{"id":810,"date":"2025-12-23T10:35:03","date_gmt":"2025-12-23T10:35:03","guid":{"rendered":"https:\/\/alandix.com\/statistics\/?page_id=810"},"modified":"2025-12-23T10:42:02","modified_gmt":"2025-12-23T10:42:02","slug":"chapter-9","status":"publish","type":"page","link":"https:\/\/alandix.com\/statistics\/second-edition\/toc\/chapter-9\/","title":{"rendered":"Chapter 9: Differences and distinctions"},"content":{"rendered":"<div class=\"embedurl\" data-url=\"https:\/\/alandix.com\/books\/hcistats\/content2e\/chaps\/chap-10.html\" ><!--  Chapter 10 Empirical and simulation methods \u2013 beyond fixed tests  -->\n\n<script>\nvar chapnos = 10;\nvar json_url = \"https:\\\/\\\/alandix.com\\\/books\\\/hcistats\\\/content2e\\\/chaps\\\/chap-10.json\";\n<\/script>\n\n\n\n\n\n\n<h3> Contents <\/h3>\n<div class=\"toc\">\n<dl>\n<dt>10.1&nbsp;&nbsp;Empirical statistics<\/dt><dd><dl>\n<dt>10.1.1&nbsp;&nbsp;Potential problems<\/dt>\n<dt>10.1.2&nbsp;&nbsp;How many?<\/dt>\n<\/dl><\/dd>\n<dt>10.2&nbsp;&nbsp;Simulation statistics &ndash; bespoke tests<\/dt><dd><dl>\n<dt>10.2.1&nbsp;&nbsp;Do the maths (or try to)<\/dt>\n<dt>10.2.2&nbsp;&nbsp;Let the computer do the work<\/dt>\n<dt>10.2.3&nbsp;&nbsp;How many?<\/dt>\n<dt>10.2.4&nbsp;&nbsp;Estimating parameters<\/dt>\n<\/dl><\/dd>\n<dt>10.3&nbsp;&nbsp;Synthetic data<\/dt><dd><dl>\n<dt>10.3.1&nbsp;&nbsp;Known model<\/dt>\n<dt>10.3.2&nbsp;&nbsp;Unknown model<\/dt>\n<\/dl><\/dd>\n<\/dl><\/div>\n\n\n<h3> Glossary items referenced in this chapter <\/h3>\n<div class=\"toc\">\n<a href=\"https:\/\/alandix.com\/glossary\/hcistats\/anova\">ANOVA (Analysis of Variance)<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/artificial%20intelligence\">artificial intelligence<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/balanced%20experiment\">balanced experiment<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/bayes%20rule\">Bayes rule<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/bayesian%20statistics\">Bayesian statistics<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/bias\">bias<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/bimodal%20distribution\">bimodal distribution<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/binomial%20distribution\">Binomial distribution<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/bootstrapping\">bootstrapping<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/categorical%20data\">categorical data<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/chatbot\">chatbot<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/closed%20formula\">closed formula<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/coin%20tossing\">coin tossing<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/combinations\">combinations<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/computer%20simulation\">computer simulation<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/continuous%20data\">continuous data<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/correlation\">correlation<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/cross-attribute%20frequencies\">cross-attribute frequencies<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/debias%20data\">debias data<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/discrete%20data\">discrete data<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/distribution%21parameters\">distribution!parameters<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/domain%20expert\">domain expert<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/empirical%20data\">empirical data<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/empirical%20methods\">empirical methods<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/empirical%20statistics\">empirical statistics<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/estimate\">estimate<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/extreme%20statistics\">extreme statistics<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/extreme%20values\">extreme values<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/game%20engine\">game engine<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/gpu\">gpu<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/independence\">independence<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/independent%20samples\">independent samples<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/interquartile%20range\">interquartile range<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/iterative%20computational%20algorithms\">iterative computational algorithms<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/large%20language%20model\">large language model<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/likelihood\">likelihood<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/mann-whitney%20test\">Mann-Whitney test<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/mathematics\">mathematics<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/matrix%20algebra\">matrix algebra<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/maximum%20likelihood%20estimator\">maximum likelihood estimator<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/mean\">mean (&amp;mu;)<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/mechanism\">mechanism<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/median\">median<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/nonparametric%20statistics\">nonparametric statistics<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/normal%20distribution\">Normal distribution<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/observed%20frequencies\">observed frequencies<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/order%20statistics\">order statistics<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/p-value\">p-value<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/parametric%20statistics\">parametric statistics<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/patient%20journey\">patient journey<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/pearson%20correlation%20coefficient\">Pearson correlation coefficient<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/permutation%20statistics\">permutation statistics<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/permuted%20values\">permuted values<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/permuting%20values\">permuting values<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/perturbation%20methods\">perturbation methods<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/perturbing%20individual%20values\">perturbing individual values<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/poisson%20distribution\">Poisson distribution<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/posterior%20distribution\">posterior distribution<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/power-law%20distribution\">power-law distribution<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/prior%20distribution\">prior distribution<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/probability%20distribution\">probability distribution<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/random%20values\">random values<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/rare%20diseases\">rare diseases<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/sampling%20bias\">sampling bias<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/simulation%20methods\">simulation methods<\/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\/statistical%20power\">statistical power<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/stochastic\">stochastic<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/stochastic%20simulation\">stochastic simulation<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/student%27s%20t-test\">Student&#039;s t-test<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/subsampling\">subsampling<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/synthetic%20data\">synthetic data<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/theoretical%20distribution\">theoretical distribution<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/traditional%20statistics\">traditional statistics<\/a>, <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 $page['prolog_examples'];\n?>\n<!-- ?php\n\tendif; \/\/ @$page['prolog_examples']\n? -->\n\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":0,"parent":801,"menu_order":9,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_themeisle_gutenberg_block_has_review":false,"footnotes":""},"class_list":["post-810","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/pages\/810","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/comments?post=810"}],"version-history":[{"count":2,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/pages\/810\/revisions"}],"predecessor-version":[{"id":842,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/pages\/810\/revisions\/842"}],"up":[{"embeddable":true,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/pages\/801"}],"wp:attachment":[{"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/media?parent=810"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}