{"id":2028,"date":"2025-10-16T16:32:34","date_gmt":"2025-10-16T13:32:34","guid":{"rendered":"https:\/\/sites.uef.fi\/biopro\/?page_id=2028"},"modified":"2026-01-20T10:04:45","modified_gmt":"2026-01-20T08:04:45","slug":"background-statistics","status":"publish","type":"page","link":"https:\/\/sites.uef.fi\/biopro\/courses\/research-methodologies-in-forest-sciences\/course-structure\/background-statistics\/","title":{"rendered":"Background Concepts"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">Background Concepts<\/h1>\n\n\n\n<p>Blas MOLA-YUDEGO<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Introduction to Statistical Thinking<\/h2>\n\n\n\n<p><em>What is randomness? What is variability? How to deal with uncertainty?<\/em> This introduction of the course deals with the philosophical approach to statistical thinking. The main tools related to statistics will be discussed, including the concept of variability and metrics associated (standard deviation, variance, standard error) as well as the concept of distribution. The&nbsp;<em>normal distribution<\/em>&nbsp;will be presented, as its main properties and how to use it for statistical inference. The normal distribution is the basis of several tests and statistical tools, but of course there are main other distributions that are common and that must be understood. This topic will conclude with ideas related to population and sampling, and how to deal with statistical inference, preparing the ground for the next topic.<\/p>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<h2 class=\"wp-block-heading\" id=\"T1.Backgroundconcepts-Objectives\">Objectives<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>To get familiar with&nbsp;<em>thinking probabilistically<\/em><\/li>\n\n\n\n<li>To introduce statistics as a discipline<\/li>\n\n\n\n<li>To describe main concepts and tools related to variability and distributions<\/li>\n\n\n\n<li>Statistical inferences and standard errors<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Lecture notes<\/h2>\n\n\n\n<p><em>Discovering Statistics<\/em>. Blas Mola (2025) [<a href=\"https:\/\/www.researchgate.net\/profile\/Blas-Mola-Yudego\/publication\/396760610_Research_Methods_in_Forest_Sciences_Lecture_notes\/links\/68f895c402d6215259bdbf5d\/Research-Methods-in-Forest-Sciences-Lecture-notes.pdf?origin=publicationDetail&amp;_sg%5B0%5D=VmAtLWYKKCl1WPuQZZSel2c5YmazgbFIBKyGgzYjvlrRsVsvA4Jf-CX4kCz9ARbNkgNAn5uDE2awzILZIG1k9g.v0oOc3sBgL105jr_eqkbhEkSrxAuz3DuJ8wHpZ3lP_ErGaI0SofjuXuGJma1Nqnic6_omNENnfzsF6IknAVEqg&amp;_sg%5B1%5D=2rEE7MS3HkHaO7qDnYY5B0rkLHG7Y6UaeHaUvqUG31SagwUqVjVrFh3mFwNUOrnz-fCXSS1BpsETcTo3u-iinqJXQAPt3zL_TRMeK0ywxfkH.v0oOc3sBgL105jr_eqkbhEkSrxAuz3DuJ8wHpZ3lP_ErGaI0SofjuXuGJma1Nqnic6_omNENnfzsF6IknAVEqg&amp;_iepl=&amp;_rtd=eyJjb250ZW50SW50ZW50IjoibWFpbkl0ZW0ifQ%3D%3D&amp;_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6ImhvbWUiLCJwYWdlIjoicHVibGljYXRpb24iLCJwb3NpdGlvbiI6InBhZ2VIZWFkZXIifX0\" target=\"_blank\" rel=\"noreferrer noopener\">PDF<\/a>]. A journey of mind discipline. Statistics is not a catalogue of tricks but a habit of mind so that evidence, fairly weighed, can change what we believe. From Bayes\u2019 quiet prior beliefs and Laplace\u2019s celestial posteriors to Gauss\u2019s least-squares symmetry, our craft learned to turn uncertainty into guidance. Pearson mapped moments and correlation, Fisher forged likelihood, sufficiency, and design, Neyman and Pearson split risk with tests that target power. Today, amid the rush of machine learning and large language models, the charge remains the same: frame causal questions, validate with right samples, expose assumptions, and advance knowledge.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Materials<\/h2>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<h3 class=\"wp-block-heading\">Datasets and exercises<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Excel for practice [<a href=\"https:\/\/studentuef.sharepoint.com\/:f:\/r\/sites\/Biopro\/Shared%20Documents\/Research%20Methodologies%20in%20Forest%20Sciences\/Material?csf=1&amp;web=1&amp;e=d63AeJ\" target=\"_blank\" rel=\"noreferrer noopener\">excel<\/a>]<\/li>\n\n\n\n<li>Excel from the lectures [<a href=\"https:\/\/studentuef.sharepoint.com\/:f:\/r\/sites\/Biopro\/Shared%20Documents\/Research%20Methodologies%20in%20Forest%20Sciences\/Material?csf=1&amp;web=1&amp;e=d63AeJ\" target=\"_blank\" rel=\"noreferrer