Muhammad Touhidul Islam's Posts - Data Science Central2021-09-28T09:34:47ZMuhammad Touhidul Islamhttps://www.datasciencecentral.com/profile/MuhammadTouhidulIslamhttps://storage.ning.com/topology/rest/1.0/file/get/8533131471?profile=RESIZE_48X48&width=48&height=48&crop=1%3A1https://www.datasciencecentral.com/profiles/blog/feed?user=198k7j1on4l1u&xn_auth=noBig Data: Effective tips to successtag:www.datasciencecentral.com,2021-08-01:6448529:BlogPost:10599942021-08-01T09:30:00.000ZMuhammad Touhidul Islamhttps://www.datasciencecentral.com/profile/MuhammadTouhidulIslam
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<p class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-paragraph rich-text" id="block-26eec6b0-6991-4843-8032-1296a8ea538c">Can <a href="https://www.statisticalaid.com/statistical-data-definition-types-and-requirements/">data</a> especially big data be considered as the new gold? Considering the pace at which data is evolving all across the globe, there is little question. Big data contains huge information and we can extract them by performing big <a href="https://www.statisticalaid.com/category/spss/">data analysis</a>. Consider the following: </p>
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<li>Netflix saves $1 billion per year on customer retention only by utilizing big data.</li>
<li>Being the highest shareholder of the search engines market, Google faces 1.2 trillion searches every year, with more than 40,000 search queries every second!</li>
<li>Additionally, among all the google searches. 15% of those are new and are never typed before, leading to the fact that a new set of data is generated by Google continuously regularly. The main agenda is to convert data into information and then convert that information into insights. </li>
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<h2 class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-heading rich-text" id="block-a436a2f4-785d-4d01-8180-2bf93654cce8">Why need a Proper Big Data Analysis Strategy?</h2>
<p class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-paragraph rich-text" id="block-70eb41e0-5ef0-450a-ba66-d2f0ea166d68">Organizations were storing tons of their data into their databases without knowing what to do with that data until big data analysis became a completely developed idea. Poor data quality can cost businesses from $9.7 billion to 14.2 millions every year. Moreover, poor data quality can surely lead to wrong business strategies or poor decision-making. This also results in low productivity and sabotages the relationship between customers and the organization, causing the organization to lose its reputation in the market. </p>
<p class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-paragraph rich-text" id="block-f4824883-c4df-46c8-bab1-6a799572f64f">To deter this problem, here is a list of five things an enterprise must acquire in order to turn their big data into a big success:</p>
<h2 class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-heading rich-text" id="block-4b7c6ece-6a25-409b-9da0-d88ffed1af8d"><strong>Strong Leadership Driving Big Data Analysis Initiatives </strong></h2>
<p class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-paragraph rich-text" id="block-36f29382-8b68-41b9-8053-119a34fd185a">The most important factor for nurturing data-driven decision-making culture is proper leadership. Organizations must have well-defined leadership roles for big data analytics to boost the successful implementation of big data initiatives. Necessary stewardship is crucial for organizations for making big data analytics an integral part of regular business operations. </p>
<p class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-paragraph rich-text" id="block-68b72edd-35b6-40d7-8e5a-20914280fe3b">Leadership-driven big data initiatives assist organizations in making their big data commercially viable. Unfortunately, only 34% of the organizations have appointed a chief data officer to handle the implementation of big data initiatives. A pioneer in the utilization of big data in the United States’s banking industry, Bank of America, specified a Chief Data Officer (CDO) who is responsible for all the data management standards and policies, simplification of It tools and infrastructures that are required for the implementation, and setting up the <a href="https://datascience.statisticalaid.com/">big data</a> platform of the bank. </p>
<p class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-paragraph rich-text" id="block-37f4e733-8578-4e3c-a9bb-d7e5cd1d6884"><strong>Invest in Appropriate Skills Before Technology</strong></p>
<p class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-paragraph rich-text" id="block-3c5089b1-f7a5-4f25-8ccb-bfa06b2dc62b">Having the right skills are crucial even before the technology has been implemented: </p>
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<li>Utilize disparate open-source software for the integration and analysis of both structured and unstructured data. </li>
<li>Framing and asking appropriate business questions with a crystal-clean line of sight such as how the insights will be utilized, and </li>
<li>Bringing the appropriate statistical tools to bear on data for performing predictive analytics and generating forward-looking insights. </li>
</ul>
<p class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-paragraph rich-text" id="block-752ff126-c6cb-4b16-b5c5-20811473e14e">All of the above-mentioned skills can be proactively developed for both hiring and training. It is essential to search for those senior leaders within the organization who not only believe in the power of big data but are also willing to take risks and perform experimentation. Such leaders play a vital role in driving swift acquisitions and the success of data applications. </p>
<p class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-paragraph rich-text" id="block-a704344b-63ac-4eb1-996d-0bb7a72dcf89"><strong>Perform Experimentation With Big Data Pilots</strong></p>
<p class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-paragraph rich-text" id="block-b0ae012c-fc5c-41c9-85cd-f36cbf8f1c76">Start with the identification of the most critical problems of the business and how big data serves as the solution to that problem. After the identification of the problem, bring numerous aspects of big data into the laboratory where these pilots can be run before making any major investment in the technology. Such pilot programs provide an enormous collection of big data tools and expertise that prove value effectively for the organization without making any hefty investments in IT costs or talent. By working with such pilots, implementation of these efforts at a grassroots level can be done with minimal investments in the technology. </p>
<p class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-paragraph rich-text" id="block-c726b5f5-351c-4051-a099-e36b14eb78b0"><strong>Search For a Needle in an Unstructured Hay </strong></p>
<p class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-paragraph rich-text" id="block-728a6d8b-6860-4901-a5c6-5304dfb7c24c">The thing that always remains on the top of the mind of businesses is unstructured and semistructured data - the information contained in documents, spreadsheets, and similar non-traditional data sources. According to Gartner, data of organizations will evolve by 800% in the upcoming five years and 80% of that data will be unstructured. There are three crucial principles associated with unstructured data. </p>
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<li>Having the appropriate technology is essential for storing and analyzing unstructured data. </li>
<li>Prioritizing such unstructured data that is rich in information value and sentiments. </li>
<li>Extracting relevant signals must be done from the insights and must be combined with structured data for boosting business predictions and insights.</li>
</ul>
<h2 class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-heading rich-text" id="block-772ac201-ca96-4acc-96bb-b859fb32e859"><strong>Incorporate Operational Analytics Engines</strong></h2>
<p class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-paragraph rich-text" id="block-a15fee0a-82f1-4c01-bd99-5bde08665034"> One potential advantage that can be attained by using big data is the capability of tailoring experiences to customers based on their most up-to-the-minute behavior. Businesses can no longer extract the data of last month, analyze that data offline for two months, and act upon the analysis three months later for making big data a competitive benefit.</p>
<p class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-paragraph rich-text" id="block-d11a77b2-c667-4b5d-bea3-45a5d9e88f31">Take, as an example, loyal customers who enter promotional codes at the time of checkout but discover that their discount is not applied to result in a poor customer experience.</p>
<p class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-paragraph rich-text" id="block-7aff6edc-8bf6-4040-b85d-84265c63caf7">Businesses need to shift their mindset of traditional offline analytics to tech-powered analytic engines that empower businesses with real-time and near-time decision-making, acquiring a measured test and learn approach. This can be achieved by making 20% of the organization’s decisions with tech-powered analytical engines and then gradually increasing the percentage of decisions processed in this way over time as comfort grows about the process. </p>
<h2 class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-heading rich-text" id="block-ab932e7f-dcdf-4f23-979f-f64fb53c9fbc"><strong>Final Thoughts </strong></h2>
<p class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-paragraph rich-text" id="block-f0a17c36-1928-487a-8f88-b9262191923b">In this tech-oriented world and digitally powered economy, big data analytics plays a vital role in the proper navigation of the market and to come up with appropriate predictions as well as decisions. Organizations must never ignore understanding patterns and deterring flows. especially as enterprises deal with different types of data each day, in different sizes, shapes, and forms. The market of big data analytics is growing dramatically and will reach up to $62.10 billion by the year 2025. Considering that progression, 97.2% of the organizations are already investing in artificial intelligence as well as big data. Hence organizations must acquire appropriate measures and keep in mind all the crucial above-mentioned tips for turning their big data into big success to stay competitive in this ever-changing world.</p>
<p class="block-editor-rich-text__editable block-editor-block-list__block wp-block wp-block-paragraph rich-text"><a href="https://datascience.statisticalaid.com/big-data-analysis-effective-tips-to-success/" target="_blank" rel="noopener">Source..</a></p>
