{"id":7117,"date":"2024-04-12T10:04:36","date_gmt":"2024-04-12T10:04:36","guid":{"rendered":"https:\/\/www.pickl.ai\/blog\/?p=7117"},"modified":"2024-06-26T10:41:41","modified_gmt":"2024-06-26T10:41:41","slug":"top-five-key-statistical-concepts-essential-for-data-science-understanding","status":"publish","type":"post","link":"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/","title":{"rendered":"Exploring The Top Key Statistical Concepts\u00a0"},"content":{"rendered":"<p><b>Summary: <\/b><span style=\"font-weight: 400;\">Statistical analysis is the key to unlocking the secrets hidden within your data. For any individual who wants to become a proficient Data Scientist, mastering the Data Science skills is imperative. Statistics for Data Science is the fundamental skill set that helps a Data Scientist complete their tasks with accuracy. <\/span><\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_81 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Statistics_for_Data_Science_Exploring_The_Top_Key_Statistical_Concepts\" >Statistics for Data Science: Exploring The Top Key Statistical Concepts<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Probability_and_Probability_Distributions\" >Probability and Probability Distributions<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Applications\" >Applications<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Descriptive_Statistics\" >Descriptive Statistics<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Applications-2\" >Applications<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Hypothesis_Testing\" >Hypothesis Testing<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Step_1_Define_the_Hypotheses\" >Step 1: Define the Hypotheses<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Step_2_Choose_Significance_Level_%CE%B1\" >Step 2: Choose Significance Level (\u03b1)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Step_3_Collect_Sample_Data\" >Step 3: Collect Sample Data<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Step_4_Calculate_Sample_Mean_x%CC%84\" >Step 4: Calculate Sample Mean (x\u0304)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Step_5_Perform_the_Statistical_Test\" >Step 5: Perform the Statistical Test<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Step_6_Make_a_Decision_Critical_Value\" >Step 6: Make a Decision (Critical Value)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Applications-3\" >Applications<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Correlation_and_Regression_Analysis\" >Correlation and Regression Analysis<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Applications-4\" >Applications<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Sampling_and_Sampling_Techniques\" >Sampling and Sampling Techniques<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Sampling_Technique_2\" >Sampling Technique 2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Applications-5\" >Applications<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Frequently_Asked_Questions\" >Frequently Asked Questions<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Whats_The_Difference_Between_Population_and_Sample_in_Data_Science\" >What&#8217;s The Difference Between Population and Sample in Data Science?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#What_Are_Descriptive_Statistics_Good_For\" >What Are Descriptive Statistics Good For?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Whats_The_Benefit_of_Using_Hypothesis_Testing_in_Data_Science\" >What&#8217;s The Benefit of Using Hypothesis Testing in Data Science?<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/www.pickl.ai\/blog\/top-five-key-statistical-concepts-essential-for-data-science-understanding\/#Concluding_Remarks\" >Concluding Remarks<\/a><\/li><\/ul><\/nav><\/div>\n<h2 id=\"statistics-for-data-science-exploring-the-top-key-statistical-concepts\"><span class=\"ez-toc-section\" id=\"Statistics_for_Data_Science_Exploring_The_Top_Key_Statistical_Concepts\"><\/span><b>Statistics for Data Science: Exploring The Top Key Statistical Concepts <\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Data Science thrives on the ability to extract meaningful insights from vast amounts of data. Statistics for Data Science forms the backbone of this process, providing a framework for analyzing, interpreting, and drawing conclusions from information.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This article explores five key statistical concepts that are fundamental for any aspiring Data Scientist. These are a must-know <\/span><a href=\"https:\/\/pickl.ai\/blog\/data-science-skills-mastering-the-essentials-for-success\/\"><span style=\"font-weight: 400;\">Data Science skills<\/span><\/a><span style=\"font-weight: 400;\"> that boosts your profile and enhances work efficiency.