{"id":764,"date":"2025-12-23T10:07:50","date_gmt":"2025-12-23T10:07:50","guid":{"rendered":"https:\/\/alandix.com\/statistics\/?page_id=764"},"modified":"2025-12-23T10:15:13","modified_gmt":"2025-12-23T10:15:13","slug":"chapter-3","status":"publish","type":"page","link":"https:\/\/alandix.com\/statistics\/book\/toc\/chapter-3\/","title":{"rendered":"Chapter 3: Properties of randomness"},"content":{"rendered":"<div class=\"embedurl\" data-url=\"https:\/\/alandix.com\/books\/hcistats\/content1e\/chaps\/chap-3.html\" ><!--  Chapter 3 Properties of randomness   -->\n\n<script>\nvar chapnos = 3;\nvar json_url = \"https:\\\/\\\/alandix.com\\\/books\\\/hcistats\\\/content1e\\\/chaps\\\/chap-3.json\";\n<\/script>\n\n\n\n\n\n\n<h3> Contents <\/h3>\n<div class=\"toc\">\n<dl>\n<dt>3.1&nbsp;&nbsp;Bias and variability <\/dt><dd><dl>\n<dt>3.1.1&nbsp;&nbsp;Bias <\/dt>\n<dt>3.1.2&nbsp;&nbsp;Bias vs. variability <\/dt>\n<\/dl><\/dd>\n<dt>3.2&nbsp;&nbsp;Independence and non-independence <\/dt><dd><dl>\n<dt>3.2.1&nbsp;&nbsp;Independence of measurements <\/dt>\n<dt>3.2.2&nbsp;&nbsp;Independence of factor effects <\/dt>\n<dt>3.2.3&nbsp;&nbsp;Independence of sample composition <\/dt>\n<\/dl><\/dd>\n<dt>3.3&nbsp;&nbsp;Play! <\/dt><dd><dl>\n<dt>3.3.1&nbsp;&nbsp;Virtual two-horse races <\/dt>\n<dt>3.3.2&nbsp;&nbsp;More (virtual) coin tossing <\/dt>\n<dt>3.3.3&nbsp;&nbsp;Fair and biased coins <\/dt>\n<dt>3.3.4&nbsp;&nbsp;No longer independent <\/dt>\n<\/dl><\/dd>\n<\/dl><\/div>\n\n\n<h3> Glossary items referenced in this chapter <\/h3>\n<div class=\"toc\">\n<strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/bias\">bias<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/causality\">causality<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/coin%20tossing\">coin tossing<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/confounding%20variables\">confounding variables<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/context%20effects\">context effects<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/controlled%20experiment\">controlled experiment<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/day%20effects\">day effects<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/effective%20sample%20size\">effective sample size<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/estimate\">estimate<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/estimate%20of%20the%20variability\">estimate of the variability<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/experimenter%20effects\">experimenter effects<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/external%20non-independence\">external non-independence<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/extreme%20values\">extreme values<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/factor%20effects\">factor effects<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/fair%20coin\">fair coin<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/fair%20estimate\">fair estimate<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/fitts%27%20law\">Fitts&#039; Law<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/independence\">independence<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/independent\">independent<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/individual%20differences\">individual differences<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/interference%20effect\">interference effect<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/internal%20non-independence\">internal non-independence<\/a><\/strong>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/learning%20effects\">learning effects<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/model%20the%20bias\">model the bias<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/negative%20correlation\">negative correlation<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/non-independence\">non-independence<\/a><\/strong>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/order%20effects\">order effects<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/peripheral%20vision\">peripheral vision<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/positive%20correlation\">positive correlation<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/positive%20learning\">positive learning<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/real%20world\">real world<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/sample%20composition\">sample composition<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/sample%20size\">sample size<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/simpson%27s%20paradox\">Simpson&#039;s paradox<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/snowball%20sample\">snowball sample<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/social%20network%20data\">social network data<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/standard%20deviation\">standard deviation (s.d., &amp;sigma;)<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/standard%20deviation%20of%20the%20population\">standard deviation of the population<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/standard%20deviation%20of%20the%20sample\">standard deviation of the sample<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/systematic%20effects\">systematic effects<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/tossing%20coins\">tossing coins<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/unbiased\">unbiased<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/uniformity%20fallacy\">uniformity fallacy<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/unintentional%20bias\">unintentional bias<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/user%20experience\">user experience<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/user%20studies\">user studies<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/user%20test\">user test<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/variability\">variability<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/variance\">variance<\/a><\/div>\n\n\n<!-- ?php\n\tif ( @$page['prolog_examples'] ):\n?>\n<h3> Prolog examples (from 1st ed.) <\/h3>\n<!-- ?php\n\techo $page['prolog_examples'];\n?>\n<!-- ?php\n\tendif; 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