Cronbach\u2019s Alpha assumptions:<\/strong><\/p>\n

1- That the indicators (items) are essentially tau-equivalent o This implies that each item is an equally strong indicator of the true score scores, but the ma differ by a constant<\/p>\n

o Basically this implies that the items can have different means<\/p>\n

2- That each item\u2019s error term is uncorrelated with every other item\u2019s error term<\/p>\n

3- That the error scores are uncorrelated with the true scores o An assumption associated with all forms of reliability<\/p>\n

4- The items used to generate the questionnaire must only measure one attribute or construct o If this is violated, Cronbach\u2019s alpha cannot be used<\/p>\n

Standardised coefficient alpha:<\/strong><\/p>\n

\n
• You apply it to scores that have been converted from a raw score to a standardised score<\/li>\n
• g. if you had z-scores and you wanted to calculate the level of internal consistency associated with a composite which consisted of a sum of two or more z-scores, you would use the standardized version of coefficient alpha<\/li>\n<\/ul>\n

  Types of reliability assumption models:<\/strong><\/p>\n

  \n
  • Parallel- equal true score variance, equal means, equal error variance<\/li>\n
  • Tau-equivalent- equal true score variance, equal means, unequal error variances<\/li>\n
  • Essentially tau-equivalent- equal true score variance, unequal means, unequal error variances<\/li>\n
  • Congeneric- unequal true score variance (but all greater than zero), unequal means, unequal error variances<\/li>\n<\/ul>\n

    What Cronbach\u2019s alpha is not?<\/strong><\/p>\n

    \n
    • Cronbach\u2019s alpha represents the ratio of true score variance to total variance<\/li>\n
    • It does not imply that a collection of items measure one psychological attribute (or dimension) and one psychological attribute only.<\/li>\n
    • It is fully possible for a collection of items to measure more than one psychological attribute, but still be associated with a reasonably high Cronbach\u2019s alpha<\/li>\n
    • Argued that CA assumes that the collection of items measure only one attribute o This can be tested using factor analysis<\/li>\n<\/ul>\n

      Factors affecting reliability:<\/strong><\/p>\n

      \n
      • Will adding this item reduce the mean inter-item correlation?<\/li>\n<\/ul>\n

        Sample homogeneity:<\/strong><\/p>\n

        \n
        • A more homogenous sample will yield lower reliability estimates than a heterogeneous sample o This is true of all correlations, not just statistics like Cronbach\u2019s alpha which is fundamentally based on correlations<\/li>\n<\/ul>\n

           <\/p>\n

          Importance:<\/strong><\/p>\n

          Mental retardation is defined as a person with an IQ score of 70 or less<\/p>\n

          \n
          • Some US states, death penalty cannot be administered to mental retards<\/li>\n<\/ul>\n

            Point estimates and confidence intervals:<\/strong><\/p>\n

            \n
            • The standard error of measurement represents the amount of error \u2018around\u2019 a point estimate in standard deviation form<\/li>\n
            • A point estimate is one\u2019s best guess of what a person\u2019s score is on the test o In the context of psychometrics, it\u2019s the score you get from the test o However a confidence interval can be estimated around a point-estimate<\/li>\n
            • A confidence interval reflects a range of values that is often interpreted as a range in which the true score is likely to fall<\/li>\n
            • Se_{m<\/sub> = so <\/sub>\u221a(1-Rxx<\/sub>) o So <\/sub>= standard deviation of the test o Rxx<\/sub> = reliability estimate<\/li>\n}
            • Typically, people calculate the 5% confidence interval around a point estimate<\/li>\n
            • rnce the standard error of estimate has been calculated, you can use this info to calculate a confidence interval around the point estimate<\/li>\n<\/ul>\n

              What confidence level should be used?<\/strong><\/p>\n

              \n
              • You probably want to use a 99% CI for a lift or death penalty<\/li>\n
              • You should keep in mind that although high levels of reliability are desired, they are not the only consideration<\/li>\n
              • rften have to sacrifice some reliability for greater validity<\/li>\n<\/ul>\n

                Reliability standards:<\/strong><\/p>\n

                \n
                • Using the standardised coefficient alpha formula, you can work out how large the mean inter-item correlation must be to achieve a reliability of a desired confidence interval<\/li>\n<\/ul>\n

                  kr<\/span><\/em>ii ‘<\/em><\/p>\n

                  \n
                  • R<\/em>xx<\/em>=1+(k<\/em>\u22121)r<\/span><\/em>ii’<\/em><\/li>\n<\/ul>\n

                    Two types of correlations:<\/strong><\/p>\n

                    \n
                    • rbserved score correlation:\n
                      \n
                      • The correlation you get based on the data you have<\/li>\n
                      • Will be compromised to the degree to which there is measurement error in your data, when scores are associated with less than perfect reliability<\/li>\n
                      • In practice this means the maximum correlation between two sets is not 1.0 but often less than that<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

                         <\/p>\n

                        \n
                        • The maximum correlation between two variables- r<\/em>max=\u221aR<\/em>xx<\/em>R<\/em>yy <\/em>o <\/strong>The correlation for attenuation formula is the ration of the observed correlation to<\/li>\n<\/ul>\n

                          r<\/em>x<\/em>O <\/em>y<\/em>O<\/em><\/p>\n

                          the square root of the product of the reliabilities- r<\/em>x<\/em>t <\/em>y<\/em>t<\/em>=\u221aR<\/em>xx<\/em>R<\/em>yy<\/em><\/p>\n

                          \n
                          • True score correlation:\n
                            \n
                            • A hypothetical correlation you can estimate, if you know the reliability associate with the scores<\/li>\n
                            • Not compromised by measurement error<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

                              Cronbach\u2019s Alpha assumptions: 1- That the indicators (items) are essentially tau-equivalent o This implies that each item is an equally strong indicator of the true score scores, but the… Continue Reading Importance of reliability<\/span><\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[107],"tags":[],"_links":{"self":[{"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/posts\/4280"}],"collection":[{"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/comments?post=4280"}],"version-history":[{"count":2,"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/posts\/4280\/revisions"}],"predecessor-version":[{"id":4871,"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/posts\/4280\/revisions\/4871"}],"wp:attachment":[{"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/media?parent=4280"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/categories?post=4280"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/tags?post=4280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}