\u00a0<\/span><\/p>\n<h2 id=\"probability-and-probability-distributions\"><span class=\"ez-toc-section\" id=\"Probability_and_Probability_Distributions\"><\/span><b>Probability and Probability Distributions<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><a href=\"https:\/\/pickl.ai\/blog\/probability-distribution-in-data-science\/\"><span style=\"font-weight: 400;\">Probability<\/span><\/a><span style=\"font-weight: 400;\"> refers to the likelihood of an event occurring. It&#8217;s expressed as a number between 0 (impossible) and 1 (certain). Probability distributions describe the range of possible values for a variable and the likelihood of each value occurring.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Common distributions include the normal distribution (bell curve), used for continuous data like height, and the binomial distribution, used for events with two possible outcomes (e.g., success\/failure).<\/span><\/p>\n<p><b>Example<\/b><\/p>\n<p><span style=\"font-weight: 400;\">A Data Scientist analyzing online customer reviews might use a binomial distribution to understand the probability of a positive review.<\/span><\/p>\n<p><b>Scenario<\/b><\/p>\n<p><span style=\"font-weight: 400;\">A bakery monitors its daily cupcake sales to understand customer preferences and optimize production. They record sales data for chocolate cupcakes over a two-week period (14 days), resulting in the following figures:<\/span><\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter wp-image-8793 size-full\" src=\"https:\/\/pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/1.png\" alt=\"\" width=\"600\" height=\"551\" srcset=\"https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/1.png 600w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/1-300x276.png 300w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/1-110x101.png 110w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/1-200x184.png 200w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/1-380x349.png 380w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/1-255x234.png 255w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/1-550x505.png 550w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/1-150x138.png 150w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/p>\n<p><b>Data Analysis: Probability and Probability Distribution<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Calculate Probability of Selling a Specific Number of Cupcakes:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For instance, let&#8217;s calculate the probability of selling exactly 20 chocolate cupcakes on a given day.<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">We know the total number of observations (days) is 14.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Favorable outcome (selling 20 cupcakes) occurred twice (on Day 1 and Day 13).<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Therefore, the probability of selling 20 cupcakes:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Probability (selling 20) = Favorable outcomes \/ Total outcomes = 2 \/ 14 \u2248 0.143<\/span><\/p>\n<p><b>Analyze Probability Distribution<\/b><\/p>\n<p><span style=\"font-weight: 400;\">We can analyze the probability distribution of daily cupcake sales by calculating the frequency of each number sold. Here&#8217;s a table summarizing the results:<\/span><\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-8794 size-full\" src=\"https:\/\/pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/stat-2.png\" alt=\"\" width=\"764\" height=\"537\" srcset=\"https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/stat-2.png 764w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/stat-2-300x211.png 300w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/stat-2-110x77.png 110w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/stat-2-200x141.png 200w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/stat-2-380x267.png 380w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/stat-2-255x179.png 255w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/stat-2-550x387.png 550w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/stat-2-150x105.png 150w\" sizes=\"(max-width: 764px) 100vw, 764px\" \/><\/p>\n<p><b>Visualization with Histogram<\/b><\/p>\n<p><span style=\"font-weight: 400;\">By plotting a histogram, we can visualize the probability distribution of the data. The histogram shows the frequency of each number of cupcakes sold on the x-axis and the frequency count on the y-axis.