noopener\">excel<\/a>]&nbsp;<\/li>\n\n\n\n<li>Exercise on std errors [<a href=\"https:\/\/studentuef.sharepoint.com\/:f:\/r\/sites\/Biopro\/Shared%20Documents\/Research%20Methodologies%20in%20Forest%20Sciences\/Material?csf=1&amp;web=1&amp;e=d63AeJ\" target=\"_blank\" rel=\"noreferrer noopener\">PDF<\/a>]<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Videos and tutorials<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The normal distribution [<a href=\"https:\/\/www.youtube.com\/watch?v=mtbJbDwqWLE\">youtube<\/a>]<\/li>\n\n\n\n<li>How to produce a normal distribution in R? [<a href=\"https:\/\/studentuef.sharepoint.com\/:v:\/r\/sites\/Biopro\/Shared%20Documents\/Research%20Methodologies%20in%20Forest%20Sciences\/Material\/Videos\/Building%20a%20Normal%20Regression.mp4?csf=1&amp;web=1&amp;e=BnGgbj\">video<\/a>]<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Tasks<\/h2>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#fcfcfc\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p><em>What is a distribution of probability?<\/em><\/p>\n\n\n\n<p><em>What is the trade-offs between&nbsp;<u>certainty<\/u>&nbsp;and&nbsp;<u>precision<\/u>? And between&nbsp;<u>precision<\/u>&nbsp;and&nbsp;<u>cost\/affordability<\/u>? How are they all related?<\/em><\/p>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"T1.Backgroundconcepts-Tasks\">Exercise<\/h3>\n\n\n\n<p>We propose you to try the following tasks to practice the concepts explain in those lectures:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Create a large sequence of numbers following a normal distribution with define&nbsp;<strong>mean (\u00b5)<\/strong>&nbsp;and&nbsp;<strong>std deviation (\u03c3)<\/strong>&nbsp;using excel\/R: explore the histogram and properties. That will be your population.<\/li>\n\n\n\n<li>Select samples from the sequence (eg. N=10), and explore the parameters (mean and standard deviation). Do they match your expectations?<\/li>\n\n\n\n<li>Increase the sample (N=5, 10, 50, 100): when can you successfully infer some properties of the population.<\/li>\n\n\n\n<li>Produce 20 samples (N=5), get the mean from each of them and the standard error: how often get the&nbsp;<strong>mean&nbsp;(\u00b5)<\/strong>&nbsp;of the population within the confidence +\/- 2 x SE?<\/li>\n\n\n\n<li>Do the same but for the&nbsp;<strong>std deviation&nbsp;(\u03c3)&nbsp;<\/strong>.<\/li>\n<\/ol>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<h3 class=\"wp-block-heading\"><strong>How to do it?<\/strong><\/h3>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>In Excel:<br>Generate random numbers in excel: =RAND()&nbsp;<br>Generate numbers following a normal distribution with&nbsp;<em>mean=<\/em><strong>100<\/strong>&nbsp;and&nbsp;<em>st dev=10<\/em>:&nbsp;=NORMINV(RAND(),100,<em>10<\/em>)<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>In R:<br>Check\u00a0<a href=\"https:\/\/studentuef.sharepoint.com\/:v:\/r\/sites\/Biopro\/Shared%20Documents\/Research%20Methodologies%20in%20Forest%20Sciences\/Material\/Videos\/Building%20a%20Normal%20Regression.mp4?csf=1&amp;web=1&amp;e=BnGgbj\">here<\/a>.<\/p>\n\n\n\n<p>For more instructions,&nbsp;<strong>google&nbsp;<\/strong>(as I do)!<\/p>\n<\/div><\/div>\n<\/div><\/div>\n<\/div><\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Background Concepts Blas MOLA-YUDEGO Introduction to Statistical Thinking What is randomness? What is variability? How to deal with uncertainty? This introduction of the course deals with the philosophical approach to statistical thinking. The main tools related to statistics will be discussed, including the concept of variability and metrics associated (standard deviation, variance, standard error) as &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/sites.uef.fi\/biopro\/courses\/research-methodologies-in-forest-sciences\/course-structure\/background-statistics\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Background Concepts&#8221;<\/span><\/a><\/p>\n","protected":false},"author":836,"featured_media":0,"parent":2019,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-2028","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Background Concepts - Biomass Production<\/title>\n<meta name=\"description\" content=\"This introduction of the course deals with the philosophical approach to statistical thinking. 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