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</div>An Introduction to Statistical Samplingtag:www.datasciencecentral.com,2021-07-28:6448529:BlogPost:10595832021-07-28T11:00:00.000ZMuhammad Touhidul Islamhttps://www.datasciencecentral.com/profile/MuhammadTouhidulIslam
<p><span><a href="https://1.bp.blogspot.com/-10QCESdrCg8/XirIjrVVsXI/AAAAAAAAAVU/4AhXj9YJDzgQXaHtsIy_heUYvA48lGRQACLcBGAsYHQ/s320/dreamstime_s_97267612_780x480.jpg" rel="noopener" target="_blank"><img class="align-center" src="https://1.bp.blogspot.com/-10QCESdrCg8/XirIjrVVsXI/AAAAAAAAAVU/4AhXj9YJDzgQXaHtsIy_heUYvA48lGRQACLcBGAsYHQ/s320/dreamstime_s_97267612_780x480.jpg?profile=RESIZE_710x" width="720"></img></a></span></p>
<p style="text-align: center;">Image Source: <a href="https://www.statisticalaid.com/" rel="noopener" target="_blank">Statistical Aid</a></p>
<p><span>Sampling is a statistical procedure of selecting some representative part from an existing population or study area.…</span></p>
<p><span><a href="https://1.bp.blogspot.com/-10QCESdrCg8/XirIjrVVsXI/AAAAAAAAAVU/4AhXj9YJDzgQXaHtsIy_heUYvA48lGRQACLcBGAsYHQ/s320/dreamstime_s_97267612_780x480.jpg" target="_blank" rel="noopener"><img src="https://1.bp.blogspot.com/-10QCESdrCg8/XirIjrVVsXI/AAAAAAAAAVU/4AhXj9YJDzgQXaHtsIy_heUYvA48lGRQACLcBGAsYHQ/s320/dreamstime_s_97267612_780x480.jpg?profile=RESIZE_710x" width="720" class="align-center"/></a></span></p>
<p style="text-align: center;">Image Source: <a href="https://www.statisticalaid.com/" target="_blank" rel="noopener">Statistical Aid</a></p>
<p><span>Sampling is a statistical procedure of selecting some representative part from an existing population or study area. Specifically, draw a </span><a href="https://www.statisticalaid.com/population-vs-sample-in-statistics/" target="_blank" rel="noopener">sample</a><span> from the study </span><a href="https://www.statisticalaid.com/population-vs-sample-in-statistics/" target="_blank" rel="noopener">population</a><span> using some statistical methods. For example-</span><br/> <span>if we want to calculate the average age of Bangladeshi people then we can not deal with the whole population. In that time we must have to deal with some representative part of this population. This representative part is called sample and the procedure is called sampling.</span></p>
<h3><b><span>Why need sampling</span></b></h3>
<div><span> It makes possible the study of a large population which contains different characteristics.</span></div>
<div><span> It is for economy.</span></div>
<div><span> It is for speed.</span></div>
<div><span> It is for accuracy.</span></div>
<div><span> It saves the sources of data from being all consumed.</span></div>
<div><span>Sometimes we can’t work with population such as </span><span>blood test</span><span>, in that situation sampling is must.</span></div>
<div><span> </span></div>
<h3><b><span>Types </span></b></h3>
<div><span> <a href="https://www.statisticalaid.com/probability-sampling-with-applicationadvantages-and-disadvantages/" target="_blank" rel="noopener">Probability sampling</a> </span></div>
<div><span> <a href="https://www.statisticalaid.com/non-probability-sampling-methods-with-application-advantages-and-disadvantages/" target="_blank" rel="noopener">Non-probability sampling</a></span></div>
<h3><b><span>Probability Sampling</span></b></h3>
<div><span>It is based on the concept of random selection where each population elements have a non-zero chance to occur as a sample. Sampling techniques can be divided into two categories: probability and non-probability. Randomization or chance is the core of probability sampling techniques.</span></div>
<div><span>For example, if a researcher is dealing with a population of 100 people, each person in the population would have the odds of 1 out of 100 for being chosen. This differs from non-probability sampling, in which each member of the population would not have the same odds of being selected.</span></div>
<h3><span>Different types of probability sampling</span></h3>
<ul>
<li><span><a href="https://www.statisticalaid.com/simple-random-sampling-definitionapplication-advantages-and-disadvantages/" target="_blank" rel="noopener">Simple Random</a></span></li>
<li><span><a href="https://www.statisticalaid.com/stratified-sampling-definition-allocation-rules-with-advantages-and-disadvantages/" target="_blank" rel="noopener">Stratified</a></span></li>
<li><span><a href="https://www.statisticalaid.com/systematic-sampling-definition-examples-advantages-and-disadvantages-and-application/" target="_blank" rel="noopener">Systematic</a></span></li>
<li><span><a href="https://www.statisticalaid.com/multistage-sampling-definition-real-life-example-advantages-and-disadvantages/" target="_blank" rel="noopener">Multi-Stage</a></span></li>
<li><span><a href="https://www.statisticalaid.com/cluster-sampling-definition-application-advantages-and-disadvantages/" target="_blank" rel="noopener">Cluster</a></span></li>
<li><a href="https://www.statisticalaid.com/quadrat-sampling-application-with-advantages-and-disadvantages/">Quadrat sampling</a></li>
</ul>
<div><span> </span></div>
<div><b><span>Applications</span></b></div>
<div><span>· In opinion poll, a relatively small number of persons are interviewed and their opinions on current issues are solicited in order to discover the attitude of the community as a whole.</span></div>
<div><span>· At border stations, customs officers enforce the laws by checking the effects of only a small number of travelers crossing the border.</span></div>
<div><span>· A departmental store wises to examine whether it is losing or gaining customers by drawing a sample from its lists of credit card holders by selecting every tenth name.</span></div>
<div><span>· In a manufacturing company, a quality control officer take one sample from every lot and if any sample is damage then he reject that lot.</span></div>
<div><b><span>Advantages</span></b></div>
<div><span> Creates samples that are highly representative of the population.</span></div>
<div><span> Sampling bias is tens to zero.</span></div>
<div><span> Higher level of reliability of research findings.</span></div>
<div><span> Increased accuracy of sample error estimation.</span></div>
<div><span> The possibility to make inferences about the population.</span></div>
<h3><b><span>Disadvantages</span></b></h3>
<div><span> Higher complexity compared to non-probability sample.</span></div>
<div><span> More time consuming, especially when creating larger sample.</span></div>
<div><span> Usually more expensive.</span></div>
<h3><span><b>Non-Probability sampling</b></span></h3>
<div><span>The process of selecting a sample from a population without using statistical probability theory is called non-probability sampling.</span></div>
<div><span>Example</span></div>
<div><span>Lets say that the university has roughly 10000 students. These 10000 students are our population (N). Each of the 10000 students is known as a unit, but its hardly possible to get known and select every student randomly.</span></div>
<div><span>Here we can use Non-Random selection of sample to produce a result.</span></div>
<div><span> </span></div>
<h3><b><span>Applications</span></b></h3>
<div><span> </span></div>
<div><span>· It can be used when demonstrating that a particular trait exist in the population.</span></div>
<div><span>· It can also be useful when the researcher has limited budget, time and workforce.</span></div>
<div><span> </span></div>
<h3><b><span>Advantages</span></b></h3>
<div><span>· Select samples purposively</span></div>
<div><span>· Enable researchers to reach difficult to identify members of the population.</span></div>
<div><span>· Lower cost</span></div>
<div><span>· Limited time.</span></div>
<div><span> </span></div>
<h3><b><span>Disadvantage</span></b></h3>
<div><span>Difficult to make valid inference about the entire population because the sample selected is not representative.</span></div>
<div><span>We cannot calculate confidence interval.</span></div>
<div><a href="https://www.statisticalaid.com/sampling-definition-examples-types-application-advantages-and-disadvantages/" target="_blank" rel="noopener">Source</a></div>
<p></p>Variance vs Standard Deviationtag:www.datasciencecentral.com,2021-07-20:6448529:BlogPost:10584242021-07-20T07:00:00.000ZMuhammad Touhidul Islamhttps://www.datasciencecentral.com/profile/MuhammadTouhidulIslam
<div> </div>
<div><a href="https://1.bp.blogspot.com/-kecAmGrewdY/X9ha8BGZ1PI/AAAAAAAAA2I/gyga7AjQf8MG4PeXel-T9bFL-Ig2HlNRACLcBGAsYHQ/s622/var.JPG"><img alt="variance and standard deviation in statistics" border="0" class="alignnone" height="451" src="https://1.bp.blogspot.com/-kecAmGrewdY/X9ha8BGZ1PI/AAAAAAAAA2I/gyga7AjQf8MG4PeXel-T9bFL-Ig2HlNRACLcBGAsYHQ/s16000/var.JPG" title="population vs sample variance" width="622"></img></a></div>
<div style="text-align: center;"> Image Source: <a href="https://www.statisticalaid.com/" rel="noopener" target="_blank">Statistical Aid</a></div>
<div><p>Variance is one of the best measures of dispersion which measure the difference of all observation from the center value of the observations.…</p>
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<div><a href="https://1.bp.blogspot.com/-kecAmGrewdY/X9ha8BGZ1PI/AAAAAAAAA2I/gyga7AjQf8MG4PeXel-T9bFL-Ig2HlNRACLcBGAsYHQ/s622/var.JPG"><img class="alignnone" title="population vs sample variance" src="https://1.bp.blogspot.com/-kecAmGrewdY/X9ha8BGZ1PI/AAAAAAAAA2I/gyga7AjQf8MG4PeXel-T9bFL-Ig2HlNRACLcBGAsYHQ/s16000/var.JPG" alt="variance and standard deviation in statistics" width="622" height="451" border="0"/></a></div>
<div style="text-align: center;"> Image Source: <a href="https://www.statisticalaid.com/" target="_blank" rel="noopener">Statistical Aid</a></div>
<div><p>Variance is one of the best measures of dispersion which measure the difference of all observation from the center value of the observations.</p>
<p></p>
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<h3><span style="font-size: 14pt;"><strong>Population variance and standard deviation</strong></span></h3>
<div><span>The average of the square of the deviations</span> <span>taken from mean is called variance. The <a href="https://www.statisticalaid.com/population-vs-sample-in-statistics/" target="_blank" rel="noopener">population</a></span> <span>variance is generally denoted by σ</span><i><span><sup>2 </sup>and</span></i> <span>its estimate</span> <span>(<a href="https://www.statisticalaid.com/population-vs-sample-in-statistics/" target="_blank" rel="noopener">sample</a> variance) by</span> <i><span>s<sup>2</sup>.</span></i> <span>For</span> <i><span>N</span></i> <span>population values X1,X2,...,XN</span><i><span> </span></i><span>having the population mean μ, the population variance is defined as,</span></div>