<\/span><\/p>\n<p><span style=\"font-family: arial, helvetica, sans-serif; font-size: revert;\"><img decoding=\"async\" class=\"aligncenter wp-image-8795 size-full\" src=\"https:\/\/pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image1-8.png\" alt=\"\" width=\"451\" height=\"339\" srcset=\"https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image1-8.png 451w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image1-8-300x225.png 300w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image1-8-110x83.png 110w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image1-8-200x150.png 200w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image1-8-380x286.png 380w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image1-8-255x192.png 255w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image1-8-150x113.png 150w\" sizes=\"(max-width: 451px) 100vw, 451px\" \/><\/span><\/p>\n<h3 id=\"applications\"><span class=\"ez-toc-section\" id=\"Applications\"><\/span><b>Applications<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Probability and probability distributions are crucial for tasks like predicting future outcomes, assessing risk, and designing A\/B tests to compare website variations.<\/span><\/p>\n<h2 id=\"descriptive-statistics\"><span class=\"ez-toc-section\" id=\"Descriptive_Statistics\"><\/span><b>Descriptive Statistics<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Descriptive statistics summarize the key characteristics of a dataset. This includes measures of central tendency (mean, median, mode) that indicate the &#8220;average&#8221; value, and measures of variability (range, standard deviation) that describe how spread out the data is.<\/span><\/p>\n<p><b>Example<\/b><\/p>\n<p><span style=\"font-weight: 400;\">A Data Scientist studying house prices in a city might calculate the mean, median, and standard deviation of the prices to understand the typical price range and the level of variation within that range.<\/span><\/p>\n<p><b>Scenario<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Imagine a company tracks the test scores of 10 new software developer applicants. Here&#8217;s the data:<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-8796 size-full\" src=\"https:\/\/pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/sats-3.png\" alt=\"\" width=\"600\" height=\"450\" srcset=\"https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/sats-3.png 600w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/sats-3-300x225.png 300w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/sats-3-110x83.png 110w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/sats-3-200x150.png 200w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/sats-3-380x285.png 380w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/sats-3-255x191.png 255w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/sats-3-550x413.png 550w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/sats-3-150x113.png 150w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">We can use various measures to summarize this data set:<\/span><\/p>\n<p><b>Measures of Central Tendency<\/b><\/p>\n<p><b>Mean:<\/b><span style=\"font-weight: 400;\"> This represents the average score. Add all scores and divide by the number of applicants (n = 10).<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Mean = (85 + 92 + 78 + 88 + 90 + 82 + 75 + 95 + 80 + 87) \/ 10 = 85.2<\/span><\/p>\n<p><b>Median:<\/b><span style=\"font-weight: 400;\"> This is the &#8220;middle&#8221; score when arranged in ascending order.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">75, 78, 80, 82, 85, 87, 88, 90, 92, 95<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Median = (85 + 87) \/ 2 = 86<\/span><\/p>\n<p><b>Mode:<\/b><span style=\"font-weight: 400;\"> This is the most frequent score. In this case, there isn&#8217;t a single most frequent score.<\/span><\/p>\n<p><b>Measures of Variability<\/b><\/p>\n<p><b>Range:<\/b><span style=\"font-weight: 400;\"> This represents the difference between the highest and lowest scores.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Range = 95 &#8211; 75 = 20<\/span><\/p>\n<p><b>Standard Deviation:<\/b><span style=\"font-weight: 400;\"> This measures how spread out the data is from the mean. Calculating the standard deviation involves more complex steps, but online tools can help.<\/span><\/p>\n<p><b>Interpretation<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Looking at the measures of central tendency, the mean and median suggest most scores fall around the mid-80s range. There isn&#8217;t a single most frequent score (mode). The range of 20 indicates some variation in scores, but the standard deviation would provide a more precise measure of this spread.<\/span><\/p>\n<h3 id=\"applications-2\"><span class=\"ez-toc-section\" id=\"Applications-2\"><\/span><b>Applications<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Descriptive statistics provide a quick overview of the data, allowing Data Scientists to identify trends, outliers, and potential areas for further investigation.