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Cronbach's alpha
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==Ideal reliability level and how to increase reliability== ===Nunnally's recommendations for the level of reliability=== Nunnally's book<ref name="n1">{{cite book|first=J. C.|last=Nunnally|title=Psychometric theory|publisher=McGraw-Hill|date=1967|isbn=0-07-047465-6|oclc=926852171}}</ref><ref name="n3">{{cite book|last1=Nunnally|first1=J. C.|last2=Bernstein|first2=I. H.|title=Psychometric theory|publisher=McGraw-Hill|edition=3rd|date=1994|isbn=0-07-047849-X|pages=|oclc=28221417}}</ref> is often mentioned as the primary source for determining the appropriate level of dependability coefficients. However, his proposals contradict his aims as he suggests that different criteria should be used depending on the goal or stage of the investigation. Regardless of the type of study, whether it is exploratory research, applied research, or scale development research, a criterion of 0.7 is universally employed.<ref name="LBM">{{cite journal|last1=Lance|first1=C. E.|last2=Butts|first2=M. M.|last3=Michels|first3=L. C.|title=What did they really say?|journal=Organizational Research Methods|volume=9|issue=2|pages=202β220|date=2006|doi=10.1177/1094428105284919|s2cid=144195175}}</ref> He advocated 0.7 as a criterion for the early stages of a study, most studies published in the journal do not fall under that category. Rather than 0.7, Nunnally's applied research criterion of 0.8 is more suited for most empirical studies.<ref name="LBM"/> {| class="wikitable" style="text-align: right; |+ Nunnally's recommendations on the level of reliability |- ! !! 1st edition<ref name=n1/> !! 2nd & 3rd<ref name=n3/> edition |- | Early stage of research|| 0.5 or 0.6|| 0.7 |- | Applied research|| 0.8|| 0.8 |- | When making important decisions|| 0.95 (minimum 0.9)|| 0.95 (minimum 0.9) |} His recommendation level did not imply a cutoff point. If a criterion means a cutoff point, it is important whether or not it is met, but it is unimportant how much it is over or under. He did not mean that it should be strictly 0.8 when referring to the criteria of 0.8. If the reliability has a value near 0.8 (e.g., 0.78), it can be considered that his recommendation has been met.<ref name = c2020>{{cite journal|first=E.|last=Cho|title=A comprehensive review of so-called Cronbach's alpha|journal=Journal of Product Research|volume=38|issue=1|pages=9β20|date=2020|doi=}}</ref> ===Cost to obtain a high level of reliability=== Nunnally's idea was that there is a cost to increasing reliability, so there is no need to try to obtain maximum reliability in every situation. ====Trade-off with validity==== Measurements with perfect reliability lack validity.<ref name = ChoKim/> For example, a person who takes the test with a reliability of one will either receive a perfect score or a zero score, because if they answer one item correctly or incorrectly, they will answer all other items in the same manner. The phenomenon where validity is sacrificed to increase reliability is known as the attenuation paradox.<ref>{{cite journal|first=J.|last=Loevinger|title=The attenuation paradox in test theory|journal=Psychological Bulletin|volume=51|issue=5|pages=493β504|date=1954|doi=10.1002/j.2333-8504.1954.tb00485.x|pmid=13204488}}</ref><ref>{{cite journal|first=L.|last=Humphreys|title=The normal curve and the attenuation paradox in test theory|journal=Psychological Bulletin|volume=53|issue=6|pages=472β6|date=1956|doi=10.1037/h0041091|pmid=13370692}}</ref> A high value of reliability can conflict with content validity. To achieve high content validity, each item should comprehensively represent the content to be measured. However, a strategy of repeatedly measuring essentially the same question in different ways is often used solely to increase reliability.<ref>{{cite journal|first=G. J.|last=Boyle|title=Does item homogeneity indicate internal consistency or item redundancy in psychometric scales?|journal=Personality and Individual Differences|volume=12|issue=3|pages=291β4|date=1991|doi=10.1016/0191-8869(91)90115-R}}</ref><ref>{{cite journal|first=D. L.|last=Streiner|title=Starting at the beginning: An introduction to coefficient alpha and internal consistency|journal=Journal of Personality Assessment|volume=80|issue=1|pages=99β103|date=2003|doi=10.1207/S15327752JPA8001_18|pmid=12584072|s2cid=3679277}}</ref> ====Trade-off with efficiency==== When the other conditions are equal, reliability increases as the number of items increases. However, the increase in the number of items hinders the efficiency of measurements. ===Methods to increase reliability=== Despite the costs associated with increasing reliability discussed above, a high level of reliability may be required. The following methods can be considered to increase reliability. Before [[data collection]]: * Eliminate the ambiguity of the measurement item. * Do not measure what the respondents do not know.<ref>{{Cite journal|last1=Beatty|first1=P.|last2=Herrmann|first2=D.|last3=Puskar|first3=C.|last4=Kerwin|first4=J.|date=July 1998|title="Don't know" responses in surveys: is what I know what you want to know and do I want you to know it?|url=https://pubmed.ncbi.nlm.nih.gov/9829099/|journal=Memory (Hove, England)|volume=6|issue=4|pages=407β426|doi=10.1080/741942605|issn=0965-8211|pmid=9829099|access-date=2023-02-20|archive-date=2023-02-20|archive-url=https://web.archive.org/web/20230220140847/https://pubmed.ncbi.nlm.nih.gov/9829099/|url-status=live}}</ref> * Increase the number of items. However, care should be taken not to excessively inhibit the efficiency of the measurement. * Use a scale that is known to be highly reliable.<ref>Lee, H. (2017). Research Methodology (2nd ed.), Hakhyunsa.</ref> * Conduct a pretest - discover in advance the problem of reliability. * Exclude or modify items that are different in content or form from other items (e.g., reverse-scored items). After data collection: * Remove the problematic items using "alpha if item deleted". However, this deletion should be accompanied by a theoretical rationale. * Use a more accurate reliability coefficient than <math>\rho_{T}</math>. For example, <math>\rho_{C}</math> is 0.02 larger than <math>\rho_{T}</math> on average.<ref name="PK">{{cite journal|last1=Peterson|first1=R. A.|last2=Kim|first2=Y.|title=On the relationship between coefficient alpha and composite reliability|journal=Journal of Applied Psychology|volume=98|issue=1|pages=194β8|date=2013|doi=10.1037/a0030767|pmid=23127213}}</ref>
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