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Unit 1
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<h1 class="title toc-ignore">Lesson 2: The Statistical Process</h1>
</div>
<!-- Lesson Introduction Section Begin ---------------------------------->
<div id="LessonIntroduction" class="section level2">
<h2>Lesson Introduction</h2>
<div class="introduction">
<div class="figure">
<img src="Images/StepsAll.png" />
</div>
<p>Statistics are used in every aspect of society. From formal scientific studies to consumer ratings on product reviews, every statistical analysis follows a pattern we will call the Statistical Process. This process will be introduced in this lesson and will be used throughout the course.</p>
<div style="padding-left:20px;width:80%;">
<table>
<thead>
<tr class="header">
<th>The Five Steps of the Statistical Process</th>
<th align="left"></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td><img src="Images/Step1.png" width="100"></td>
<td align="left"><strong>D</strong>esign the Study</td>
</tr>
<tr class="even">
<td><img src="Images/Step2.png" width="100"></td>
<td align="left"><strong>C</strong>ollect the Data</td>
</tr>
<tr class="odd">
<td><img src="Images/Step3.png" width="100"></td>
<td align="left"><strong>D</strong>escribe the Data</td>
</tr>
<tr class="even">
<td><img src="Images/Step4.png" width="100"></td>
<td align="left"><strong>M</strong>ake Inference</td>
</tr>
<tr class="odd">
<td><img src="Images/Step5.png" width="100"></td>
<td align="left"><strong>T</strong>ake Action</td>
</tr>
</tbody>
</table>
</div>
<p>The above icons have a letter and an image to help you remember each of the five steps.</p>
</div>
<!-- Lesson Outcomes Section Begin ------------------------------------->
</div>
<div id="LessonOutcomes" class="section level2">
<h2>Lesson Outcomes</h2>
<div class="outcomes">
<p>By the end of this lesson you should be able to do the following.</p>
<ul>
<li><a href="#LessonIntroduction">State the five steps of the Statistical Process.</a></li>
<li><a href="#TypesOfStudies">Distinguish between an observational study and an experiment.</a></li>
<li><a href="#ParametersStatistics">Distinguish between a population and a sample.</a></li>
<li><a href="#TypesOfVariables">Distinguish between a categorical and a quantitative variable.</a></li>
<li><a href="#ParametersStatistics">Distinguish between a parameter and a statistic.</a></li>
<li><a href="#Sampling">Distinguish between and give an example of each of the following sampling schemes:</a>
<ul>
<li><a href="#SRS">Simple random sampling</a></li>
<li><a href="#Stratified">Stratified random sampling</a></li>
<li><a href="#Systematic">Systematic random sampling</a></li>
<li><a href="#Cluster">Cluster random sampling</a></li>
<li><a href="#Convenience">Convenience sampling</a></li>
</ul></li>
<li><a href="#Randomness">Explain the significance of using a random sample.</a></li>
</ul>
<p>The following Case Study will show you how these outcomes apply to a real life scenario.</p>
</div>
<!-- Case Study Section Begin ------------------------------------------->
</div>
<div id="casestudy" class="section level2">
<h2>Case Study: Daniel Can Discern More Truth</h2>
<div class=casestudy>
<p><strong>Case Study Objective:</strong> <a href="#LessonOutcomes">Demonstrate the five steps of the Statistical Process.</a></p>
<hr />
<iframe class="casestudyimage" src="https://www.youtube.com/embed/aSDdRqQy8Pk" frameborder="0" allowfullscreen>
</iframe>
<p>After taking Israel captive, Babylon’s King Nebuchadnezzar asked his chief officer to bring Israelite children who were “well favoured, and skilful in all wisdom, and cunning in knowledge, and understanding science…to stand in the king’s palaces” <a href="https://www.lds.org/scriptures/ot/dan/1.4?lang=eng#3">(Daniel 1:4)</a>. To aid their preparation, Nebuchadnezzar planned to feed them his meat and wine for three years <a href="https://www.lds.org/scriptures/ot/dan/1.5?lang=eng#4">(Daniel 1:5)</a>.</p>
<p>Daniel did not want to defile himself by partaking of the king’s meat and wine. He asked permission to eat pulse<sup><a href="http://www.lds.org/scriptures/bd/pulse?lang=eng&query=pulse" target=_blank>1</a></sup> and drink water instead. His supervisor, Melzar, was afraid to displease the king. He thought that after eating pulse and water, the selected Israelites would look worse than their peers, and he would be punished <a href="https://www.lds.org/scriptures/ot/dan/1.8-10?lang=eng#7">(Daniel 1:8-10)</a>.</p>