<\/span><\/p>\n<h2 id=\"hypothesis-testing\"><span class=\"ez-toc-section\" id=\"Hypothesis_Testing\"><\/span><b>Hypothesis Testing<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Hypothesis testing is a statistical method to assess the validity of a claim (hypothesis) about a population based on a sample of data. It involves formulating a null hypothesis (no difference exists) and an alternative hypothesis (a difference exists), and then conducting a statistical test to determine if the evidence supports rejecting the null<\/span><a href=\"https:\/\/pickl.ai\/blog\/hypothesis-testing-in-statistics\/\"><span style=\"font-weight: 400;\"> hypothesis<\/span><\/a><span style=\"font-weight: 400;\">.<\/span><\/p>\n<p><b>Example<\/b><\/p>\n<p><span style=\"font-weight: 400;\">A marketing team believes a new social media campaign will increase website traffic. They run a hypothesis test to determine if the observed increase in traffic after launching the campaign is statistically significant, meaning it&#8217;s unlikely to be due to chance.<\/span><\/p>\n<p><b>Plant Growth and Fertilizer: A Hypothesis Test<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Let&#8217;s say a botanist wants to investigate if a new fertilizer increases plant growth. Here&#8217;s a numerical example of hypothesis testing:<\/span><\/p>\n<p><b>Scenario<\/b><\/p>\n<p><span style=\"font-weight: 400;\">We measure the heights (in centimeters) of 10 randomly chosen tomato plants (sample size, n=10) that haven&#8217;t received the new fertilizer. We want to see if there&#8217;s evidence to suggest the average plant height (population mean, \u03bc) is greater than 20cm after using the fertilizer.<\/span><\/p>\n<h3 id=\"step-1-define-the-hypotheses\"><span class=\"ez-toc-section\" id=\"Step_1_Define_the_Hypotheses\"><\/span><b>Step 1: Define the Hypotheses<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Null Hypothesis (H\u2080):<\/b><span style=\"font-weight: 400;\"> \u03bc \u2264 20cm. There&#8217;s no significant difference in plant height with or without fertilizer (average height is 20cm or less).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Alternative Hypothesis (H\u2081):<\/b><span style=\"font-weight: 400;\"> \u03bc &gt; 20cm. The new fertilizer increases plant height (average height is greater than 20cm).<\/span><\/li>\n<\/ul>\n<h3 id=\"step-2-choose-significance-level-%ce%b1\"><span class=\"ez-toc-section\" id=\"Step_2_Choose_Significance_Level_%CE%B1\"><\/span><b>Step 2: Choose Significance Level (\u03b1)<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Let&#8217;s set the significance level (\u03b1) at 5%. This means we&#8217;re willing to risk a 5% chance of rejecting the null hypothesis when it&#8217;s actually true (a type I error).<\/span><\/p>\n<h3 id=\"step-3-collect-sample-data\"><span class=\"ez-toc-section\" id=\"Step_3_Collect_Sample_Data\"><\/span><b>Step 3: Collect Sample Data<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Suppose we measure the heights of 10 tomato plants that received the new fertilizer and get the following data (in centimeters):<\/span><\/p>\n<p><span style=\"font-weight: 400;\">23, 25, 21, 27, 22, 24, 28, 20, 26, 29<\/span><\/p>\n<h3 id=\"step-4-calculate-sample-mean-x\"><span class=\"ez-toc-section\" id=\"Step_4_Calculate_Sample_Mean_x%CC%84\"><\/span><b>Step 4: Calculate Sample Mean (x\u0304)<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Average the heights: x\u0304 = (23 + 25 + 21 + &#8230; + 29) \/ 10 = 24.8 cm<\/span><\/p>\n<h3 id=\"step-5-perform-the-statistical-test\"><span class=\"ez-toc-section\" id=\"Step_5_Perform_the_Statistical_Test\"><\/span><b>Step 5: Perform the Statistical Test<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Since our sample size (n) is less than 30 and the population standard deviation (\u03c3) is unknown, we&#8217;ll use a t-test.<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Calculate the t-statistic (assuming equal variances):<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">t = (x\u0304 &#8211; \u03bc\u2080) \/ (s \/ \u221an)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Here:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">x\u0304 = sample mean (24.8 cm)<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u03bc\u2080 = value from the null hypothesis (20 cm)<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">s = sample standard deviation (we&#8217;ll need to calculate this from the sample data)<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u221an = square root of sample size (\u221a10)<\/span><\/li>\n<\/ul>\n<h3 id=\"step-6-make-a-decision-critical-value\"><span class=\"ez-toc-section\" id=\"Step_6_Make_a_Decision_Critical_Value\"><\/span><b>Step 6: Make a Decision (Critical Value)<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Look up the critical t-value for a two-tailed test with \u03b1 = 0.05 and degrees of freedom (df) = n-1 = 9. (You can find t-value tables online).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>If the calculated t-statistic (t) is greater than the critical t-value, reject H\u2080.<\/b><span style=\"font-weight: 400;\"> This suggests evidence for the alternative hypothesis (increased plant height).