Factorial validity:<\/strong><\/p>\n

\n
• Pertains to the internal structures<\/u> of test scores<\/li>\n
• A tests internal structure is the way that parts of the test are related to each other<\/li>\n
• The actual (empirical) structure of the test should match the theoretical or intended structure of the test<\/li>\n
• In a very simplistic sense, factorial validity helps specify what the test measures<\/li>\n
• That is, with respect to the number<\/u> of dimensions, and the definition<\/u> of those dimensions<\/li>\n
• The definitions of the dimensions are determined by which items \u2018load\u2019<\/u> onto which dimension<\/li>\n
• To determine the number of dimensions that underlie an inventory, as well as their definitions, we (can) use a data analytic technique known as factor analysis o <\/strong>Helps us clarify the number of factors within a set of terms<\/li>\n<\/ul>\n

  o <\/strong>Helps us determine the which items are linked to which factor, which facilitates the interpretation of those factors<\/p>\n

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

  \n
  • Typically, when we attempt to measure an attribute, we try to do so in such a way that the score represents a single attribute<\/li>\n
  • g. based on six item questions (3 on social interaction, 3 on intellect), if the total was calculated, what would that composite score mean?\n
    \n
    • It would be a compromised score, because the items do not all measure the same dimension<\/li>\n
    • We try to avoid these situations, want composite scores that are \u2018factor pure\u2019<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

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

      \n
      • Generally, three types of tests:<\/li>\n
      • Unidimensional test o Consists of items which all measure one, single factor<\/li>\n
      • Multidimensional test (uncorrelated)<\/li>\n<\/ul>\n

         <\/p>\n

        o Consists of items which measure two or more dimensions which are unrelated to each other<\/p>\n

        \n
        • Multidimensional test (correlated) o Consists of items which measure two or more dimensions which are correlated with each other (positively or negatively)<\/li>\n<\/ul>\n

          Unidimensional tests:<\/strong><\/p>\n

          \n
          • Include items that reflect only a single attribute<\/li>\n
          • The items are not affected by other attributes<\/li>\n
          • Consider a multi choice exam, students get one score on the final exam (presumes the test is also Unidimensional\/justifiable to yield one score)<\/li>\n<\/ul>\n

            Multidimensional test:<\/strong><\/p>\n

            \n
            • This is a model of a correlated multidimensional test<\/li>\n
            • Each item is linked to one attribute only, but there are there are two distinct attributes which are correlated with each other<\/li>\n
            • This is a model of an uncorrelated multidimensional test, each items is linked to one attribute only.<\/li>\n<\/ul>\n

              o There is no link between the two dimensions<\/p>\n

              Implications of factorial validity:<\/strong><\/p>\n

              \n
              • Test dimensionality has implications for the scoring:<\/li>\n<\/ul>\n

                o Scoring o Evaluation and o Use of the test scores<\/p>\n

                \n
                • Multidimensional tests with correlated dimensions can produce a variety of scores<\/li>\n<\/ul>\n

                  o Subtest score \u2013 based on the items of a single dimension o Area score- based on the items of a single dimension o Total score \u2013 used in higher order composite scores<\/p>\n

                  The psychological meaning of dimensions:<\/strong><\/p>\n

                  \n
                  • After the number of dimensions have been determined<\/li>\n
                  • And the associations between the dimensions have been determined<\/li>\n
                  • It is now time to understand the psychological meaning of each test dimension<\/li>\n
                  • This is accomplished by evaluating which items load onto each respective dimension<\/li>\n<\/ul>\n

                    Inter item correlations (hypothetical):<\/strong><\/p>\n

                    \n
                    • Furthermore, it appears that the two dimensions are not correlated with each other<\/li>\n
                    • This is an eye-ball approach to conducting a factor analysis<\/li>\n
                    • In practice, it is not especially useful because o <\/strong>There are usually a lot more than six variables included in a factor analysis o <\/strong>The pattern of correlation is not usually as clear cut as those in the above table<\/li>\n<\/ul>\n

                      Conducting a principle component analysis (PCA):<\/strong><\/p>\n

                      \n
                      • Note a PCA is almost equivalent to a factor analysis<\/li>\n
                      • Conduct a PCA twice:<\/li>\n<\/ul>\n

                        o rnce to determine the number of components (factors) to extract o Then again based on the number of components that you want extracted<\/p>\n

                        \n
                        • Find the break in the scree plot, this separation is obvious to how many dimensions are in the data o Scree plot consists of the eigenvalues ordered from smallest to largest in a scatter plot<\/li>\n<\/ul>\n

                          o Eigenvalues are essentially numerical representations of components with respect to their size.<\/p>\n

                          \n
                          • Now that I know how many components to extract from analysis, rerun with the specification of two components.<\/li>\n<\/ul>\n

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

                            \n
                            • Represent the percentage of variance associated with a particular variable that was included in the analysis<\/li>\n
                            • Generally, want to see communalities that or at least .04 or .09 (depending on the type of data being analysed:\n
                              \n
                              • .04 or greater for items<\/li>\n
                              • .09 or greater for subscales<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

                                Component landings:<\/strong><\/p>\n

                                \n
                                • Are useful when greater than either .20 or .30\n
                                  \n
                                  • .20 for items<\/li>\n
                                  • .30 for subscales<\/li>\n
                                  • Hence the minimum expectation of a communality of either .04 or .09 o Communality = sum of the squared component landings<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

                                    Simple structure:<\/strong><\/p>\n

                                    \n
                                    • The degree to which an item (or scale or any variable included in the analysis) is associated with only one substantial loading on a single dimension (i.e. component) and negligible loadings on the remaining dimensions<\/li>\n
                                    • rne way to achieve simple structure is to rotate the solution, should always be done<\/li>\n
                                    • You can only rotate a solution if you extract two or more components<\/li>\n<\/ul>\n

                                      Component correlations:<\/strong><\/p>\n

                                      \n
                                      • The correlation between the two components is equal to zero<\/li>\n
                                      • They are two totally separate dimensions with no overlap<\/li>\n
                                      • You cannot predict how high someone might score on openness to experience if you know how high they were on extraversion<\/li>\n<\/ul>\n

                                        Sample size requirements:<\/strong><\/p>\n

                                        \n
                                        • There are no simple guidelines to follow, because the size of the sample required will be dependent upon two main factors o The amount of communality associated with the variables (higher communality means less sample size required)<\/li>\n<\/ul>\n

                                          o The number of variables per factor (higher number of variables per factor means less sample size required)<\/p>\n","protected":false},"excerpt":{"rendered":"

                                          Is relevant to determining whether the scores of a measure correspond to the number and nature of dimensions of theorised dimensions that underlie the construct of interest Researchers use… Continue Reading Factorial validity<\/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\/4284"}],"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=4284"}],"version-history":[{"count":0,"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/posts\/4284\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/media?parent=4284"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/categories?post=4284"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/tags?post=4284"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}