<div id="design-the-study" class="section level3">
<h3><img src="Images/Step1.png" /> Design the Study</h3>
<div class="casestudystep">
<p>With an understanding of the background of the situation, Daniel proposed an experiment. He said,</p>
<div class="blockquote">
<p>“Prove thy servants, I beseech thee, ten days; and let them give us pulse to eat, and water to drink. Then let our countenances be looked upon before thee, and the countenance of the children that eat of the portion of the king’s meat: and as thou seest, deal with thy servants” <a href="https://www.lds.org/scriptures/ot/dan/1.12,13?lang=eng#11">(Daniel 1:12-13)</a>.</p>
</div>
<p>In short, Daniel’s implied <strong>research question</strong> can be stated as: Will those who eat pulse and drink water appear healthier than those who eat the king’s meat and drink his wine?</p>
<p>Daniel’s study, which Melzar agreed to, provides an ancient example of a <strong>designed experiment</strong> because the diet individuals were given was selected by the researchers. If the researchers had just let individuals select their diet themselves, then it would have been an <strong>observational study</strong>. While both of these are useful <a href="#outcomes">types of studies</a>, only the experiment can help determine cause and effect relationships.</p>
<p>Daniel’s experiment included two groups of people.</p>
<table style="width:83%;">
<colgroup>
<col width="41%" />
<col width="41%" />
</colgroup>
<thead>
<tr class="header">
<th>Group 1: Treatment</th>
<th>Group 2: Control</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>Those who had the experimental treatment of eating pulse and drinking water</td>
<td>Those who ate the standard food consisting of the king’s meat.</td>
</tr>
</tbody>
</table>
<p>Note that if there was no <strong>control group</strong>, then there would be no way to compare the effect of the diets (the treatments). For Daniel, the control group (who ate the king’s meat and drank his wine) provided a basis for comparing the effect of the new treatment (i.e. eating pulse and drinking water.)</p>
<p>Daniel’s hypothesis is that the Israelite children who eat pulse and drink water will appear healthier in just ten days, compared to those who eat the king’s meat and drink his wine.</p>
</div>
</div>
<div id="collect-the-data" class="section level3">
<h3><img src="Images/Step2.png" /> Collect the Data</h3>
<div class="casestudystep">
<p>When designing a study, much attention is given to the process by which data are collected. Similarly, when examining a study, it is also important to understand the data collection procedures. Typically data is collected from a <strong>sample</strong>, in other words a subset (or a portion), of a <strong>population</strong>.</p>
<p>In Daniel’s experiment, the <strong>population</strong> was all of the Israelite children that were “well favoured, and skilful in all wisdom, and cunning in knowledge, and understanding science” <a href="https://www.lds.org/scriptures/ot/dan/1.4?lang=eng#3">(Daniel 1:4)</a>. In Daniel’s experiment, a <strong>sample</strong> of this population consisting of at least Daniel, Hananiah, Mishael, and Azariah was given the pulse and water to eat and drink. The remainder of the population was given the king’s meat.</p>
<p>Daniel’s study design stated that data be collected at the end of 10 days on the “countenance of the children” <a href="https://www.lds.org/scriptures/ot/dan/1.12,13?lang=eng#11">(Daniel 1:12-13)</a>. Note that the scriptures do not provide enough detail to know how the “countenance of the children” was measured. It is likely that <strong>quanititative</strong> measurements were not made, just overall impressions that were <strong>categorical</strong> in nature, like “improved” or “not improved.”</p>
<p>Whatever data Melzar officially recorded would be used to compare the appearances of two groups of people: (1) Israelites who ate pulse and drank water versus (2) Israelites who ate the king’s meat and drank his wine.</p>
</div>
</div>
<div id="describe-the-data" class="section level3">