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>If the calculated t-statistic (t) is less than the critical t-value, fail to reject H\u2080.<\/b><span style=\"font-weight: 400;\"> There isn&#8217;t enough evidence to conclude the fertilizer definitively affects plant height.<\/span><\/li>\n<\/ul>\n<h3 id=\"applications-3\"><span class=\"ez-toc-section\" id=\"Applications-3\"><\/span><b>Applications<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Hypothesis testing is essential for making informed decisions based on data. It helps Data Scientists differentiate between random fluctuations and genuine effects.<\/span><\/p>\n<h2 id=\"correlation-and-regression-analysis\"><span class=\"ez-toc-section\" id=\"Correlation_and_Regression_Analysis\"><\/span><b>Correlation and Regression Analysis<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-8797 size-full\" src=\"https:\/\/pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image4-3.png\" alt=\"\" width=\"1000\" height=\"333\" srcset=\"https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image4-3.png 1000w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image4-3-300x100.png 300w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image4-3-768x256.png 768w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image4-3-110x37.png 110w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image4-3-200x67.png 200w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image4-3-380x127.png 380w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image4-3-255x85.png 255w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image4-3-550x183.png 550w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image4-3-800x266.png 800w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/image4-3-150x50.png 150w\" sizes=\"(max-width: 1000px) 100vw, 1000px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Correlation measures the strength and direction of the linear relationship between two variables. A positive correlation indicates values of one variable tend to increase with the other, while a negative correlation indicates they tend to move in opposite directions. Regression analysis builds on correlation, but it aims to predict the value of one variable (dependent variable) based on another variable (independent variable).<\/span><\/p>\n<p><b>Example<\/b><\/p>\n<p><span style=\"font-weight: 400;\">A Data Scientist analyzing retail sales data might find a positive correlation between online advertising spending and customer traffic in stores. Regression analysis could then be used to predict store traffic based on planned advertising expenditure.<\/span><\/p>\n<p><b>Numerical Example: Studying Hours and Exam Scores<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Let&#8217;s say we&#8217;re investigating the relationship between the number of hours spent studying (independent variable, x) and exam scores (dependent variable, y) for a small group of students.<\/span><\/p>\n<p><b>Here&#8217;s a table with some example data:<\/b><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-8798 size-full\" src=\"https:\/\/pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/stats-4.png\" alt=\"\" width=\"440\" height=\"222\" srcset=\"https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/stats-4.png 440w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/stats-4-300x151.png 300w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/stats-4-110x56.png 110w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/stats-4-200x101.png 200w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/stats-4-380x192.png 380w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/stats-4-255x129.png 255w, https:\/\/www.pickl.ai\/blog\/wp-content\/uploads\/2024\/04\/stats-4-150x76.png 150w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">We can calculate the correlation coefficient (r) to measure the strength and direction of the linear relationship between studying hours and exam scores. There are different correlation coefficients, but a common one for continuous data is Pearson&#8217;s correlation coefficient.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Using a calculator or statistical software, we find r = 0.87 for this data set.<\/span><\/p>\n<p><b>Interpretation<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Positive correlation (r = 0.87): There&#8217;s a positive association between studying hours and exam scores. As students study more, their scores tend to go up.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Strength of correlation (r close to 1): The value of 0.87 is relatively high, indicating a strong positive correlation.<\/span><\/li>\n<\/ul>\n<p><b>Regression Analysis<\/b><\/p>\n<p><a href=\"https:\/\/pickl.ai\/blog\/regression-in-machine-learning-types-examples\/\"><span style=\"font-weight: 400;\">Regression analysis<\/span><\/a><span style=\"font-weight: 400;\"> helps us find an equation to represent the relationship between the variables. In this case, we&#8217;re looking for a linear equation to predict exam scores (y) based on studying hours (x).