<div> </div>
<div><span><a href="https://www.codecogs.com/eqnedit.php?latex=%5Csigma&space;%5E%7B2%7D=%5Cfrac%7B%5Csum&space;(x_%7Bi%7D-%5Cmu&space;)%5E%7B2%7D%7D%7BN%7D;&space;%5Csigma&space;%5E%7B2%7D=Population&space;Variance" target="_blank" rel="noopener"><img class="alignnone" title="sigma ^{2}=frac{sum (x_{i}-mu )^{2}}{N}; sigma ^{2}=Population Variance" src="https://latex.codecogs.com/gif.latex?%5Csigma&space;%5E%7B2%7D=%5Cfrac%7B%5Csum&space;(x_%7Bi%7D-%5Cmu&space;)%5E%7B2%7D%7D%7BN%7D;&space;%5Csigma&space;%5E%7B2%7D=Population&space;Variance" alt="population variance formula" width="348" height="41"/></a></span></div>
<div> </div>
<div><span>Where, μ is the <a href="https://www.statisticalaid.com/arithmetic-mean-definition-formula-and-applications/" target="_blank" rel="noopener">mean</a> of all the observations in the population and N is the total number of observations in the population. Because the operation of squaring, the variance is expressed in square units and not of the original units.</span></div>
<div> </div>
<div><span>So, we can define the population standard deviation as</span></div>
<div><span> </span></div>
<div><span><a href="https://www.codecogs.com/eqnedit.php?latex=%5Csigma&space;=%5Csqrt%7B%5Cfrac%7B%5Csum&space;(x_%7Bi%7D-%5Cmu&space;)%5E%7B2%7D%7D%7BN%7D%7D;&space;%5Csigma&space;=Population&space;Standard&space;Deviation" target="_blank" rel="noopener"><img class="alignnone" title="sigma =sqrt{frac{sum (x_{i}-mu )^{2}}{N}}; sigma =Population Standard Deviation" src="https://latex.codecogs.com/gif.latex?%5Csigma&space;=%5Csqrt%7B%5Cfrac%7B%5Csum&space;(x_%7Bi%7D-%5Cmu&space;)%5E%7B2%7D%7D%7BN%7D%7D;&space;%5Csigma&space;=Population&space;Standard&space;Deviation" alt="standard deviation formula" width="433" height="44"/></a></span></div>
<div><span> </span></div>
<div><span>Thus, the standard deviation is the positive square root of the mean square deviations of the observations from their arithmetic mean. More simply, standard deviation is the positive square root of σ<i><sup>2</sup></i>.</span></div>
<div><span> </span></div>
<h3><span style="font-size: 14pt;"><strong>Sample variance</strong></span></h3>
<div><span>In maximum <a href="https://www.statisticalaid.com/statistics-definition-scope-with-real-life-examples/" target="_blank" rel="noopener">statistical applications</a>, we deal with a sample rather than a population. Thus, while a set of population observations yields a σ<i><sup>2</sup></i> and a set of sample observations will yield a <i>s<sup>2</sup></i>. If x1,x2,...,xn is a set of sample observations of size n, then the <i>s<sup>2</sup></i> is define as,</span></div>
<div><span> </span></div>
<div><span><a href="https://www.codecogs.com/eqnedit.php?latex=S%5E%7B2%7D&space;=%5Cfrac%7B%5Csum&space;(x_%7Bi%7D-%5Cbar%7Bx%7D&space;)%5E%7B2%7D%7D%7Bn%7D;&space;S%5E%7B2%7D=SampleVariance" target="_blank" rel="noopener"><img class="alignnone" title="S^{2} =frac{sum (x_{i}-bar{x} )^{2}}{n}; S^{2}=SampleVariance" src="https://latex.codecogs.com/gif.latex?S%5E%7B2%7D&space;=%5Cfrac%7B%5Csum&space;(x_%7Bi%7D-%5Cbar%7Bx%7D&space;)%5E%7B2%7D%7D%7Bn%7D;&space;S%5E%7B2%7D=SampleVariance" alt="sample variance formula" width="321" height="41"/></a></span></div>
<h3><span style="font-size: 14pt;"><strong>Properties</strong></span></h3>
<div><span><b>Effect of changes in origin:</b> Variance and standard deviation have certain appealing properties. Let each of the numbers x1,x2,...,xn increases or decreases by a constant c. Let y be the transformed variable defined as,</span></div>
<div><span> </span></div>
<div><a href="https://www.codecogs.com/eqnedit.php?latex=y_%7Bi%7D=x_%7Bi%7D%5Cpm&space;c;i=1,2,...,n" target="_blank" rel="noopener"><span><img title="y_{i}=x_{i}pm c;i=1,2,...,n" src="https://latex.codecogs.com/gif.latex?y_%7Bi%7D=x_%7Bi%7D%5Cpm&space;c;i=1,2,...,n"/></span></a></div>
<div><span> </span></div>
<div><span>where, c is a constant.</span></div>
<div><span>Finally we get that any linear change in the variable x does not have any effect on its σ<i><sup>2</sup></i>. So, σ<i><sup>2</sup></i> is independent of change of origin.</span></div>
<div><span> </span></div>
<div><span><b>Effect of changes in the scale:</b> When each observation of the variable is multiplied or divided by a certain constant c then there occur changes in the σ<i><sup>2</sup></i>.</span></div>
<div><span> </span></div>
<div><a href="https://www.codecogs.com/eqnedit.php?latex=y_%7Bi%7D=%5Cfrac%7Bx_%7Bi%7D%7D%7Bc%7D;i=1,2,...,n" target="_blank" rel="noopener"><span><img class="alignnone" title="y_{i}=frac{x_{i}}{c};i=1,2,...,n" src="https://latex.codecogs.com/gif.latex?y_%7Bi%7D=%5Cfrac%7Bx_%7Bi%7D%7D%7Bc%7D;i=1,2,...,n" alt="scale " width="163" height="33"/></span></a></div>
<div><span> </span></div>
<div><span>So, we can say that changes in scale affects and it depends on scale.</span></div>
<div> </div>
<div> </div>
<h3><span style="font-size: 14pt;"><strong>Uses of variance and standard deviation</strong></span></h3>
<div><span>A thorough understanding of the uses of standard deviation is difficult for us as this stage, unless we acquire some knowledge on some theoretical <a href="https://www.statisticalaid.com/probability-distributions-in-statistics/" target="_blank" rel="noopener">distributions</a> in statistics. The variance and standard deviation of a population is a measure of the dispersion in the population while the variance and standard deviation of sample observations is a measure of the dispersion in the distribution constructed from the sample. It can be the best understood with reference to a <a href="https://www.statisticalaid.com/normal-distribution-definition-exampleproperties-applications-and-special-cases/" target="_blank" rel="noopener">normal distribution</a> because normal distribution is completely defined by mean and standard deviation.</span></div>
<div><a href="https://www.statisticalaid.com/variance-and-standard-deviation-in-statistics/" target="_blank" rel="noopener">Source</a></div>
<p> </p>Cluster sampling: A probability sampling techniquetag:www.datasciencecentral.com,2021-07-13:6448529:BlogPost:10569642021-07-13T17:18:01.000ZMuhammad Touhidul Islamhttps://www.datasciencecentral.com/profile/MuhammadTouhidulIslam
<p><img alt="cluster sampling" src="https://www.statisticalaid.com/wp-content/uploads/2020/10/4.png"></img></p>
<p style="text-align: center;">Image source: <a href="https://www.statisticalaid.com/cluster-sampling-definition-application-advantages-and-disadvantages/" rel="noopener" target="_blank">Statistical Aid</a></p>
<p><span>Cluster sampling is defined as a </span><a href="https://www.statisticalaid.com/sampling-definition-examples-types-application-advantages-and-disadvantages/" rel="noopener" target="_blank">sampling method</a><span> where multiple clusters of people are created…</span></p>
<p><img src="https://www.statisticalaid.com/wp-content/uploads/2020/10/4.png" alt="cluster sampling"/></p>
<p style="text-align: center;">Image source: <a href="https://www.statisticalaid.com/cluster-sampling-definition-application-advantages-and-disadvantages/" target="_blank" rel="noopener">Statistical Aid</a></p>
<p><span>Cluster sampling is defined as a </span><a href="https://www.statisticalaid.com/sampling-definition-examples-types-application-advantages-and-disadvantages/" target="_blank" rel="noopener">sampling method</a><span> where multiple clusters of people are created from a population where they are indicative of homogenous characteristics and have an equal chance of being a part of the </span><a href="https://www.statisticalaid.com/population-vs-sample-in-statistics/" target="_blank" rel="noopener">sample</a><span>. In this sampling method, a </span><a href="https://www.statisticalaid.com/simple-random-sampling-definitionapplication-advantages-and-disadvantages/" target="_blank" rel="noopener">simple random sample</a><span> is created from the different clusters in the </span><a href="https://www.statisticalaid.com/population-vs-sample-in-statistics/" target="_blank" rel="noopener">population</a><span>. This is a </span><a href="https://www.statisticalaid.com/probability-sampling-with-applicationadvantages-and-disadvantages/" target="_blank" rel="noopener">probability sampling</a><span> procedure.</span></p>
<h3><span>Examples</span></h3>
<div><span><strong>Area sampling:</strong> Area sampling is a method of sampling used when no complete frame of reference is available. The total area under investigation is divided into small sub-areas which are sampled at random or according to a restricted process (stratification of sampling). Each of the chosen sub-areas is then fully inspected and enumerated, and may form the basis for further sampling if desired.</span></div>
<h3><span>Types of cluster sampling</span></h3>
<p>There are three types as following,</p>
<div class="code-block code-block-1"><strong>Single stage Cluster:</strong><span> </span>In this process sampling is applied in only one time. For example, An NGO wants to create a sample of girls across five neighboring towns to provide education. Using single-stage sampling, the NGO randomly selects towns (clusters) to form a sample and extend help to the girls deprived of education in those towns.</div>
<p><strong>Two-stage Cluster:</strong><span> </span>In this process, first choose a cluster and then draw sample from the cluster using simple random sampling or other procedure. For example, A business owner wants to explore the performance of his/her plants that are spread across various parts of the U.S. The owner creates clusters of the plants. He/she then selects random samples from these clusters to conduct research.</p>
<p><strong>Multistage Cluster:</strong><span> </span>Few step added to two-stage then it is called multistage cluster sampling. For example, An organization intends to survey to analyze the performance of smartphones across Germany. They can divide the entire country’s population into cities (clusters) and select cities with the highest population and also filter those using mobile devices.</p>
<div class="afw afw-ga afw_ad afwadid-553"><b><span>Advantages</span></b></div>
<div><span>· Consumes less time and cost</span></div>
<div><span>· Convenient access</span></div>
<div><span>· Least loss in accuracy of data</span></div>
<div><span>· Ease of implementation</span></div>
<div><a href="https://www.statisticalaid.com/cluster-sampling-definition-application-advantages-and-disadvantages/" target="_blank" rel="noopener">Source</a></div>A Few Useful Techniques for Business Forecastingtag:www.datasciencecentral.com,2021-07-09:6448529:BlogPost:10564482021-07-09T12:00:00.000ZMuhammad Touhidul Islamhttps://www.datasciencecentral.com/profile/MuhammadTouhidulIslam
