{"id":6068,"date":"2016-03-06T20:38:30","date_gmt":"2016-03-06T15:08:30","guid":{"rendered":"http:\/\/ucanalytics.com\/blogs\/?p=6068"},"modified":"2016-09-11T10:59:27","modified_gmt":"2016-09-11T05:29:27","slug":"right-sample-size-analysis","status":"publish","type":"post","link":"https:\/\/ucanalytics.com\/blogs\/right-sample-size-analysis\/","title":{"rendered":"What is the Right Sample Size for Your Analysis?"},"content":{"rendered":"<div id=\"attachment_6012\" style=\"width: 307px\" class=\"wp-caption alignright\"><a href=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/09\/Presentation1.jpg\" rel=\"attachment wp-att-6012\"><img aria-describedby=\"caption-attachment-6012\" data-attachment-id=\"6012\" data-permalink=\"https:\/\/ucanalytics.com\/blogs\/?attachment_id=6012\" data-orig-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/09\/Presentation1.jpg?fit=475%2C714&amp;ssl=1\" data-orig-size=\"475,714\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Presentation1\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Sample Size &#038; Simulation &#8211; by Roopam&lt;\/p&gt;\n\" data-medium-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/09\/Presentation1.jpg?fit=200%2C300&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/09\/Presentation1.jpg?fit=475%2C714&amp;ssl=1\" decoding=\"async\" loading=\"lazy\" class=\" wp-image-6012\" src=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/09\/Presentation1.jpg?resize=297%2C447\" alt=\"Sample Size &amp; Simulation - by Roopam\" width=\"297\" height=\"447\" srcset=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/09\/Presentation1.jpg?w=475&amp;ssl=1 475w, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/09\/Presentation1.jpg?resize=166%2C250&amp;ssl=1 166w, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/09\/Presentation1.jpg?resize=200%2C300&amp;ssl=1 200w\" sizes=\"(max-width: 297px) 100vw, 297px\" data-recalc-dims=\"1\" \/><\/a><p id=\"caption-attachment-6012\" class=\"wp-caption-text\">Sample Size &amp; Simulation &#8211; by Roopam<\/p><\/div>\n<hr \/>\n<p>A few years ago, I did a day-long workshop on <em>Statistical Thinking<\/em>\u00a0for a large German shipping &amp; cargo company in Mumbai. During the Q&amp;A session, the Vice President of operations asked a tricky question: what is a good sample size to achieve precision and accuracy for your analysis?\u00a0He was looking for a one-size-fits-all answer and I wish it were that simple.<\/p>\n<p>On the surface, this might seem to be an extremely fundamental and basic question but in practice, so many professionals struggle to answer this. In this article, I\u00a0will try to answer this question.<\/p>\n<h2><span style=\"color: #0000ff;\">Sample Size<\/span><\/h2>\n<p>Like ingredients are at the core of taste of the food, sample size and data quality are at the core of the analysis. With bad ingredients, even a master chef can&#8217;t produce a good dish. Hence, representative sample\u00a0and sample size are the two most important aspects on which every data scientist needs to keep a\u00a0cautious eye.<\/p>\n<p>One of the most intuitive ways to identify the right sample size is through data simulation. In this article, we will simulate coin tosses to understand the significance of sample size. As you know tossing a coin is one of the easiest and fastest experiments with random binary outcomes.<\/p>\n<p>Before you brush off coin tosses as too elementary and textbook-ish please check out the\u00a0following practical events with random binary outcomes similar to coin tosses.<\/p>\n<ul style=\"list-style-type: square;\">\n<li>Creating triggers for fraudulent credit card transactions<\/li>\n<li>Identifying customers for cross\/up sell opportunities<\/li>\n<li>Detecting malignant cancer cells<\/li>\n<li>Measuring credit risk of a borrower<\/li>\n<li>Autoflagging spam emails<\/li>\n<li>Predicting employees&#8217; likelihood for attrition<\/li>\n<\/ul>\n<h2><span style=\"color: #0000ff;\">Data Simulation and Sample Size<\/span><\/h2>\n<p>In this section, we will toss\u00a0a fair coin many times to estimate the probability of heads. This coin is fair because it\u00a0has the equal probability of both heads and tails i.e. 0.5. We will use different sample sizes to observe at what point we get a precise value for the probability of heads.