<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Using linear regression, we get an equation like this (example formula, actual coefficients may vary):<\/span><\/p>\n<p><span style=\"font-weight: 400;\">y = 5 + 8.5x<\/span><\/p>\n<p><b>Interpretation<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The y-intercept (5) represents the predicted exam score when students study for 0 hours (which wouldn&#8217;t be realistic, but it helps with the equation).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The slope (8.5) indicates that for every additional hour studied, the predicted exam score increases by 8.5 points on average.<\/span><\/li>\n<\/ul>\n<h3 id=\"applications-4\"><span class=\"ez-toc-section\" id=\"Applications-4\"><\/span><b>Applications<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Correlation and regression analysis are invaluable tools for understanding relationships between variables and making predictions. They can be used to identify trends, develop marketing strategies, and optimize business operations.<\/span><\/p>\n<h2 id=\"sampling-and-sampling-techniques\"><span class=\"ez-toc-section\" id=\"Sampling_and_Sampling_Techniques\"><\/span><b>Sampling and Sampling Techniques<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Rarely can Data Scientists analyze an entire population (all possible data points). Instead, they rely on samples &#8211; a subset of the population that is used to make inferences about the whole. Choosing the right sampling technique is crucial for ensuring the sample accurately represents the population.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Common techniques include random sampling (each member has an equal chance of being selected), stratified sampling (ensures subgroups within the population are adequately represented), and cluster sampling (groups of individuals are chosen instead of individual observations).<\/span><\/p>\n<p><b>Example<\/b><\/p>\n<p><span style=\"font-weight: 400;\">A Data Scientist studying customer satisfaction wants to survey a representative sample of the company&#8217;s customer base. They might choose a stratified sampling technique to ensure the survey includes a proportional number of customers from different age groups and geographical locations.<\/span><\/p>\n<p><b>Numerical Example: Sampling Techniques in a Bakery<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Let&#8217;s say a bakery owner wants to understand customer preferences for their cupcakes. They have a record of 100 customers who bought cupcakes in the last week.<\/span><\/p>\n<p><b>Population:<\/b><span style=\"font-weight: 400;\"> All 100 customers of the bakery in the last week.<\/span><\/p>\n<p><b>Sample Size:<\/b><span style=\"font-weight: 400;\"> We want to survey 20 customers.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Sampling Technique 1: Simple Random Sampling<\/span><\/p>\n<p><b>Assign Numbers:<\/b><span style=\"font-weight: 400;\"> Assign a unique number (1-100) to each customer on the record.<\/span><\/p>\n<p><b>Random Selection:<\/b><span style=\"font-weight: 400;\"> Use a random number generator to pick 20 unique numbers between 1 and 100.<\/span><\/p>\n<p><b>Survey:<\/b><span style=\"font-weight: 400;\"> Survey the customers corresponding to the chosen numbers.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This ensures each customer has an equal chance of being selected, providing an unbiased sample.<\/span><\/p>\n<h3 id=\"sampling-technique-2\"><span class=\"ez-toc-section\" id=\"Sampling_Technique_2\"><\/span><b>Sampling Technique 2<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><b>Stratification:<\/b><span style=\"font-weight: 400;\"> Knowing cupcake preferences might differ by age, the bakery owner divides the customers into two age groups (20-35 &amp; 36-55) with 60 and 40 customers respectively.<\/span><\/p>\n<p><b>Proportional Selection:<\/b><span style=\"font-weight: 400;\"> Since the age groups are not equal, proportional sampling is used. We need to select 12 customers from the younger group (60% of 20) and 8 customers from the older group (40% of 20).<\/span><\/p>\n<p><b>Random Selection Within Groups:<\/b><span style=\"font-weight: 400;\"> Use random number generation to pick 12 customers from the younger group and 8 from the older group.<\/span><\/p>\n<p><b>Survey:<\/b><span style=\"font-weight: 400;\"> Survey the selected customers from each age group.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This ensures the sample reflects the age distribution of the customer base, providing a more targeted view of preferences.