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/9238290274?profile=original" rel="noopener" target="_blank"><img class="align-full" src="https://storage.ning.com/topology/rest/1.0/file/get/9238290274?profile=RESIZE_710x" width="720"></img></a></p>
<p style="text-align: center;"><a href="https://www.statisticalaid.com/" rel="noopener" target="_blank"></a></p>
<p>Forecasting is the process of making prediction of the future based on past and present<span> </span><a href="https://www.statisticalaid.com/statistical-data-definition-types-and-requirements/" target="_self">data</a>.</p>
<p>In many cases…</p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/9238290274?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/9238290274?profile=RESIZE_710x" width="720" class="align-full"/></a></p>
<p style="text-align: center;"><a href="https://www.statisticalaid.com/" target="_blank" rel="noopener"></a></p>
<p>Forecasting is the process of making prediction of the future based on past and present<span> </span><a href="https://www.statisticalaid.com/statistical-data-definition-types-and-requirements/" target="_self">data</a>.</p>
<p>In many cases a reliable forecast can be worth a lot of money, such as consistently and correctly guessing the behavior of the stock market for enough in advance to act upon such a guess.</p>
<p></p>
<p><img src="https://1.bp.blogspot.com/-lAfX2QYEFGk/YBwx2MIWKfI/AAAAAAAAA8w/8uNUmFL2ZkoCx2hZLJNdPiW3vg5L6U9HgCLcBGAsYHQ/s645/forecasting.JPG"/></p>
<p>Image Source:<span> </span><a href="https://www.statisticalaid.com/" target="_blank" rel="noopener">Statistical Aid: A School of Statistics</a></p>
<h3>Objectives of forecasting</h3>
<p>In narrow sense, the objectives of forecasting is to produce better forecast. But in the broader sense, the objective is to improve organizational performance, more revenue, more profit, increased customer satisfaction etc. Better forecast by themselves are no inherent value of those forecast are ignored by management or otherwise not used to improve organizational performance.</p>
<h3>Steps in forecasting</h3>
<p>There are six steps in business forecasting. They are given below-</p>
<ul>
<li><strong>Identify the problem:</strong><span> </span>This is the most difficult step of forecasting. Defining the problem carefully requires an understanding of the way the forecasts will be used.</li>
<li><strong>Collect information:</strong><span> </span>In this steps we collect information not data, because data may not be available if for example the forecast is aimed at a new product. The information comes essentially in two ways: the knowledge gathered by expert and from actual data.</li>
<li><strong>Performing a preliminary analysis:</strong><span> </span>An early analysis of data may tell us right away if the data usable or not. It also helps in choosing the model that best fit it.</li>
<li><strong>Choose a forecasting model:</strong><span> </span>Once all the information is collected and treated then we may choose the model that will give the best prediction possible. If we may not even have historical data then we have to use qualitative forecasting otherwise quantitative forecasting.</li>
<li><strong>Data analysis:</strong><span> </span>This step is very simple. After choosing the suitable model, run the data through it.</li>
<li><strong>Verify model performance:</strong><span> </span>Finally, we have to compare forecast to actual data.</li>
</ul>
<h3><span>Methods of business forecasting</span></h3>
<div><span>There are various important forecasting methods in time series analysis. They are-</span></div>
<div><ul>
<li><span>Historical analogy method</span></li>
<li><span>Field survey and opinion poll</span></li>
<li><span>Business barometers</span></li>
<li><span>Extrapolation</span></li>
<li><span><a rel="nofollow noopener" href="https://www.statisticalaid.com/regression-analysis-with-its-types-objectives-and-application/" target="_blank">Regression analysis</a></span></li>
<li><span><a rel="nofollow noopener" href="https://www.statisticalaid.com/an-intuitive-study-of-time-series-analysis/" target="_blank">Time series analysis</a></span></li>
<li><span>Exponential smoothing</span></li>
<li><span>Econometric model</span></li>
<li><span>Lead-lag analysis</span></li>
<li><span>Input-output analysis</span></li>
</ul>
</div>
<h3><span>Importance of forecasting</span></h3>
<div><ul>
<li><span><b>Formation of new business:</b> Forecasting is utmost important in setting up a new business. with the help of forecasting the promoter can find out whether he can succeed in new business, whether he can face the existing competition.</span></li>
<li><span><b>Estimation of financial requirements:</b> Financial estimates can be calculated in the light of probable sales and cost there of. How much capital is needed for expansion, development etc will depend upon accurate forecasting.</span></li>
<li><span><b>Correctness of management decision:</b> The correctness of management decisions to a great extent depends upon accurate forecasting. The forecasting is considered as the indispensable components of business, because it helps management to take correct decisions.</span></li>
<li><span><b>Plan formation:</b> The importance of correct forecasting apparent from the key role it plays in planning. Infact, planning under all circumstance and in all occassions involve a good deal of forecasting.</span></li>
<li><span><b>Success in business:</b> The accurate forecasting of sales helps to produce necessary raw materials on the basis of which many business activities are undertaken. It is difficult to decide as to how much production should be done. Thus the success of a business unit depends on the accurate forecasting.</span></li>
<li><span><b>Complete control:</b> Forecasting provides the information which helps in the achievement of effective control. The managers become aware of their weakness during forecasting and through implementing better effective control they can overcome these weakness.</span></li>
</ul>
<p></p>
<p><a href="https://www.statisticalaid.com/business-forecasting-definition-steps-modeling-and-importance/" target="_blank" rel="noopener">Source..</a></p>
</div>An Overview of Logistic Regression Analysistag:www.datasciencecentral.com,2021-07-06:6448529:BlogPost:10560372021-07-06T15:30:00.000ZMuhammad Touhidul Islamhttps://www.datasciencecentral.com/profile/MuhammadTouhidulIslam
<p class="has-medium-font-size"></p>
<div class="wp-block-image"><img alt="An Intuitive study of Logistic Regression Analysis" src="https://www.statisticalaid.com/wp-content/uploads/2021/05/tempsnip2.png"></img> <br></br><div class="code-block code-block-10" style="text-align: center;">Image Source: <a href="https://www.statisticalaid.com/an-intuitive-study-of-logistic-regression-analysis/" rel="noopener" target="_blank">Statistical Aid</a></div>
<div class="code-block code-block-10"></div>
<div class="code-block code-block-10">Logistic regression is a statistical technique to find the association between the categorical dependent…</div>
</div>
<p class="has-medium-font-size"></p>
<div class="wp-block-image"><img src="https://www.statisticalaid.com/wp-content/uploads/2021/05/tempsnip2.png" alt="An Intuitive study of Logistic Regression Analysis"/><br/><div class="code-block code-block-10" style="text-align: center;">Image Source: <a href="https://www.statisticalaid.com/an-intuitive-study-of-logistic-regression-analysis/" target="_blank" rel="noopener">Statistical Aid</a></div>
<div class="code-block code-block-10"></div>
<div class="code-block code-block-10">Logistic regression is a statistical technique to find the association between the categorical dependent (response)<span> </span><a href="https://www.statisticalaid.com/random-variable-and-its-types-with-properties/" target="_blank" rel="noopener">variable</a><span> </span>and one or more categorical or continuous independent (explanatory) variable.</div>
<div class="code-block code-block-10"></div>
<div class="code-block code-block-10"><span>We can define the regression model as,</span></div>
<div class="code-block code-block-10"><p class="has-medium-font-size">G(probability of event)=β<sub>0</sub>+β<sub>1</sub>x<sub>1</sub>+β<sub>2</sub>x<sub>2</sub>+…+β<sub>k</sub>x<sub>k</sub></p>
<p class="has-medium-font-size">We determine G using link function as following,</p>
<p class="has-medium-font-size">Y={1 ; β<sub>0</sub>+β<sub>1</sub>x<sub>1</sub>+ϵ>0</p>
<p class="has-medium-font-size">{0 ; else</p>
<p class="has-medium-font-size">There are three types of link fuction. They are,</p>
<ul class="has-medium-font-size">
<li>Logit</li>
<li>Normit (probit)</li>
<li>Gombit</li>
</ul>
<p></p>
<p> </p>
<div class="wp-block-image"><img src="https://www.statisticalaid.com/wp-content/uploads/2021/05/tempsnip.png" alt="An Intuitive study of Logistic Regression Analysis"/></div>
<h2 style="text-align: center;"><span style="font-size: 10pt;">Image Source: <a href="https://www.statisticalaid.com/" target="_blank" rel="noopener">Statistical Aid</a></span></h2>
<p></p>
<h2>Why we use logistic regression?</h2>
<p class="has-medium-font-size">We use it when there exists,</p>
<ul class="has-medium-font-size">
<li>One Categorical response variable</li>
<li>One or more explanatory variable.</li>
<li>No linear relationship between dependent and independent variables.</li>
</ul>
<h2>Assumptions of Logistic Regression</h2>
<ul class="has-medium-font-size">
<li>The dependent variable should be categorical (binary,<span> </span><a href="https://www.statisticalaid.com/levels-of-measurement-nominal-ordinal-interval-ratio-in-statistics/" target="_blank" rel="noopener">ordinal, nominal</a><span> </span>or count occurrences).</li>
<li>The predictor or independent variable should be continuous or categorical.</li>
<li>The correlation among the predictors or independent variable (multi-collinearity) should not be severe but there exists linearity of independent variables and log odds.</li>
<li>The data should be the representative part of population and record the data in the order its collected.</li>
<li>The model should provide a good fit of the data.</li>
</ul>
<h2>Logistic regression vs Linear regression</h2>
<ul class="has-medium-font-size">
<li>In the case of <a href="https://www.statisticalaid.com/regression-analysis-with-its-types-objectives-%20and-application/" target="_blank" rel="noopener">Linear Regressio</a>n, the outcome is continuous while in the case of logistic regression outcome is discrete (not continuous)</li>
<li>To perform linear regression, we require a linear relationship between the dependent and independent variables. But to perform Logit we do not require a linear relationship between the dependent and independent variables.</li>