<h3><img src="Images/Step3.png" /> Describe the Data</h3>
<div class="casestudystep">
<p>When we describe data, we use any tools appropriate to the situation. This can include verbal descriptions of the data or <strong>statistics</strong> and graphics to help visualize and summarize the <strong>sample</strong> data. The <strong>statistics</strong> and graphics from the <strong>sample</strong> data are then used to make conclusions about the <strong>population parameters</strong> in the “Make Inference” step of the Statistical Process.</p>
<p>For Daniel’s experiment, the data are described in <a href="https://www.lds.org/scriptures/ot/dan/1.15?lang=eng#14">Daniel 1:15</a> using only words instead of graphs and statistics: “And at the end of ten days [the] countenances [of those who ate pulse] appeared fairer and fatter in flesh than all the children which did eat the portion of the king’s meat.”</p>
</div>
</div>
<div id="make-inference" class="section level3">
<h3><img src="Images/Step4.png" /> Make Inference</h3>
<div class="casestudystep">
<p><strong>Inference</strong> is the process of using the information contained in a <em>sample</em> to make a general statement (i.e. to infer something) about the entire <em>population</em>. It applies the logic that if something is true for the sample, then it must also be true for the population. The methods we will learn in this course help us know when it is appropriate to make such a bold conclusions about the population and when it would be unwise to do so.</p>
<p>Melzar made an inference. Based on the results of the sample, he determined that (in general) those who eat pulse and drink water will be healthier than those who eat the king’s meat and drink his wine <a href="https://www.lds.org/scriptures/ot/dan/1.15-16?lang=eng#14">(Daniel 1:15-16.)</a>. This is a bold generalization about all of the Israelite children, that was made possible through the experiment performed on Daniel, Hananiah, Mishael, and Azariah.</p>
</div>
</div>
<div id="take-action" class="section level3">
<h3><img src="Images/Step5.png" /> Take Action</h3>
<div class="casestudystep">
<p>The goal of a statistical analysis is to determine which action to take in a particular situation. Actions can include many things: launching an internet ad campaign (or not), expressing gratitude (or not), getting vaccinated (or not), etc.</p>
<p>Melzar took action as described in <a href="https://www.lds.org/scriptures/ot/dan/1.16?lang=eng#15">Daniel 1:16</a>: “Thus Melzar took away the portion of their meat, and the wine that they should drink; and gave [all the Israelite children] pulse.”</p>
<p>The experiment was a success! “Now at the end of the days that the king had said he should bring them in…the king communed with them; and among them all was found none like Daniel, Hananiah, Mishael, and Azariah… And in all matters of wisdom and understanding, that the king enquired of them, he found them ten times better than all the magicians and astrologers that were in all his realm” <a href="https://www.lds.org/scriptures/ot/dan/1.18-20?lang=eng#15">(Daniel 1:18-20)</a>.</p>
</div>
<hr />
</div>
<div id="note" class="section level3">
<h3>Note</h3>
<p>Daniel’s experience can also help you learn the Statistical Process. Look at the first letter of each of the steps in the Statistical Process. You can use the phrase “<strong>D</strong>aniel <strong>C</strong>an <strong>D</strong>iscern <strong>M</strong>ore <strong>T</strong>ruth” to help you to help you remember the five steps in the Statistical Process.</p>
<table>
<thead>
<tr class="header">
<th> </th>
<th></th>
<th></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td><img src="Images/Step1.png" width="100"></td>
<td><strong>D</strong>aniel</td>
<td><strong>D</strong>esign the Study</td>
</tr>
<tr class="even">
<td><img src="Images/Step2.png" width="100"></td>
<td><strong>C</strong>an</td>
<td><strong>C</strong>ollect the Data</td>
</tr>
<tr class="odd">
<td><img src="Images/Step3.png" width="100"></td>
<td><strong>D</strong>iscern</td>
<td><strong>D</strong>escribe the Data</td>
</tr>
<tr class="even">
<td><img src="Images/Step4.png" width="100"></td>
<td><strong>M</strong>ore</td>
<td><strong>M</strong>ake inferences</td>
</tr>
<tr class="odd">
