very popular among researchers. Calculation of Cronbach's <math>{\alpha}</math> is included in many standard statistical packages such as [[SPSS]] and [[SAS System|SAS]].<ref name="Lei2007">{{cite journal| title=CTTITEM: SAS macro and SPSS syntax for classical item analysis| author=Pui-Wa Lei and Qiong Wu| journal=Behavior Research Methods| volume=39| issue=3| year=2007| pages=527–530| url=http://brm.psychonomic-journals.org/content/39/3/527.full.pdf| pmid=17958163| doi=10.3758/BF03193021}}</ref>
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| As has been noted above, the entire exercise of classical test theory is done to arrive at a suitable definition of reliability. Reliability is supposed to say something about the general quality of the test scores in question. The general idea is that, the higher reliability is, the better. Classical test theory does not say how high reliability is supposed to be. Too high a value for <math>{\alpha}</math>, say over .9, indicates redundancy of items. Around .8 is recommended for personality research, while .9+ is desirable for individual high-stakes testing.<ref>{{Cite journal | doi = 10.1207/S15327752JPA8001_18 | last1 = Streiner | first1 = D. L. | year = 2003 | title = Starting at the Beginning: An Introduction to Coefficient Alpha and Internal Consistency | url = | journal = Journal of Personality Assessment | volume = 80 | issue = 1| pages = 99–103 | pmid = 12584072 }}</ref> These 'criteria' are not based on formal arguments, but rather are the result of convention and professional practice. The extent to which they can be mapped to formal principles of statistical inference is unclear.
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| ==Evaluating items: P and item-total correlations==
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| Reliability provides a convenient index of test quality in a single number, reliability. However, it does not provide any information for evaluating single items. Item analysis within the classical approach often relies on two statistics: the [[P-value]] (proportion) and the [[item-total correlation]] ([[point-biserial correlation coefficient]]). The [[P-value]] represents the proportion of examinees responding in the keyed direction, and is typically referred to as ''item difficulty''. The item-total correlation provides an index of the discrimination or differentiating power of the item, and is typically referred to as ''item discrimination''. In addition, these statistics are calculated for each response of the oft-used [[multiple choice]] item, which are used to evaluate items and diagnose possible issues, such as a confusing distractor. Such valuable analysis is provided by specially-designed [[psychometric software]].
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| ==Alternatives==
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| Classical test theory is an influential theory of test scores in the social sciences. In psychometrics, the theory has been superseded by the more sophisticated models in [[Item Response Theory]] (IRT) and [[Generalizability theory]] (G-theory). However, IRT is not included in standard statistical packages like [[SPSS]] and [[SAS System|SAS]], but there are IRT packages for the open source statistical programming language [[R (programming language)|R]] (e.g., CTT). While commercial packages routinely provide estimates of Cronbach's <math>{\alpha}</math>, specialized [[psychometric software]] may be preferred for IRT or G-theory. However, general statistical packages often do not provide a complete classical analysis (Cronbach's <math>{\alpha}</math> is only one of many important statistics), and in many cases, specialized software for classical analysis is also necessary.
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| ==Shortcomings of Classical Test Theory==
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| One of the most important or well known shortcomings of Classical Test Theory is that examinee characteristics and test characteristics cannot be separated: each can only be interpreted in the context of the other. Another shortcoming lies in the definition of Reliability that exists in Classical Test Theory, which states that reliability is "the correlation between test scores on parallel forms of a test".<ref name="Hambleton, R. 1991">Hambleton, R., Swaminathan, H., Rogers, H. (1991). ''Fundamentals of Item Response Theory''. Newbury Park, California: Sage Publications, Inc.</ref> The problem with this is that there are differing opinions of what parallel tests are. Various reliability coefficients provide either lower bound estimates of reliability or reliability estimates with unknown biases. A third shortcoming involves the standard error of measurement. The problem here is that, according to Classical Test Theory, the standard error of measurement is assumed to be the same for all examinees. However, as Hambleton explains in his book, scores on any test are unequally precise measures for examinees of different ability, thus making the assumption of equal errors of measurement for all examinees implausible (Hambleton, Swaminathan, Rogers, 1991, p. 4). A fourth, and final shortcoming of the Classical Test Theory is that it is test oriented, rather than item oriented. In other words, Classical Test Theory cannot help us make predictions of how well an individual or even a group of examinees might do on a test item.<ref name="Hambleton, R. 1991"/>
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| ==Notes==
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| {{reflist}}
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| ==References==
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| * <cite id=Allen2002>Allen, M.J., & Yen, W. M. (2002). ''Introduction to Measurement Theory.'' Long Grove, IL: Waveland Press.</cite>
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| * <cite id=Novick1966>Novick, M.R. (1966) ''The axioms and principal results of classical test theory'' Journal of Mathematical Psychology Volume 3, Issue 1, February 1966, Pages 1-18</cite>
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| * Lord, F. M. & Novick, M. R. (1968). ''Statistical theories of mental test scores.'' Reading MA: Addison-Welsley Publishing Company
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| == Further reading ==
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| *{{Cite book |title=Psychological Testing: History, Principles, and Applications |last=Gregory |first=Robert J. |year=2011 |edition=Sixth |publisher=Allyn & Bacon |location=Boston |isbn=978-0-205-78214-7 |page= |pages= |laysummary=http://www.pearsonhighered.com/bookseller/product/Psychological-Testing-History-Principles-and-Applications-6E/9780205782147.page |laydate=7 November 2010 |ref=harv }}
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| *{{Cite book |title=Psychological Testing: A Practical Introduction |last=Hogan |first=Thomas P. |authorlink= |coauthors=Brooke Cannon |year=2007 |edition=Second |publisher=John Wiley & Sons |location=Hoboken (NJ) |isbn=978-0-471-73807-7 |laysummary=http://www.wiley.com/WileyCDA/WileyTitle/productCd-EHEP000675.html |laydate=21 November 2010 |ref=harv }}
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| ==External links==
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| * [http://www.intestcom.org/Publications/ORTA/Classical+test+theory.php International Test Commission article on Classical Test Theory]
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| ==See also==
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| * [[Concept inventory]]
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| * [[Psychometrics]]
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| * [[Standardized test]]
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| * [[Educational psychology]]
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| * [[Generalizability theory]]
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| [[Category:Psychometrics]]
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| [[Category:Statistical models]]
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| [[Category:Comparison of assessments]]
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