\u00a0We could either toss the coin ourselves or make our computer run a simulation of coin tosses. I will choose the latter. Let&#8217;s say we tossed the coin 5 times and got the following results<\/p>\n<p style=\"text-align: center;\"><strong>Heads, Tails, Heads, Heads, Tails<\/strong><\/p>\n<p>With just the first result (Heads), i.e. sample size = 1, we get the sample probability of heads equal to 1. With the sample size of 2 (Heads, Tails) the sample probability of heads is 1\/2 or 0.5. With the sample size of 5, we will get the sample probability of heads = 3\/5.<\/p>\n<p>Now to extend the above experiment, I will perform 10 experiments with 500 tosses each and estimate probability at each step. I will simulate these experiments for the obvious reason that I don&#8217;t want to toss a coin 5000 times (i.e. 10 \u00d7 500 times). The following are the results of\u00a0these simulations (<a href=\"http:\/\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Coin-Tosses-Sample-Size.txt\">R code for these simulations<\/a>).<\/p>\n<p><a href=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-Coin-Toss-Simulation.gif\" rel=\"attachment wp-att-7867\"><img data-attachment-id=\"7867\" data-permalink=\"https:\/\/ucanalytics.com\/blogs\/right-sample-size-analysis\/sample-size-coin-toss-simulation\/\" data-orig-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-Coin-Toss-Simulation.gif?fit=480%2C480&amp;ssl=1\" data-orig-size=\"480,480\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Sample Size Coin Toss Simulation\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-Coin-Toss-Simulation.gif?fit=300%2C300&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-Coin-Toss-Simulation.gif?fit=480%2C480&amp;ssl=1\" decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-7867\" src=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-Coin-Toss-Simulation.gif?resize=480%2C480\" alt=\"Sample Size Coin Toss Simulation\" width=\"480\" height=\"480\" data-recalc-dims=\"1\" \/><\/a><\/p>\n<p>In this graph, the orange line is the actual probability i.e. 0.5, and the blue line is the estimated probability for each step. As expected the estimated probability is getting closer to actual probability with the increase in sample size (left to right).<\/p>\n<p>Now the\u00a0question is how good is 500 as the sample size to estimate the probability of heads? For this, we will simulate 1000 experiments each with the sample size of 500, and estimate the probability of heads after each experiment. This histogram shows the estimated probability of 1000 experiments (<a href=\"http:\/\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-for-Coin-Tosses-1.txt\">R code for this simulation<\/a>)<a href=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-500.jpeg\" rel=\"attachment wp-att-7807\"><img data-attachment-id=\"7807\" data-permalink=\"https:\/\/ucanalytics.com\/blogs\/right-sample-size-analysis\/sample-size-500\/\" data-orig-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-500.jpeg?fit=718%2C432&amp;ssl=1\" data-orig-size=\"718,432\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Sample Size 500\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-500.jpeg?fit=300%2C181&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-500.jpeg?fit=640%2C385&amp;ssl=1\" decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-7807\" src=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-500.jpeg?resize=573%2C344\" alt=\"Sample Size 500\" width=\"573\" height=\"344\" srcset=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-500.jpeg?w=718&amp;ssl=1 718w, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-500.jpeg?resize=250%2C150&amp;ssl=1 250w, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-500.jpeg?resize=300%2C181&amp;ssl=1 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" data-recalc-dims=\"1\" \/><\/a><\/p>\n<p>The histogram looks like a normal distribution or bell curve as would have expected from\u00a0the central limit theorem (CLT) &#8211; we will come back to CLT in the next segment.