<td><img src="Images/Step5.png" width="100"></td>
<td><strong>T</strong>ruth</td>
<td><strong>T</strong>ake action</td>
</tr>
</tbody>
</table>
<p>The Statistical Process will be used throughout the course. Take time to memorize the five steps. Also take some time to study in more detail the concepts discussed in this Case Study using the Concepts and Definitions section below.</p>
</div>
<!-- Concepts and Definitions Section Begin ----------------------------->
</div>
</div>
<div id="concepts-and-definitions" class="section level2">
<h2>Concepts and Definitions</h2>
<div class=concepts>
<div id="types-of-studies-observational-experimental" class="section level3 tabset">
<h3>Types of Studies: Observational & Experimental</h3>
<div id="overview" class="section level4">
<h4>Overview</h4>
<p>Most research projects can be classified into one of two basic study designs:</p>
<table style="width:97%;">
<colgroup>
<col width="48%" />
<col width="48%" />
</colgroup>
<thead>
<tr class="header">
<th><strong>Observational Study</strong></th>
<th><strong>Designed Experiment</strong></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>A type of statistical study design where researchers observe the responses of the individuals, without controlling the conditions experienced by the individuals.</td>
<td>A type of statistical study design where researchers manipulate the conditions experienced by the participants.</td>
</tr>
</tbody>
</table>
<hr class=conceptsplit>
<p><br /></p>
</div>
<div id="examples" class="section level4">
<h4>Examples</h4>
<div id="observational-studies" class="section level5 tabset tabset-fade tabset-pills">
<h5>Observational Studies</h5>
<div id="example-1" class="section level6">
<h6>Example 1</h6>
<div class="conceptparagraph">
<p><strong>Study Design</strong> - Students at a university watch to see which gender is more likely to clean up after themselves after finishing their meal in the school’s cafeteria.</p>
<p><strong>Explanation</strong> - This is observational because the students simply observed the behavior of students eating in the cafeteria.</p>
</div>
</div>
<div id="example-2" class="section level6">
<h6>Example 2</h6>
<div class="conceptparagraph">
<p><strong>Study Design</strong> - Researchers follow a group of people over a long period of time and track whether or not the individuals develop lung cancer. They also record whether or not the individual smoked or not. They use this information to determine if the risk of developing cancer is higher for those that smoke than for those that do not.</p>
<p><strong>Explanation</strong> - This is observational because the researchers did not determine which individuals smoked and which did not smoke. They simply observed the rates of cancer for those that smoked and those that did not smoke.</p>
</div>
</div>
<div id="example-3" class="section level6">
<h6>Example 3</h6>
<div class="conceptparagraph">
<p><strong>Study Design</strong> - The administration of a university studies their student population to determine if those receiving scholarships typically maintain higher GPA’s than those who do not receive scholarships.</p>
<p><strong>Explanation</strong> - This is observational because the university did not randomly assign scholarships to students, they simply observed the behavior of students that received scholarships as compared to those that did not receive scholarships.</p>
</div>
</div>
</div>
<div id="experimental-studies" class="section level5 tabset tabset-fade tabset-pills">
<h5>Experimental Studies</h5>
<div id="example-1-1" class="section level6">
<h6>Example 1</h6>
<div class="conceptparagraph">
<p><strong>Study Design</strong> - A teacher decides to implement a new textbook in one section of a certain course while continuing the use of the old textbook in another section of the course. They hope to learn if the new textbook has higher student approval than the old textbook.</p>
<p><strong>Explanation</strong> - This is a designed experiment because the teacher decided which textbook the students would use. The teacher manipulated the environment that the students experienced.</p>
</div>
<hr class=conceptsplit>
<p><br /></p>
</div>
<div id="example-2-1" class="section level6">
<h6>Example 2</h6>
<div class="conceptparagraph">