<\/span><\/p>\n<h3 id=\"applications-5\"><span class=\"ez-toc-section\" id=\"Applications-5\"><\/span><b>Applications<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Understanding sampling and sampling techniques is vital for drawing valid conclusions from data. It helps to avoid bias and ensures that findings can be reliably generalized to the broader population.<\/span><\/p>\n<h2 id=\"frequently-asked-questions\"><span class=\"ez-toc-section\" id=\"Frequently_Asked_Questions\"><\/span><b>Frequently Asked Questions<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 id=\"whats-the-difference-between-population-and-sample-in-data-science\"><span class=\"ez-toc-section\" id=\"Whats_The_Difference_Between_Population_and_Sample_in_Data_Science\"><\/span><b>What&#8217;s The Difference Between Population and Sample in Data Science?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Data Scientists often analyze samples because studying the entire population can be impractical or expensive.\u00a0 Understanding the difference helps ensure your conclusions about the population are accurate.<\/span><\/p>\n<p><b>Population:<\/b><span style=\"font-weight: 400;\"> The entire collection of individuals or items you&#8217;re interested in studying. Imagine it as all the cookies in a bakery.<\/span><\/p>\n<p><b>Sample: <\/b><span style=\"font-weight: 400;\">A smaller group chosen to represent the entire population. It&#8217;s like grabbing a handful of cookies from the bakery to understand the overall flavor profile.<\/span><\/p>\n<h3 id=\"what-are-descriptive-statistics-good-for\"><span class=\"ez-toc-section\" id=\"What_Are_Descriptive_Statistics_Good_For\"><\/span><b>What Are Descriptive Statistics Good For?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Descriptive statistics\u00a0 summarize the key characteristics of your data. They&#8217;re like giving a brief description of your handful of cookies. For example, you might\u00a0 calculate the average size (mean), how many chocolate chip cookies there are (frequency), or the spread of sizes (standard deviation).<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Descriptive statistics help you understand the basic properties of your data and identify potential patterns or trends.\u00a0\u00a0<\/span><\/p>\n<h3 id=\"whats-the-benefit-of-using-hypothesis-testing-in-data-science\"><span class=\"ez-toc-section\" id=\"Whats_The_Benefit_of_Using_Hypothesis_Testing_in_Data_Science\"><\/span><b>What&#8217;s The Benefit of Using Hypothesis Testing in Data Science?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Hypothesis testing allows you to make informed guesses about the population based on your sample. Like wondering if the bakery uses a standard cookie cutter based on the similar sizes in your handful.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">You set up a hypothesis (e.g., &#8220;all cookies are the same size&#8221;) and then use statistical tests to see if the sample data supports it\u00a0 (strong evidence) or suggests otherwise (weak evidence). This helps Data Scientists draw reliable conclusions that go beyond just describing the sample itself.\u00a0<\/span><\/p>\n<h2 id=\"concluding-remarks\"><span class=\"ez-toc-section\" id=\"Concluding_Remarks\"><\/span><b>Concluding Remarks<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">These five key statistical concepts are just the foundation. Data Science is a rapidly evolving field with numerous advanced statistical methods.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">However, a strong understanding of these core concepts will equip you to analyze data effectively, identify patterns, and extract valuable insights that can drive informed decision-making.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">To start your learning journey in Data Science, you can enroll for the Data Science course that will equip you with the right Data Science skills and tools. Pickl.AI offers a perfect learning platform for all tech neophytes as well as professionals. To learn more about the Data Science course, log on to <\/span><a href=\"http:\/\/pickl.ai\"><span style=\"font-weight: 400;\">pickl.ai<\/span><\/a><span style=\"font-weight: 400;\"> today.\u00a0<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"Master Data Science with these statistical concepts: probability, distributions, hypothesis testing.\n","protected":false},"author":14,"featured_media":8808,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[46],"tags":[2212,2121,2211],"ppma_author":[2180,2179],"class_list":{"0":"post-7117","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-data-science","8":"tag-data-science-courses","9":"tag-data-science-skills","10":"tag-statistical"},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v20.3 (Yoast SEO v27.0) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Statistics for Data Science: Top Key Statistical Concepts<\/title>\n<meta name=\"description\" content=\"Statistics for Data Science is pivotal. 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