<li>Linear Regression is all about fitting a straight line in the data while Logit is about fitting a curve to the data.</li>
<li>Linear Regression is a regression algorithm for Machine Learning while Logit is a classification Algorithm for machine learning.</li>
<li>Linear regression assumes Gaussian (or normal) distribution of the dependent variable. Logit assumes the binomial distribution of the dependent variable.</li>
</ul>
<p class="has-medium-font-size">*Logit=logistic regression</p>
<h2>Types</h2>
<p class="has-medium-font-size">There are four types of logistic regression. They are,</p>
<ul class="has-medium-font-size">
<li><strong>Binary logistic:</strong><span> </span>When the dependent variable has two categories and the characteristics are at two levels such as yes or no, pass or fail, high or low etc. then the regression is called binary logistic regression.</li>
<li><strong>Ordinal logistic:</strong><span> </span>When the dependent variable has three categories and the characteristics are at natural ordering of the levels such as survey results (disagree, neutral, agree) then the regression is called ordinal logistic regression.</li>
<li><strong>Nominal logistic:</strong><span> </span>When the dependent variable has three or more categories but the characteristics are not at natural ordering of the levels such as colors (red, blue, green) then the regression is called nominal logistic.</li>
<li><strong>Poisson logistic:</strong><span> </span>When the dependent variable has three or more categories but the characteristics are the number of time of an event occurs such as 0, 1, 2, 3, …, etc. then the regression is called Poisson logistic regression.</li>
</ul>
<p><a href="https://www.statisticalaid.com/an-intuitive-study-of-logistic-regression-analysis/" target="_blank" rel="noopener">Source...</a></p>
</div>
</div>An overview of Quadrat Samplingtag:www.datasciencecentral.com,2021-06-05:6448529:BlogPost:10528232021-06-05T15:00:00.000ZMuhammad Touhidul Islamhttps://www.datasciencecentral.com/profile/MuhammadTouhidulIslam
<p></p>
<div><a href="https://www.statisticalaid.com/2020/12/26/quadrat-sampling-application-with-advantages-and-disadvantages/?swcfpc=1" rel="noopener" target="_blank"></a><a href="https://1.bp.blogspot.com/-Ocd3zDBR5j4/X-ckVTv5OhI/AAAAAAAAA5U/GN1kyYk6BWA61rwsM8-2bwG7mo38H8hHACLcBGAsYHQ/s16000/quadrat.JPG" rel="noopener" target="_blank"><img class="align-full" src="https://1.bp.blogspot.com/-Ocd3zDBR5j4/X-ckVTv5OhI/AAAAAAAAA5U/GN1kyYk6BWA61rwsM8-2bwG7mo38H8hHACLcBGAsYHQ/s16000/quadrat.JPG?profile=RESIZE_710x" width="720"></img></a><div class="code-block code-block-10"><span style="font-size: 15.21px;"> Image source:…</span></div>
</div>
<p></p>
<div><a href="https://www.statisticalaid.com/2020/12/26/quadrat-sampling-application-with-advantages-and-disadvantages/?swcfpc=1" target="_blank" rel="noopener"></a><a href="https://1.bp.blogspot.com/-Ocd3zDBR5j4/X-ckVTv5OhI/AAAAAAAAA5U/GN1kyYk6BWA61rwsM8-2bwG7mo38H8hHACLcBGAsYHQ/s16000/quadrat.JPG" target="_blank" rel="noopener"><img src="https://1.bp.blogspot.com/-Ocd3zDBR5j4/X-ckVTv5OhI/AAAAAAAAA5U/GN1kyYk6BWA61rwsM8-2bwG7mo38H8hHACLcBGAsYHQ/s16000/quadrat.JPG?profile=RESIZE_710x" width="720" class="align-full"/></a><div class="code-block code-block-10"><span style="font-size: 15.21px;"> Image source: <a href="https://www.statisticalaid.com/quadrat-sampling-application-with-advantages-and-disadvantages/" target="_blank" rel="noopener">Statistical Aid</a></span></div>
</div>
<p></p>
<p><span>Quadrat <a href="https://www.statisticalaid.com/sampling-definition-examples-types-application-advantages-and-%20disadvantages/?swcfpc=1" target="_blank" rel="noopener">sampling </a></span><span>is a classic tool for the study of ecology, especially biodiversity</span><span>. It is an important method by which organisms in a certain proportion (sample) of the habitat are counted directly. It is used to estimate <a href="https://www.statisticalaid.com/population-vs-sample-in-statistics/?swcfpc=1" target="_blank" rel="noopener">population</a> abundance (number), density, frequency and <a href="https://www.statisticalaid.com/probability-distributions-in-statistics/?swcfpc=1" target="_blank" rel="noopener">distributions</a>.</span><span> The quadrat method has been widely used in plant studies. A quadrat is a four-sided figure which delimits the boundaries of a sample plot. The term quadrat is used more widely to include circular plots and other shapes.</span></p>
<p><span>Quadrat sampling methods are time-tested sampling techniques that are best suited for coastal areas where access to a habitat is relatively easy.</span></p>
<h3>Assumptions of quadratic sampling</h3>
<p><span>The quadrat <a href="https://www.statisticalaid.com/sampling-definition-examples-types-application-advantages-and-disadvantages/?swcfpc=1" target="_blank" rel="noopener">sampling method</a> has the following assumptions,</span></p>
<ul>
<li class="code-block code-block-1"><span>The number of individuals in each quadrat is counted.</span></li>
<li class="code-block code-block-1"><span>The size of the quadrats is known.</span></li>
<li class="code-block code-block-1"><span>The quadrat samples are representative of the study area as a whole.</span></li>
</ul>
<h3><b><span>Advantages</span></b></h3>
<p><span>Some advantages are given below-</span></p>
<ul>
<li><span>It sampling is easy to use, inexpensive.</span></li>
<li><span>It is suitable for studying plants, slow-moving animals and faster-moving animals with a small range.</span></li>
<li><span>It requires the researcher to perform the work in the field and, without care.</span></li>
<li><span>It measures abundance and needed cheap equipment.</span></li>
</ul>
<h3><b><span>Disadvantages</span></b></h3>
<p><span>Some disadvantages are given below-</span></p>
<p><span>Quadrat sampling is not useful for studying very fast-moving animals which are not stay within the quadrat boundaries.</span></p>
<ul>
<li><span>There exists biasness in favor of slow moving taxa.</span></li>
<li><span>Collect only taxa that are present in the sampling time and not buried too deeper in sediment.</span></li>
<li><span>It is a low estimate of taxonomic richness and assemblage composition.</span></li>
<li><span>It is also a low detectability of among-site differences in assemblage composition.</span></li>
<li><span>Some animals may experience harm if the scientist collects the population within the quadrat rather than studying it in the field.</span></li>
</ul>
<p><a href="https://www.statisticalaid.com/quadrat-sampling-application-with-advantages-and-disadvantages" target="_blank" rel="noopener">Source</a></p>Levels of Measurement (Nominal, Ordinal, Interval, Ratio) in Statisticstag:www.datasciencecentral.com,2021-02-26:6448529:BlogPost:10380452021-02-26T06:14:19.000ZMuhammad Touhidul Islamhttps://www.datasciencecentral.com/profile/MuhammadTouhidulIslam
<h3><img alt="nominal, ordinal, interval, ratio" src="https://1.bp.blogspot.com/-H9leXc2bg6E/YCg_7SzwzCI/AAAAAAAAA-I/EuJ-Mvi_ans9p3hsFbB7YVBGFGSIbnWDQCLcBGAsYHQ/s16000/me.JPG"></img></h3>
<p style="text-align: center;">Image Source: <a href="https://www.statisticalaid.com/" rel="noopener" target="_blank">Statistical Aid: A School of Statistics</a></p>
<h3>Definition</h3>
<p style="font-weight: 400;">In<span> </span><a href="https://www.blogger.com/blog/post/edit/3601041159698509340/6721085136288217763#">statistics</a>, the<span> </span><a href="https://www.blogger.com/blog/post/edit/3601041159698509340/6721085136288217763#">statistical…</a></p>
<h3><img src="https://1.bp.blogspot.com/-H9leXc2bg6E/YCg_7SzwzCI/AAAAAAAAA-I/EuJ-Mvi_ans9p3hsFbB7YVBGFGSIbnWDQCLcBGAsYHQ/s16000/me.JPG" alt="nominal, ordinal, interval, ratio"/></h3>
<p style="text-align: center;">Image Source: <a href="https://www.statisticalaid.com/" target="_blank" rel="noopener">Statistical Aid: A School of Statistics</a></p>
<h3>Definition</h3>
<p style="font-weight: 400;">In<span> </span><a href="https://www.blogger.com/blog/post/edit/3601041159698509340/6721085136288217763#">statistics</a>, the<span> </span><a href="https://www.blogger.com/blog/post/edit/3601041159698509340/6721085136288217763#">statistical data</a><span> </span>whether qualitative or quantitative, are generated or obtain through some measurement or some observational process. Measurement is essentially the task of assigning numbers to observations according to certain rules. The way in which the numbers are assigned to observations determines the scale of measurement being used. There are four level of measurements in statistics. They are-</p>
<ul style="font-weight: 400;">
<li>Nominal Level</li>
<li>Ordinal Level</li>
<li>Interval Level</li>
<li>Ratio Level</li>
</ul>
<h3>Nominal Level of Measurement</h3>
<p style="font-weight: 400;">All qualitative measurements are nominal, regardless of whether the categories are designed by names (male, female) or numerals (bank account no., id no etc.). In nominal level of measurement, the categories differ from one another only in names. In other words, one category of a characteristic is not higher or lower, greater or smaller than the other category. For example, gender (male or female), religion (Muslim, Hindu or others), etc. The nominal level of measurement gives rise to nominal data. </p>
<p style="font-weight: 400;">We must ensure that the categories of nominal level of measurement must be follow some important properties. They are-</p>
<ul style="font-weight: 400;">
<li>The categories are must be homogeneous.</li>
<li>The categories are mutually exclusive and exhaustive.</li>
</ul>
<h3>Ordinal level of Measurement</h3>
<p style="font-weight: 400;">In ordinal level of measurement there exist an ordered relationship among the categories. For example, we use less, more, higher, greater, lower etc. for define the categories such as costly, less profitable, more difficult etc. More precisely, the relationships are expressed in terms of the algebra of inequalities: a less than b (a<b) or is greater than b (a>b). So, the socio-economic status (low, medium, high), academic performance (poor, good, very good), agreement on some issue (strongly disagree, disagree, agree, strongly agree) are some practical<span> </span><a href="https://www.blogger.com/blog/post/edit/3601041159698509340/6721085136288217763#">variable</a><span> </span>of ordinal level of measurement. Ordinal level of measurement gives ordinal data. </p>
<p style="font-weight: 400;">Ordinal level maintains some important properties as,</p>
<ul style="font-weight: 400;">
<li>The categories are distinct, mutually exclusive and exhaustive.</li>
<li>The categories are possible to be ranked or ordered.</li>
<li>The distance from one category to the other is not necessarily constant.</li>
</ul>
<p style="font-weight: 400;"><span> </span></p>
<h3>Interval Level of Measurement</h3>