<\/p>\n<p>The summary statistics for this data:<\/p>\n<table style=\"border-color: #000000;\" border=\"2\" width=\"384\">\n<tbody>\n<tr>\n<td style=\"width: 64px; text-align: center; background-color: #ffc926;\" width=\"64\">Min.<\/td>\n<td style=\"width: 64px; text-align: center; background-color: #ffc926;\" width=\"64\">1st Qu.<\/td>\n<td style=\"width: 64px; text-align: center; background-color: #ffc926;\" width=\"64\">Median<\/td>\n<td style=\"width: 64px; text-align: center; background-color: #ffc926;\" width=\"64\">Mean<\/td>\n<td style=\"width: 64px; text-align: center; background-color: #ffc926;\" width=\"64\">3rd Qu.<\/td>\n<td style=\"width: 64px; text-align: center; background-color: #ffc926;\" width=\"64\">Max.<\/td>\n<td style=\"width: 64px; text-align: center; background-color: #ffc926;\" width=\"64\">Std Dev.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"64\">0.43<\/td>\n<td style=\"text-align: center;\" width=\"64\">0.484<\/td>\n<td style=\"text-align: center;\" width=\"64\">0.5<\/td>\n<td style=\"text-align: center;\" width=\"64\">0.5006<\/td>\n<td style=\"text-align: center;\" width=\"64\">0.5160<\/td>\n<td style=\"text-align: center;\" width=\"64\">0.5620<\/td>\n<td style=\"text-align: center;\" width=\"64\">0.0226<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Both mean and median for 1000 experiments (sample size = 500) is close to 0.5. The standard deviation of these experiments is 0.0226. This standard deviation for multiple experiments is also known as the standard error of the estimate as we will learn later in this article.<\/p>\n<p>We could have estimated the same values for mean and standard error\u00a0through the theory suggested by the central limit theorem.<\/p>\n<h2><span style=\"color: #3366ff;\">Central Limit Theorem &amp; Sample Size<\/span><\/h2>\n<p>Let&#8217;s try to simplify the central limit theorem for our purpose of coin tossing. It states that mean of all the probabilities of heads estimated through all the experiments is equal to the actual probability of heads. In mathematical form, this is stated as:<\/p>\n<pre><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=E%28%5Coverline%7Bp%7D%29%3D%5Cpi+&#038;bg=ffffff&#038;fg=000&#038;s=1&#038;c=20201002\" alt=\"E(&#92;overline{p})=&#92;pi \" class=\"latex\" \/><\/pre>\n<p>We know that the actual probability of heads or \u03c0\u00a0is 50%. Unlike this problem, for\u00a0most practical problems the value of\u00a0\u03c0 is unknown. In such cases, we assume the probability obtained from experiment (p) as the expected probability.<\/p>\n<pre><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=E%28%5Coverline%7Bp%7D%29%3D%5Cpi+%3D+0.5&#038;bg=ffffff&#038;fg=000&#038;s=1&#038;c=20201002\" alt=\"E(&#92;overline{p})=&#92;pi = 0.5\" class=\"latex\" \/><\/pre>\n<p>For our one thousand experiments, we got the mean\u00a0as 0.5006. Had we performed an infinite number of experiments we will have got an exact value for actual probability i.e. 0.5. But none of us has the\u00a0time to do an infinite number of experiments. Only mathematicians can do these experiments in their heads but for all practical purposes, most of us can rely on simulations.