{"id":4271,"date":"2018-09-18T18:43:13","date_gmt":"2018-09-18T22:43:13","guid":{"rendered":"https:\/\/www.amyork.ca\/academic\/zz\/?p=4271"},"modified":"2019-05-25T23:54:19","modified_gmt":"2019-05-26T03:54:19","slug":"differences-in-correlations","status":"publish","type":"post","link":"https:\/\/www.amyork.ca\/academic\/zz\/psychological-measurement\/differences-in-correlations\/","title":{"rendered":"Differences in correlations"},"content":{"rendered":"<p><strong>Variance:<\/strong><\/p>\n<ul>\n<li>Represents the amount of variability in the data<\/li>\n<li>Three main methods of representing variability o Range (smallest and largest data points) o Standard deviation o Variance<\/li>\n<\/ul>\n<p><strong>Correlation:<\/strong><\/p>\n<ul>\n<li>Standardised representation of the associations between two variables<\/li>\n<li>Can range from -1.0 to 1.0<\/li>\n<li>Coefficient of determination is the correlation squared<\/li>\n<\/ul>\n<p><strong>Composite variables:<\/strong><\/p>\n<ul>\n<li>Test scores tend to be based on the sum of two or more items<\/li>\n<li>g. the Beck Depression inventory consists of 21 items:<\/li>\n<\/ul>\n<p>o Items are scored on an ordinal scale from 0-3 o Thus the range of scores possible is 0-63<\/p>\n<ul>\n<li>Such \u2018sum scores\u2019 are known as \u2018composite scores\u2019.<\/li>\n<\/ul>\n<p><strong>Composite variables and variance:<\/strong><\/p>\n<ul>\n<li>The variance of a composite score is a function of:<\/li>\n<\/ul>\n<p>o The variance associated with the individual items o The correlation amongst the items<\/p>\n<ul>\n<li>A positive correlation between two variables increases the variance associated with the composite derived from those two variables.<\/li>\n<\/ul>\n<p>o i.e. as correlation increases (positive), the magnitude of the corresponding composite score variance also increases.<\/p>\n<p><strong>Binary items- Variance:<\/strong><\/p>\n<ul>\n<li>Most frequently encountered in achievement type tests, e.g. dichotomous items such as exam or intelligent test items<\/li>\n<li>All other things equal, having more variance is typically better than having less variance with respect to some important psychometric characteristics<\/li>\n<li>Calculating the variance of a composite based on dichotomous items works the same way as demonstrated for ordinal\/continuous items<\/li>\n<\/ul>\n<p><strong>Interpreting test scores:<\/strong><\/p>\n<p>Most scores produced by psychological tests are not clearly interpretable in their own right<\/p>\n<ul>\n<li>Two of the most common psychological test score interpretations are (1) relative and (2) abstract<\/li>\n<li>Relative interpretations are based on the analysis of data<\/li>\n<li>Abstract interpretations are based on theoretically relevant characteristics of the body of research which supports the test scores as valid indicators of a psychological construct<\/li>\n<\/ul>\n<p><strong>Relative interpretations:<\/strong><\/p>\n<ul>\n<li>From the relative perspective, to interpret an individual\u2019s score we need to:<\/li>\n<\/ul>\n<p>o Make reference to an entire distribution of scores on the test and o Identify where the individual falls in the distribution<\/p>\n<ul>\n<li>In practical terms this involves knowing the mean distribution of scores and the standard deviation of the distribution of scores<\/li>\n<\/ul>\n<p><strong>Raw scores- limitations:<\/strong><\/p>\n<ul>\n<li>Although knowledge of the mean and standard deviation associated with a group of scores allows us to interpret a particular score in a relative way, it is not a precise method unless you are a human calculator.<\/li>\n<li>Instead raw scores can be converted into standardised scores which incorporate information about the mean and standard deviation- z-scores.<\/li>\n<\/ul>\n<p><strong>Z-scores:<\/strong><\/p>\n<ul>\n<li>Have a mean of zero and a SD of one<\/li>\n<li>To convert raw scores into z-scores: z = X &#8211; \u03bc \/ \u03c3<\/li>\n<li>By framing the meaning of a score in terms of \u2018distance from the mean\u2019, the z score frees us from worrying about the units of the original test score<\/li>\n<li>Can be used to compare scores across tests that are on different sized units<\/li>\n<\/ul>\n<p><strong>Converted standard scores:<\/strong><\/p>\n<ul>\n<li>Ideally don\u2019t want to use negative numbers (in z scores), so you can easily convert them into alternated standard scores<\/li>\n<li>Accomplished by rescaling the scores so that the converted scores have a different mean and standard deviation- T scores.<\/li>\n<li>With t-scores the mean is always 50 and the standard deviation is always 10<\/li>\n<\/ul>\n<p><strong>T-scores:<\/strong><\/p>\n<ul>\n<li>Convert raw scores to z scores<\/li>\n<\/ul>\n<p>Convert z scores using the formula:\u00a0 T=z(10) +50<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Variance: Represents the amount of variability in the data Three main methods of representing variability o Range (smallest and largest data points) o Standard deviation o Variance Correlation: Standardised&hellip; <a class=\"continue\" href=\"https:\/\/www.amyork.ca\/academic\/zz\/psychological-measurement\/differences-in-correlations\/\">Continue Reading<span> Differences in correlations<\/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\/4271"}],"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=4271"}],"version-history":[{"count":1,"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/posts\/4271\/revisions"}],"predecessor-version":[{"id":4872,"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/posts\/4271\/revisions\/4872"}],"wp:attachment":[{"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/media?parent=4271"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/categories?post=4271"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/tags?post=4271"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}