<p style="font-weight: 400;">The interval level of measurement includes all the properties of the nominal and ordinal level of measurement but it has an additional property that the difference (interval) between the values is known and constant size. In this measurement 0 is used as an arbitrary point. The interval measurement scale has some important properties. They are-</p>
<ul style="font-weight: 400;">
<li>The data classifications are mutually exclusive and exhaustive.</li>
<li>The data can be meaningfully ranked or ordered.</li>
<li>The difference between the categories is known and constant.</li>
</ul>
<p style="font-weight: 400;">For example, in Gregorian calendar 0 is used to separate B.C. and A.D. We refer to the years before 0 as B.C. and to those after 0 as A.D. Incidentally 0 is a hypothetical date in the Gregorian calendar because there never was a year 0.</p>
<p style="font-weight: 400;">Another example, a thermometer measures temperature in degrees, which are of the same size at any point of the scale. The difference between 20<sup>0</sup>C and 21<sup>0</sup>C is the same as the difference between 12<sup>0</sup>C and 13<sup>0</sup>C. The temperature 12<sup>0</sup>C, 13<sup>0</sup>C, 20<sup>0</sup>C, 21<sup>0</sup>C can be ranked and the differences between the temperatures can easily be determined. When the temperature is 0<sup>0</sup>C, it means not the absence of heat but it is cold. In fact, 0<sup>0</sup>C is equal to 32<sup>0</sup>F.</p>
<h3>Ratio level of Measurement</h3>
<p style="font-weight: 400;">In ratio level, there is an ordered relationship among the categories where exist an absolute zero and follow the all properties of nominal level of measurement. All quantitative data fall under the ratio level of measurement. For example, wages, stock price, sales value, age, height, weight, etc. are the<span> </span><a href="https://www.blogger.com/blog/post/edit/3601041159698509340/6721085136288217763#">real life variable</a><span> </span>of ratio level measurement. If we say the sales value is 0, then there is no sale.</p>
<p style="font-weight: 400;">There exist some important properties in this level. They are-</p>
<ul style="font-weight: 400;">
<li>The categories are mutually exclusive and exhaustive.</li>
<li>The categories can be ordered or ranked.</li>
<li>The differences among the categories are constant.</li>
<li>There exist an absolute zero point.</li>
</ul>
<p style="font-weight: 400;"><span><a href="https://www.statisticalaid.com/2021/02/levels-of-measurement-nominal-ordinal.html" target="_blank" rel="noopener">(Source)</a></span></p>An Overview of Simple Random Sampling (SRS)tag:www.datasciencecentral.com,2021-02-13:6448529:BlogPost:10270762021-02-13T10:28:52.000ZMuhammad Touhidul Islamhttps://www.datasciencecentral.com/profile/MuhammadTouhidulIslam
<p><img alt="simple random sampling by statisticalaid.com" src="https://1.bp.blogspot.com/-c2MaG3V2rt4/XitAgHShF2I/AAAAAAAAAVk/7q6EysvuTmABChycq7MbGC_NMhA6aqS0ACLcBGAsYHQ/s16000/Capture.PNG"></img></p>
<p style="text-align: center;">Image Source: <a href="https://www.statisticalaid.com/2020/03/simple-random-sampling.html" rel="noopener" target="_blank">Statistical Aid: A School of Statistics</a></p>
<h3><strong>Simple random sampling</strong></h3>
<p style="font-weight: 400;">Simple random<span> </span><a href="https://www.statisticalaid.com/2020/01/sampling-definition.html">sampling</a><span> </span>is considered the easiest and most popular method of<span> …</span></p>
<p><img src="https://1.bp.blogspot.com/-c2MaG3V2rt4/XitAgHShF2I/AAAAAAAAAVk/7q6EysvuTmABChycq7MbGC_NMhA6aqS0ACLcBGAsYHQ/s16000/Capture.PNG" alt="simple random sampling by statisticalaid.com"/></p>
<p style="text-align: center;">Image Source: <a href="https://www.statisticalaid.com/2020/03/simple-random-sampling.html" target="_blank" rel="noopener">Statistical Aid: A School of Statistics</a></p>
<h3><strong>Simple random sampling</strong></h3>
<p style="font-weight: 400;">Simple random<span> </span><a href="https://www.statisticalaid.com/2020/01/sampling-definition.html">sampling</a><span> </span>is considered the easiest and most popular method of<span> </span><a href="https://www.statisticalaid.com/2020/01/probability-sampling-with.html">probability sampling</a>. To perform simple random sampling, all a researcher must do is ensure that all members of the<span> </span><a href="https://www.statisticalaid.com/2018/10/population-sample-in-statistics.html">population</a><span> </span>are included in a master list, and that subjects are then selected randomly from this master list.</p>
<p style="font-weight: 400;">While simple random sampling creates<span> </span><a href="https://www.statisticalaid.com/2018/10/population-sample-in-statistics.html">samples</a><span> </span>that are highly representative of the population, it can be time consuming and tedious when creating large samples. </p>
<p style="font-weight: 400;"><strong>The following 8-step procedure may be followed in drawing a simple random sample of n units from a population of N units.</strong></p>
<ul style="font-weight: 400;">
<li> <span> </span>Assign serial numbers to the units in the population from 1 through N.</li>
<li> Decide on the random number table to be used.</li>
<li> Choose an N-digit random number from any point in the random number table.</li>
<li> If this random number is less than or equal to N, this is your first selected unit.</li>
<li> Move on to the next random number not exceeding N, vertically, horizontally or in any other direction systematically and choose your second unit.</li>
<li> If at any stage of your selection, the random number chosen exceeds N, discard it and choose the next random number.</li>
<li> If, further, any random number is repeated, it must also be discarded and be replaced by a fresh random number appearing next.</li>
<li> The process stops once you arrive at your desired sample size.</li>
</ul>
<p style="font-weight: 400;"><strong>There are two approaches that aim to minimize any biases in the process of simple random sampling:</strong></p>
<ul>
<li style="font-weight: 400;"><a href="https://www.statisticalaid.com/2020/03/simple-random-sampling.html" target="_blank" rel="noopener">Methods of lottery</a></li>
<li style="font-weight: 400;"><a href="https://www.statisticalaid.com/2020/03/simple-random-sampling.html" target="_blank" rel="noopener">Random number table method</a></li>
</ul>
<p style="font-weight: 400;"><strong>Application of simple random sampling</strong></p>
<ul style="font-weight: 400;">
<li> A list of all members of population is prepared. Each element is marked with a specific number (suppose from 1 to <em>N</em>).</li>
<li> <em>n </em>items are chosen among a population size of <em>N. </em>This can be done either with the use of random number tables or random number generator software.</li>
<li> The Aromatic Company is planning to conduct a study to estimate the proportion of toilet soap users who prefer a certain color or flavor of their product. A simple random sample of customers may be used for this purpose. It is assumed in this case that a list (sampling frame) of the consumers is available to the research team.</li>
<li> A forester in Chittagong Hill Tracts may wish to estimate the volume of timber or proportion of diseased trees in a forest by se geographic points in the area covered by the forest and then attaching a plot of fixed size and shape to that point. All the trees within the sample plots may be studied. But again the basic design is a simple random sample.</li>
</ul>
<p><b><span>Advantages of Simple Random Sampling</span></b></p>
<ul>
<li><span>It is a fair method of sampling and if applied appropriately it helps to reduce any bias involved as compared to any other sampling method involved.</span></li>
<li><span>Since it involves a large sample frame it is usually easy to pick smaller sample size from the existing larger population.</span></li>
<li><span>The person who is conducting the research doesn’t need to have a prior knowledge of the data being collected. One can simply ask a question to gather the researcher need not be a subject expert.</span></li>
<li><span>This sampling method is a very basic method of collecting the data. There is no technical knowledge required and need basic listening and recording skills....<a href="https://www.statisticalaid.com/2020/03/simple-random-sampling.html" target="_blank" rel="noopener">(more)</a></span></li>
</ul>
<p><a href="https://www.statisticalaid.com/" target="_blank" rel="noopener">(Source)</a></p>Statistical Hypothesis Testing: Step by Steptag:www.datasciencecentral.com,2021-02-11:6448529:BlogPost:10260482021-02-11T21:58:31.000ZMuhammad Touhidul Islamhttps://www.datasciencecentral.com/profile/MuhammadTouhidulIslam
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<span> Image Source: <a href="https://www.statisticalaid.com/" target="_blank" rel="noopener">Statistical Aid: A School of Statistics</a><br/></span>
<h2><span>What is hypothesis testing?</span></h2>
<p><span>In <a href="https://www.statisticalaid.com/2018/10/what-do-you-mean-by-statistic.html" target="_blank" rel="noopener">statistics</a>, we may divide statistical inference into two major part: one is estimation and another is hypothesis testing. Before hypothesis testing we must know about hypothesis. so we can define hypothesi as below-</span></p>
<p><span>A statistical hypothesis is a statement about a <a href="https://www.statisticalaid.com/2018/10/population-sample-in-statistics.html" target="_blank" rel="noopener">population</a> which we want to verify on the basis of information which contained in a <a href="https://www.statisticalaid.com/2018/10/population-sample-in-statistics.html" target="_blank" rel="noopener">sample</a>.</span></p>
<p></p>
<p><strong>Example of statistical hypothesis</strong></p>
<div><span> </span></div>
<p><span>Few examples of statistical hypothesis related to our daily life are given below-</span></p>
<ul>
<li><span>The court assumes that the indicted person is innocent.</span></li>
<li><span>A teacher assumes that 80% of the student of his college is from a lower-middle-class family. </span></li>
<li><span>A doctor assumes that 3D(Diet, Dose, Discipline) is 95% effective to the diabetes patient.</span></li>
<li><span>A beverage company claims that its new cold drinks are superior to the other drinks available in the market, etc.</span></li>
</ul>
<div><span> </span></div>
<p><span>A statistical test mainly involves four steps:</span></p>
<ul>
<li><span>Evolving a test <a href="https://www.statisticalaid.com/2018/10/population-sample-in-statistics.html" target="_blank" rel="noopener">statistic</a></span></li>
<li><span>To know the sampling distribution of the test statistic</span></li>