<\/p>\n<p>Another part of the central limit theorem states that standard error\u00a0for estimation of proportions or probabilities is:<\/p>\n<pre><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Csigma+_%7B%5Coverline%7Bp%7D%7D%3D%5Csqrt%5Cfrac%7B%5Cpi+%281-%5Cpi+%29%7D%7B%7Bn%7D%7D+&#038;bg=ffffff&#038;fg=000&#038;s=2&#038;c=20201002\" alt=\"&#92;sigma _{&#92;overline{p}}=&#92;sqrt&#92;frac{&#92;pi (1-&#92;pi )}{{n}} \" class=\"latex\" \/><\/pre>\n<p>Here,\u00a0\u03c0 is the actual probability of heads for the fair coin which is 0.5. Hence, the standard error for a fair coin is:<\/p>\n<pre><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Csigma+_%7B%5Coverline%7Bp%7D%7D%3D%5Csqrt%5Cfrac%7B0.5+%281-0.5+%29%7D%7B%7B500%7D%7D+%3D+0.0223+&#038;bg=ffffff&#038;fg=000&#038;s=2&#038;c=20201002\" alt=\"&#92;sigma _{&#92;overline{p}}=&#92;sqrt&#92;frac{0.5 (1-0.5 )}{{500}} = 0.0223 \" class=\"latex\" \/><\/pre>\n<p>In our simulated experiments, we got the standard error or standard deviation of estimated probabilities of heads:<\/p>\n<pre><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Csigma+_%7B%5Coverline%7Bp%7D%7D%3D+0.0226+&#038;bg=ffffff&#038;fg=000&#038;s=1&#038;c=20201002\" alt=\"&#92;sigma _{&#92;overline{p}}= 0.0226 \" class=\"latex\" \/><\/pre>\n<p>The simulated results gave almost the same result as the theory suggested.<\/p>\n<h2><span style=\"color: #3366ff;\">Identify the Right Sample Size<\/span><\/h2>\n<p>Now, let us come back to our original question for this article of identification of sample size. In the previous section, we have found the theoretical definition for standard error as:<\/p>\n<pre><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Csigma+_%7B%5Coverline%7Bp%7D%7D%3D%5Csqrt%5Cfrac%7B%5Cpi+%281-%5Cpi+%29%7D%7B%7Bn%7D%7D+&#038;bg=ffffff&#038;fg=000&#038;s=2&#038;c=20201002\" alt=\"&#92;sigma _{&#92;overline{p}}=&#92;sqrt&#92;frac{&#92;pi (1-&#92;pi )}{{n}} \" class=\"latex\" \/><\/pre>\n<p>We can reorganize the above equation to measure the value of n which is sample size.<\/p>\n<pre><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=n%3D%5Cfrac%7B%5Cpi+%281-%5Cpi+%29%7D%7B%5Csigma+_%7B%5Coverline%7Bp%7D%7D%5E%7B2%7D%7D+&#038;bg=ffffff&#038;fg=000&#038;s=2&#038;c=20201002\" alt=\"n=&#92;frac{&#92;pi (1-&#92;pi )}{&#92;sigma _{&#92;overline{p}}^{2}} \" class=\"latex\" \/><\/pre>\n<p>Now, if you are OK with standard error as 10% of the actual probability of head (i.e. 10% of 0.5 i.e. 0.05). In this case, 95% of your results will be in the confidence interval of 0.4 to 0.6. This is calculated through 2\u00a0\u00d7 standard error on either side of 0.5. A sample size of 100 will be good enough to achieve this confidence as shown in the calculation<\/p>\n<pre><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=n%3D%5Cfrac%7B0.5+%5Ctimes+%281-0.5%29%7D%7B%7B%2810%5C%25%5Ctimes+0.5%29%7D%5E%7B2%7D%7D%3D100+&#038;bg=ffffff&#038;fg=000&#038;s=2&#038;c=20201002\" alt=\"n=&#92;frac{0.5 &#92;times (1-0.5)}{{(10&#92;%&#92;times 0.5)}^{2}}=100 \" class=\"latex\" \/><\/pre>\n<p>On the other hand, if you want standard error as 0.5% of the actual probability of head (i.e. 0.005). In this case, 95% of your results will be in the confidence interval range of 0.495 to 0.505. However, to achieve this high level of precision the requirement of sample size is whopping 40000 tosses.<\/p>\n<pre><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=n%3D%5Cfrac%7B0.5+%5Ctimes+%281-0.5%29%7D%7B%7B%280.5%5C%25%5Ctimes+0.5%29%7D%5E%7B2%7D%7D%3D40000+&#038;bg=ffffff&#038;fg=000&#038;s=2&#038;c=20201002\" alt=\"n=&#92;frac{0.5 &#92;times (1-0.5)}{{(0.5&#92;%&#92;times 0.5)}^{2}}=40000 \" class=\"latex\" \/><\/pre>\n<p>Hence, the entire sampling strategy is a trade-off between sample size and standard error. This table shows sample size requirement for the desired standard error as a percentage of probability of heads for a fair coin.<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"background-color: #f5db5b;\">Standard Error as % of Actual Probability of Heads (i.e. 0.5)<\/td>\n<td>20%<\/td>\n<td>10%<\/td>\n<td>5%<\/td>\n<td>2%<\/td>\n<td>1%<\/td>\n<td>0.5%<\/td>\n<\/tr>\n<tr>\n<td style=\"background-color: #f5db5b;\"><strong>Standard Error<\/strong><\/td>\n<td>0.1<\/td>\n<td>0.05<\/td>\n<td>0.025<\/td>\n<td>0.01<\/td>\n<td>0.005<\/td>\n<td>0.0025<\/td>\n<\/tr>\n<tr>\n<td style=\"background-color: #f5db5b;\"><strong>Sample Size<\/strong><\/td>\n<td>25<\/td>\n<td>100<\/td>\n<td>400<\/td>\n<td>2500<\/td>\n<td>10000<\/td>\n<td>40000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>When we plot a sample size vs standard error plot, because of the inverse square relationship between them, toward the right side of the plot standard error doesn&#8217;t decrease as drastically as towards the left. This is an important concept to keep in mind while choosing the sample size for your analysis.