{"id":4385,"date":"2026-05-25T10:30:18","date_gmt":"2026-05-25T08:30:18","guid":{"rendered":"https:\/\/ellistat.com\/?p=4385"},"modified":"2026-05-27T10:32:05","modified_gmt":"2026-05-27T08:32:05","slug":"compare-distributions-cramer-von-mises-test-and-energie-test","status":"publish","type":"post","link":"https:\/\/ellistat.com\/en\/comparer-des-distributions-test-de-cramer-von-mises-et-test-energie\/","title":{"rendered":"Comparing distributions: Cram\u00e9r-von Mises test and Energy test"},"content":{"rendered":"

Comparing distributions rather than means: a key advance for quality control with the Cram\u00e9e-von Mises and Energy tests<\/h2>\n\n\n\n

Two lots of parts. Same mean. Same apparent standard deviation. <\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

Means and variances here are virtually identical, yet intuitively, you can feel the difference between these two machines.<\/p>\n\n\n\n

However, conventional hypothesis testing shows no difference between the two distributions.<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

But mean and variance only tell part of the story of a machining process. To detect real differences between measurement groups, between two suppliers, two machines, two shifts, two production periods...you need to compare complete distributions. This is precisely what two statistical tests integrated into Ellistat Data Analysis<\/a> test: the Cram\u00e9r-von Mises<\/a> and the Energy test.<\/p>\n\n\n\n

The Cram\u00e9r-von Mises test<\/h2>\n\n\n\n

This test compares :<\/p>\n\n\n\n

    \n
  • either a sample with a theoretical distribution<\/li>\n\n\n\n
  • or two samples between them<\/li>\n<\/ul>\n\n\n\n

    The principle:<\/strong> the test compares the cumulative distribution functions (ogives) of the two distributions.<\/p>\n\n\n\n

    In other words, it measures \u00abhow far apart the cumulative curves are\u00bb?<\/p>\n\n\n\n

    If the two distributions are close, the warheads overlap. If they differ, the cumulative deviation increases.<\/p>\n\n\n

    \n
    \"\"<\/figure>\n<\/div>\n\n\n

    The energy test<\/h2>\n\n\n\n

    This test generalizes this approach to several groups. It is particularly suitable when :<\/p>\n\n\n\n

      \n
    • more than two populations are compared<\/li>\n\n\n\n
    • distributions are unknown<\/li>\n\n\n\n
    • data are multidimensional<\/li>\n<\/ul>\n\n\n\n

      The principle <\/strong>The test is based on an intuitive idea: comparing distances between points.<\/p>\n\n\n\n

      It measures :<\/p>\n\n\n\n

        \n
      • average distances within groups<\/li>\n\n\n\n
      • then distances between groups <\/li>\n<\/ul>\n\n\n\n

        If the groups come from the same distribution, the intra- and inter-group distances are similar. Otherwise, distances between groups become greater.<\/p>\n\n\n\n

        What this means in practice<\/h2>\n\n\n\n

        Compare two suppliers on a critical diameter. Validate a change of machine setting. Analyze a before\/after on an unstable process. Differentiate between two machining centers that produce the same parts...in appearance.<\/p>\n\n\n\n

        In all these cases, looking only at the mean and variance can be misleading.<\/p>\n\n\n\n

        Comparing complete distributions gives a true picture of what's really going on.<\/p>\n\n\n\n

        In Ellistat's Data Analysis module, these tests are coupled with visualizations: ogives, KDE, superimposed histograms, because a p-value without a visual context doesn't convince anyone on the shop floor.<\/p>\n\n\n\n

        \"\"<\/figure>\n\n\n\n

        The aim is not to produce a statistical result, but to understand why two processes behave differently and to take action.<\/p>","protected":false},"excerpt":{"rendered":"

        Comparer les distributions plut\u00f4t que les moyennes : une avanc\u00e9e cl\u00e9 pour le contr\u00f4le qualit\u00e9 gr\u00e2ce aux test de Cram\u00e9e-von Mises et test Energie Deux lots de pi\u00e8ces. M\u00eame moyenne. M\u00eame \u00e9cart-type apparent. Les moyennes et les variances sont ici sensiblement identiques, et pourtant, intuitivement, on peut sentir une diff\u00e9rence entre ces deux machines. Les […]<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[7],"tags":[],"class_list":["post-4385","post","type-post","status-publish","format-standard","hentry","category-data-analysis"],"acf":[],"yoast_head":"\nComparer des distributions : Test de Cram\u00e9r\u2013von Mises et test Energie - Ellistat<\/title>\n<meta name=\"description\" content=\"Moyenne identique, qualit\u00e9 diff\u00e9rente : d\u00e9couvrez pourquoi comparer les distributions compl\u00e8tes est plus fiable que la moyenne ou la variance.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ellistat.com\/en\/compare-distributions-cramer-von-mises-test-and-energie-test\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Comparer des distributions : Test de Cram\u00e9r\u2013von Mises et test Energie - Ellistat\" \/>\n<meta property=\"og:description\" content=\"Moyenne identique, qualit\u00e9 diff\u00e9rente : d\u00e9couvrez pourquoi comparer les distributions compl\u00e8tes est plus fiable que la moyenne ou la variance.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/ellistat.com\/en\/compare-distributions-cramer-von-mises-test-and-energie-test\/\" \/>\n<meta property=\"og:site_name\" content=\"Ellistat\" \/>\n<meta property=\"article:published_time\" content=\"2026-05-25T08:30:18+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-05-27T08:32:05+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/ellistat.com\/wp-content\/uploads\/t1xOgQeJwdjWtepZ.png\" \/>\n\t<meta property=\"og:image:width\" content=\"547\" \/>\n\t<meta property=\"og:image:height\" content=\"568\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Camille Forest\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Camille Forest\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/ellistat.com\\\/comparer-des-distributions-test-de-cramer-von-mises-et-test-energie\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/ellistat.com\\\/comparer-des-distributions-test-de-cramer-von-mises-et-test-energie\\\/\"},\"author\":{\"name\":\"Camille Forest\",\"@id\":\"https:\\\/\\\/ellistat.com\\\/#\\\/schema\\\/person\\\/b757d2fa4e8a73814cb00474e7653681\"},\"headline\":\"Comparer des distributions : Test de Cram\u00e9r\u2013von Mises et test Energie\",\"datePublished\":\"2026-05-25T08:30:18+00:00\",\"dateModified\":\"2026-05-27T08:32:05+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/ellistat.com\\\/comparer-des-distributions-test-de-cramer-von-mises-et-test-energie\\\/\"},\"wordCount\":471,\"image\":{\"@id\":\"https:\\\/\\\/ellistat.com\\\/comparer-des-distributions-test-de-cramer-von-mises-et-test-energie\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/ellistat.com\\\/wp-content\\\/uploads\\\/t1xOgQeJwdjWtepZ.png\",\"articleSection\":[\"Data Analysis\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/ellistat.com\\\/comparer-des-distributions-test-de-cramer-von-mises-et-test-energie\\\/\",\"url\":\"https:\\\/\\\/ellistat.com\\\/comparer-des-distributions-test-de-cramer-von-mises-et-test-energie\\\/\",\"name\":\"Comparer des distributions : Test de Cram\u00e9r\u2013von Mises et test Energie - 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