<li><span>Selling of hypotheses testing conventions</span></li>
<li><span>Establishing a decision rule that leads to an inductive inference about the probable truth. </span></li>
</ul>
<div><span> </span></div>
<h3><span>Types of statistical hypothesis</span></h3>
<ul>
<li><span>Null hypothesis</span></li>
<li><span>Alternative hypothesis</span></li>
</ul>
<div><span> </span></div>
<h3><strong><span>Null hypothesis</span></strong></h3>
<div><strong><span> </span></strong></div>
<p><span>A null hypothesis is a statement, which tells us that no difference exists between the parameter and the statistic being compared to it. According to Fisher, any hypothesis tested for its possible rejection is called a null hypothesis and is denoted by <em>H0.</em></span></p>
<h3><strong><span>Alternative hypothesis</span></strong></h3>
<div><strong><span> </span></strong></div>
<p><span>The alternative hypothesis is the logical opposite of the null hypothesis. The rejection of the null hypothesis leads to the acceptance of the alternative hypothesis. It is denoted by H1.</span></p>
<p><span>For example, with a coin-tossing experiment, the null and alternative hypothesis may be formed as,</span></p>
<p><span>H0: the coin is unbiased.</span></p>
<p><span>H1: the coin is biased.</span></p>
<p><span> </span></p>
<p><span>Depending on the population distribution, the statistical hypothesis are two types,</span></p>
<ul>
<li><span><strong>Simple hypothesis:</strong>when a hypothesis completely specifies the distribution of the population, then the hypothesis is called a simple hypothesis.</span></li>
<li><span><strong>Composite hypothesis:</strong> when a hypothesis does not completely specify the distribution of the population, then the hypothesis is called a composite hypothesis...<a href="https://www.statisticalaid.com/2020/12/statistical-hypothesis-testing.html" target="_blank" rel="noopener">(Source)</a></span></li>
</ul>
</div>
</div>
</div>
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</div>An Intuitive Study of Time Series Analysistag:www.datasciencecentral.com,2021-02-09:6448529:BlogPost:10239712021-02-09T14:47:29.000ZMuhammad Touhidul Islamhttps://www.datasciencecentral.com/profile/MuhammadTouhidulIslam
<p><img alt="Components of time series" src="https://1.bp.blogspot.com/-1HlXUEzA3To/YBvJaXtzafI/AAAAAAAAA8k/HF7YAMLwQrQ_2724NVAleO7aSyj98vYmACLcBGAsYHQ/s16000/ts.JPG"></img></p>
<p style="text-align: center;">Image source: <a href="https://www.statisticalaid.com/" rel="noopener" target="_blank">Statistical Aid: A School of statistics</a></p>
<p></p>
<h2>Time series data</h2>
<p style="font-weight: 400;">A time series data is a set of observation on the value that a<span> </span><a href="https://www.statisticalaid.com/2020/12/random-variable.html">variable</a><span> </span>takes of different time, such data may be collected at regular time intervals…</p>
<p><img src="https://1.bp.blogspot.com/-1HlXUEzA3To/YBvJaXtzafI/AAAAAAAAA8k/HF7YAMLwQrQ_2724NVAleO7aSyj98vYmACLcBGAsYHQ/s16000/ts.JPG" alt="Components of time series"/></p>
<p style="text-align: center;">Image source: <a href="https://www.statisticalaid.com/" target="_blank" rel="noopener">Statistical Aid: A School of statistics</a></p>
<p></p>
<h2>Time series data</h2>
<p style="font-weight: 400;">A time series data is a set of observation on the value that a<span> </span><a href="https://www.statisticalaid.com/2020/12/random-variable.html">variable</a><span> </span>takes of different time, such data may be collected at regular time intervals such as daily stock price, monthly money supply figures, annual GDP etc. Time series data have a natural temporal ordering. This makes time series analysis distinct from other common data analysis problems in which there is no natural order of the observation. In simple word we can say, the data which are collected in according to time is called time series data.</p>
<p style="font-weight: 400;">On the other hand, the data which are collected by observing many subject at the same point of time is called cross sectional data.</p>
<h3>Time series analysis</h3>
<p style="font-weight: 400;">A time series is a set of observations measured at time or space intervals arranged in chronological order. For instance, the yearly demand of a commodity, weekly prices of an item, food production in India from year to year, etc. Many economists and statisticians have defined time series in different words. Some of them are quoted below:</p>
<p style="font-weight: 400;"><strong>Wessel and Wellet:</strong><span> </span>When quantitative data are arranged in the order of their occurrence, the resulting statistical series is called a time series.</p>
<p style="font-weight: 400;"><strong>Moris Hamburg:</strong><span> </span>A time series is a set of statistical observations arranged in chronological order.</p>
<p style="font-weight: 400;"><strong>Patterson:</strong><span> </span>A time series consists of<span> </span><a href="https://www.statisticalaid.com/2020/11/statistical-data-statistical-aid.html">statistical data</a><span> </span>which are collected, recorded or observed over successive increments.</p>
<p style="font-weight: 400;"><strong>Ya-Lun-Chou:</strong><span> </span>A time series may be defined as a collection of magnitudes belonging to different time periods, of some variable or composite of variables such as production of steel, per capita income, gross national product, price of tobacco or index of industrial production.</p>
<p style="font-weight: 400;"><strong>Cecil H. Meyers:</strong><span> </span>A time series may be defined as a sequence of repeated measurements of a variable made periodically through time.</p>
<p style="font-weight: 400;"><strong>Werner Z. Hirsch:</strong><span> </span>A time series is a sequence of values of the same variate corresponding to successive points of time.</p>
<p style="font-weight: 400;"><strong>Spiegel:</strong><span> </span>A time series is a set of observations taken at specified times, usually at equal intervals.</p>
<p style="font-weight: 400;"> So, time series analysis is a statistical technique which deals with the time series data or trend.</p>
<h3>Objectives of time series analysis</h3>
<ul style="font-weight: 400;">
<li>To identify the pattern, trend and isolate the influencing factor or effects.</li>
<li>To apply the idea obtained from analyzing the pattern of time series data for future planning and control.</li>
</ul>
<p style="font-weight: 400;"></p>
<h3>Importance of time series analysis</h3>
<ul style="font-weight: 400;">
<li>This is the most popular and so far the effective method for business forecasting.</li>
<li>It helps in understanding the past behavior of economic process and in predicting the future.</li>
<li>It helps in planning future operations.</li>
<li>It helps in evaluating current achievement.</li>
</ul>
<h3>Components of time series</h3>
<p style="font-weight: 400;">There are four important component or elements exist in time series analysis. They are-</p>
<p style="font-weight: 400;"><strong>Secular trend (T<sub>t</sub>):</strong><span> </span>Many time series met in practice exhibit a tendency of either growing or reducing fairly steadily over time. This tendency of time series data over a long period of time is called secular trend. Some series increase slowly, some fast, others decrease at varying rate and some remain constant for long period of time. There are several factors that affect trend in time series data such as population, technology, institution and culture of the study area etc.</p>
<p style="font-weight: 400;"><strong>Cyclical components (C<sub>t</sub>):</strong><span> </span>It generally refers the long term oscillations about a trend line. The cycler may or may not be periodic and the periodic of oscillation is usually more than 1 year. The cyclical movement are the so called business cycler representing intervals of prosperity, recession, depression, recovery and may last from seven to eleven years.</p>
<p style="font-weight: 400;"><strong>Seasonal components (S<sub>t</sub>):</strong><span> </span>Seasonal movement are periodic and regular in a time series with period less than 1 year. In a time series, seasonal movement refers to identical or almost identical patterns of movements during corresponding months of successive year. The vary name suggest that weather plays an important role in such movement.</p>
<p style="font-weight: 400;"><strong>Irregular components (I<sub>t</sub>):</strong><span> </span>Apart from the components, the time series contains another factor called irregular fluctuations which are purely random, erratic, unforeseen, unpredictable and are due to some irregular circumstance which are beyond the control of human hand but at the same time are a part of our system such as earth quakes, revolution, flood etc.</p>
<h3>Measurement of trend components</h3>
<p style="font-weight: 400;">To measure the four components of time series, we use the following methods-</p>
<ul style="font-weight: 400;">
<li>Graphic or free hand curve method.</li>
<li>Semi-average method.</li>
<li>Least square method.</li>
<li>Moving average method.</li>
</ul>
<h3>Drawbacks of time series analysis</h3>
<p style="font-weight: 400;">The drawbacks of the time series analysis can be summarized as follows-</p>
<ul style="font-weight: 400;">
<li>The conclusions drawn on the basis of time series analysis are not cent per cent true.</li>
<li>Time series analysis is unable to fully adjust the influences affecting a time series like customs, climate, policy changes, etc.</li>
<li>The complex forces affecting a time series existing at certain period may nut he having the same complex forces in future. Hence, the forecasts may not hold true.<a href="https://www.statisticalaid.com/2021/02/time-series-analysis.html" target="_blank" rel="noopener">Source</a></li>
</ul>Skewness and Kurtosis in statisticstag:www.datasciencecentral.com,2021-02-08:6448529:BlogPost:10178852021-02-08T19:00:00.000ZMuhammad Touhidul Islamhttps://www.datasciencecentral.com/profile/MuhammadTouhidulIslam
<div><font size="4"><img alt="Skewness and kurtosis by statisticalaid.com" src="https://1.bp.blogspot.com/-zIOkeB_6Cls/X9fNwKkcS2I/AAAAAAAAA1w/XVVoH8RtVnAh76N4Fmv3YYshhu4kZfPHACLcBGAsYHQ/s16000/skw.png"></img></font></div>
<div><font size="4"> Image Source: <a href="https://www.statisticalaid.com/" rel="noopener" target="_blank">Statistical Aid: A School of Statistics</a></font></div>
<div><font size="4">Literally, skewness means the 'lack of symmetry'. We study skewness to have an idea about the shape of the curve which we can draw with the help of the given data. A<span> …</span></font></div>
<div><font size="4"><img src="https://1.bp.blogspot.com/-zIOkeB_6Cls/X9fNwKkcS2I/AAAAAAAAA1w/XVVoH8RtVnAh76N4Fmv3YYshhu4kZfPHACLcBGAsYHQ/s16000/skw.png" alt="Skewness and kurtosis by statisticalaid.com"/></font></div>