<\/p>\n<h2><a href=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-Vs-Standard-Error.jpeg\" rel=\"attachment wp-att-7872\"><img data-attachment-id=\"7872\" data-permalink=\"https:\/\/ucanalytics.com\/blogs\/right-sample-size-analysis\/sample-size-vs-standard-error\/\" data-orig-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-Vs-Standard-Error.jpeg?fit=718%2C432&amp;ssl=1\" data-orig-size=\"718,432\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Sample Size Vs Standard Error\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-Vs-Standard-Error.jpeg?fit=300%2C181&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-Vs-Standard-Error.jpeg?fit=640%2C385&amp;ssl=1\" decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-7872\" src=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-Vs-Standard-Error.jpeg?resize=601%2C361\" alt=\"Sample Size Vs Standard Error\" width=\"601\" height=\"361\" srcset=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-Vs-Standard-Error.jpeg?w=718&amp;ssl=1 718w, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-Vs-Standard-Error.jpeg?resize=250%2C150&amp;ssl=1 250w, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/03\/Sample-Size-Vs-Standard-Error.jpeg?resize=300%2C181&amp;ssl=1 300w\" sizes=\"(max-width: 601px) 100vw, 601px\" data-recalc-dims=\"1\" \/><\/a><\/h2>\n<h4><span style=\"color: #3366ff;\">Sign-off Note<\/span><\/h4>\n<p>We have done the entire calculation of sample size based on the assumption that means is the measure that you want to estimate for a population. This is usually a good assumption for most analysis. However, it is always good for you to ask : is mean the right measure for your analysis? The right measure for your analysis depends on\u00a0the question you are trying to answer.<\/p>\n<p>For example, consider these two questions:<\/p>\n<p>1. What is the salinity of the Pacific Ocean?<br \/>\n2. Is there another planet with intelligent life in the Universe?<\/p>\n<p>In terms of population size, the number of drops in the ocean and planets in the Universe is similar. A couple of drops of water are enough to answer the first question since the salinity of oceans is fairly constant. On the other hand, the second question is a black swan problem. You may need to visit every single planet to rule our possibility of an intelligent form of life. \u00a0Hence the sample size depends on the degree of similarity or homogeneity of the population in question.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A few years ago, I did a day-long workshop on Statistical Thinking\u00a0for a large German shipping &amp; cargo company in Mumbai. During the Q&amp;A session, the Vice President of operations asked a tricky question: what is a good sample size to achieve precision and accuracy for your analysis?\u00a0He was looking for a one-size-fits-all answer and<\/p>\n<p><a class=\"excerpt-more blog-excerpt\" href=\"https:\/\/ucanalytics.com\/blogs\/right-sample-size-analysis\/\">Read More&#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":6012,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_newsletter_tier_id":0,"jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[62],"tags":[],"jetpack_publicize_connections":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What is the Right Sample Size for Your Analysis? &ndash; YOU CANalytics |<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ucanalytics.com\/blogs\/right-sample-size-analysis\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the Right Sample Size for Your Analysis? &ndash; YOU CANalytics |\" \/>\n<meta property=\"og:description\" content=\"A few years ago, I did a day-long workshop on Statistical Thinking\u00a0for a large German shipping &amp; cargo company in Mumbai. 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