<div><font size="4"> Image Source: <a href="https://www.statisticalaid.com/" target="_blank" rel="noopener">Statistical Aid: A School of Statistics</a></font></div>
<div><font size="4">Literally, skewness means the 'lack of symmetry'. We study skewness to have an idea about the shape of the curve which we can draw with the help of the given data. A<span> </span><a href="https://www.blogger.com/blog/post/edit/3601041159698509340/1482876214819496319#">distribution</a><span> </span>is said to be skewed if-</font></div>
<div><ul>
<li><font size="4"><a href="https://www.blogger.com/blog/post/edit/3601041159698509340/1482876214819496319#">Mean, median, mode</a><span> </span>fall at different points, i.e, Mean ≠ Median ≠ Mode.</font></li>
<li><font size="4">Quartiles are not equidistant from median.</font></li>
<li><font size="4">The curve drawn with the help of the given data is not symmetrical but stretched more to one side than the other.</font></li>
</ul>
<p><font size="4">The lack of symmetry in a distribution is always determined with reference to a<span> </span><a href="https://www.blogger.com/blog/post/edit/3601041159698509340/1482876214819496319#">normal distribution</a>, which is always symmetrical. Any departure of a distribution from symmetry leads to an asymmetric distribution and in such cases, we call this distribution as skewed. The skewness may be either positive or negative. Absence of skewness makes the distribution symmetrical.</font></p>
</div>
<div><font size="4">It is important to emphasize that skewness of a distribution cannot be determined simply by inspection. If we understand the differences between the mean, median and the mode, we should be able to suggest a direction of skew.We can define the skewness of a frequency distribution in three different shapes as following-</font></div>
<div><font size="4"><b> </b></font></div>
<div><font size="4"><b>(1). Symmetrical distributions</b></font></div>
<div><font size="4">This type of distribution is known as normal distribution. We can obtain this distribution with height, weight, iq score and many other<span> </span><a href="https://www.blogger.com/blog/post/edit/3601041159698509340/1482876214819496319#">random variable</a><span> </span>from real life data. An important characteristics of such distribution is that the mean, median and mode have same value.</font></div>
<div><font size="4"> </font></div>
<div><div class="separator"><a href="https://www.blogger.com/blog/post/edit/3601041159698509340/1482876214819496319#"><img alt="symmetrical distribution by statisticalaid.com" border="0" src="https://1.bp.blogspot.com/-gccMKy8HY08/YBaiEawwjiI/AAAAAAAAA7k/PjRSFrlR1okhRy6CrB0wgocqAp6-LWwsgCLcBGAsYHQ/s16000/1.JPG" title="symmetrical distribution"/></a></div>
<br/> <font size="4"><br/></font></div>
<div><font size="4"><b>(2). Positively skewed distributions</b></font></div>
<div><font size="4">In this distribution, the right tail is long which indicates the presence of extreme values at the positive end of the distribution. This pulls the mean to the right tail. this types of distribution is known as positively skewed distribution. This distributions occur with some real life variable such as family size, wages of the worker etc.</font></div>
<div><font size="4"> </font></div>
<div><div class="separator"><a href="https://www.blogger.com/blog/post/edit/3601041159698509340/1482876214819496319#"><img alt="Positively skewed distribution by statisticalaid.com" border="0" src="https://1.bp.blogspot.com/-DusW3C298vw/YBaiWo3SQ9I/AAAAAAAAA7s/Kq_v35M6NhEOsOlbVM9RTic3n59hT57WgCLcBGAsYHQ/s16000/2.JPG" title="Positively skewed distribution"/></a></div>
<br/> <font size="4"><br/></font></div>
<div><font size="4"><b>(3). Negatively skewed distributions</b></font></div>
<div><font size="4">In this types of distribution, the mean is pulled in the negative direction. This occurs in some real life variable such as daily maximum temperature for a month in winter.</font></div>
<div><font size="4"> </font></div>
<div><div class="separator"><a href="https://www.blogger.com/blog/post/edit/3601041159698509340/1482876214819496319#"><img alt="negatively skewed distribution by statisticalaid.com" border="0" src="https://1.bp.blogspot.com/-v3tYKu2wPLY/YBaippnDnEI/AAAAAAAAA70/HoG1ZGcjeBYdsaixVuBDciOYe7N6JiChACLcBGAsYHQ/s16000/3.JPG" title="negatively skewed distribution"/></a></div>
</div>
<h3><font size="4">Measures of skewness</font></h3>
<div><font size="4">We can simply measure the skewness using pearson's coefficient of skewness as below-</font></div>
<div><font size="4"> </font></div>
<div><font size="4"><b>Skewness(p)= (Mean-Mode) / Standard Deviation</b></font></div>
<div><font size="4"> </font></div>
<div><font size="4">We can make following decissions from the pearson's coefficient of skewness as following-</font></div>
<div><ul>
<li><font size="4">If mean > mode, the distribution is positively skewed.</font></li>
<li><font size="4">If mean < mode, the distribution is negatively skewed.</font></li>
<li><font size="4">If mean = mode, the distribution is not skewed or symmetrical.</font></li>
</ul>
</div>
<div><font size="5">In some case, mode cannot be uniquely defined, so we cannot apply the above formula. For alternative we use the following formula pearson's coefficient of skewness-</font></div>
<div><font size="4"> </font></div>
<div><font size="4"><b>Skewness(p)= 3(Mean-Mode) / Standard Deviation</b></font></div>
<div><font size="4"> </font></div>
<div><font size="4">We can also mesure the skewness using moments. The formula of skewness using moments is following-</font></div>
<div><font size="4"> </font></div>
<div><a href="https://www.blogger.com/blog/post/edit/3601041159698509340/1482876214819496319#"><font size="4"><img src="https://latex.codecogs.com/gif.latex?/beta&space;_{1}=/frac{/mu&space;_{3}^{2}}{/mu&space;_{2}^{3}};&space;where&space;/beta&space;_{1}=skewness,/mu&space;_{3}=3rdCentralMoment,/mu&space;_{2}=2ndCentralMoment" title="\beta _{1}=\frac{\mu _{3}^{2}}{\mu _{2}^{3}}; where \beta _{1}=skewness,\mu _{3}=3rdCentralMoment,\mu _{2}=2ndCentralMoment"/></font></a></div>
<div><font size="4"> </font></div>
<div><font size="4">And Karl pearson suggest skewness as,</font></div>
<div><font size="4"> </font></div>
<div><a href="https://www.blogger.com/blog/post/edit/3601041159698509340/1482876214819496319#"><font size="4"><b><img src="https://latex.codecogs.com/gif.latex?/gamma&space;_{1}=/sqrt{/frac{/mu&space;_{3}^{2}}{/mu&space;_{2}^{3}}};&space;where&space;/gamma&space;_{1}=skewness,/mu&space;_{3}=3rdCentralMoment,/mu&space;_{2}=2ndCentralMoment" title="\gamma _{1}=\sqrt{\frac{\mu _{3}^{2}}{\mu _{2}^{3}}}; where \gamma _{1}=skewness,\mu _{3}=3rdCentralMoment,\mu _{2}=2ndCentralMoment"/></b></font></a></div>
<h3><a href="https://www.statisticalaid.com/2021/01/skewness-and-kurtosis-statistical-aid.html" target="_blank" rel="noopener">(kurtosis)</a></h3>Correlation Analysis definition, formula and step by step proceduretag:www.datasciencecentral.com,2021-02-07:6448529:BlogPost:10222352021-02-07T09:30:00.000ZMuhammad Touhidul Islamhttps://www.datasciencecentral.com/profile/MuhammadTouhidulIslam
<h2><span><a href="https://storage.ning.com/topology/rest/1.0/file/get/8532854671?profile=original" rel="noopener" target="_blank"><img class="align-full" src="https://storage.ning.com/topology/rest/1.0/file/get/8532854671?profile=RESIZE_710x" width="620"></img></a></span></h2>
<h2><span>Correlation Analysis</span></h2>
<p><span>The relationship between two or more <a href="https://www.statisticalaid.com/2020/12/random-variable.html" rel="noopener" target="_blank">random variables</a> are generally defined as the correlation. It is the major part of …</span></p>
<h2><span><a href="https://storage.ning.com/topology/rest/1.0/file/get/8532854671?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/8532854671?profile=RESIZE_710x" width="620" class="align-full"/></a></span></h2>
<h2><span>Correlation Analysis</span></h2>
<p><span>The relationship between two or more <a href="https://www.statisticalaid.com/2020/12/random-variable.html" target="_blank" rel="noopener">random variables</a> are generally defined as the correlation. It is the major part of <a href="https://www.statisticalaid.com/2020/02/bivariate-analysis-how-to-analyze-data.html" target="_blank" rel="noopener">bivariate analysis</a>. When variables are found to be related, we often want to know how close the relationship is. The study of the relationship is known as correlation analysis. The primary objective of correlation is to measure the strength or degree of linear association between two or more variables. For example, we may be interested in measuring the relationship between the-</span></p>
<ul>
<li><span>Height and weight of the people of certain area.</span></li>
<li><span>Ages of husband and their wives.</span></li>
<li><span>Amount of rice production and fertilizer.</span></li>
<li><span>Income and expenditure.</span></li>
<li><span>Total sales and experience of the sales persons..etc.</span></li>
</ul>
<h3><span>Correlation vs Regression</span></h3>
<p><span>The contradictions between <a href="https://www.statisticalaid.com/2018/11/what-is-standard-deviation-in.html" target="_blank" rel="noopener">regression</a> and correlation are given below-</span></p>
<p><span>In correlation, we are generally interested in the measurement of the linear relationship between two or more variables. On the other hand, <a href="https://www.statisticalaid.com/2018/11/what-is-standard-deviation-in.html" target="_blank" rel="noopener">regression analysis</a> doesn't asses such relationship.</span></p>
<p><span>In correlation analysis we consider any two or more variables. On the otherhand, in regression there must need one dependent and one or more independent variables. Here the dependent variable is stochastic or random variable and the independent or explanatory variable is fixed.</span></p>
<p><span>Correlation analysis provides a means of measuring the goodness of fit of the estimated regression line to the observed <a href="https://www.statisticalaid.com/2020/11/statistical-data-statistical-aid.html" target="_blank" rel="noopener">statistical data</a>. On the other hand, regression analysis doesn't provide any means to measure the goodness of fit but it tells about the average amount of change in the dependent variable to one unit change in the independent variable.</span></p>
<p><span><img src="https://1.bp.blogspot.com/-dLPWRVUzQsA/YBmawLAT-CI/AAAAAAAAA8M/HN3gZf7J92Yuf81QcIQedJx5RygWWfqBwCLcBGAsYHQ/s16000/correlation.JPG" alt="Correlation interpretation"/></span></p>
<h3><a href="https://www.statisticalaid.com/2021/02/correlation-analysis.html" target="_blank" rel="noopener">Measuring the Correlation</a></h3>