<p><strong>Study Design</strong> - Researchers use a driving simulator to have students drive through a virtual road. They randomly assign some of the students to “text while driving” and assign the other students to just drive in order to determine if texting while driving has detrimental effects on driving.</p>
<p><strong>Explanation</strong> - This is a designed experiment because the researchers assigned students to either “text while driving” or “not text”. They manipulated the environment that the students experienced.</p>
</div>
<hr class=conceptsplit>
<p><br /></p>
</div>
<div id="example-3-1" class="section level6">
<h6>Example 3</h6>
<div class="conceptparagraph">
<p><strong>Study Design</strong> - A bank emails out two different types of offers. Several randomly selected individuals receive a letter with notice that they will be given a $100 cash reward for opening up a new account. Another randomly selected group of individuals is offered $150 cash reward for opening up a new account. The response rate of each group is recorded as well as how much money is deposited by each group to determine if the bank benefits more from one type of offer than the other.</p>
<p><strong>Explanation</strong> - This is a designed experiment because the bank sent one type of offer to a selection of individuals and another type of offer to a different selection of individuals. They manipulated the type of offer that individuals received.</p>
</div>
<hr class=conceptsplit>
<p><br /></p>
</div>
</div>
</div>
<div id="explanation" class="section level4">
<h4>Explanation</h4>
<p>Both observational studies and designed experiments follow the five step procedure of the Statistical Process.</p>
<p>Designed <strong>experiments</strong> are often performed by randomly assigning subjects to one of two groups, a <strong>treatment</strong> group and a <strong>control</strong> group. The experiment is conducted by applying different kinds of treatment to the subjects in each group, and comparing the results between the two groups.</p>
<p>Often, those in the treatment group receive the actual treatment. Those in the control group either do not receive the treatment or receive a different treatment. Sometimes a <strong>placebo</strong> is given to the control group, which is meant to make individuals think they are receiving the treatment when they are not. In this way researchers can determine the effect of the treatments compared to when no treatment is given.</p>
<hr class=conceptsplit>
<p><br /></p>
</div>
</div>
<div id="types-of-variables-quantitative-categorical" class="section level3 tabset">
<h3>Types of Variables: Quantitative & Categorical</h3>
<div id="overview-1" class="section level4">
<h4>Overview</h4>
<p>There are two basic types of data, i.e. variables:</p>
<table style="width:97%;">
<colgroup>
<col width="48%" />
<col width="48%" />
</colgroup>
<thead>
<tr class="header">
<th><strong>Quantitative Variables</strong></th>
<th><strong>Categorical Variables</strong></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>Provide numeric measurements from each individual in the dataset, like height, weight, price, etc.</td>
<td>Categorize the individual observations into groups, like gender, nationality, job title, area code of a telephone number, etc.</td>
</tr>
</tbody>
</table>
<p><strong>Note</strong>: not all things are data. Social security numbers or email addresses are not data. Thus, they are neither quantitative nor categorical variables, just ID variables.</p>
<hr class=conceptsplit>
<p><br /></p>
</div>
<div id="examples-1" class="section level4">
<h4>Examples</h4>
<div id="quantitative-data" class="section level5 tabset tabset-fade tabset-pills">
<h5>Quantitative Data</h5>
<div id="height" class="section level6">
<h6>Height</h6>
<div class="conceptparagraph">
<p>A researcher takes a sample of men from a certain population and measures each male’s height in inches.</p>
<p>This is quantitative data because each individual was measured. Further, it would make sense to compute the average height of the males in the sample.</p>
</div>
</div>
<div id="weight" class="section level6">
<h6>Weight</h6>
<div class="conceptparagraph">
<p>A hospital records the birth weight of every child that is born in ounces.</p>
<p>This is quantitative data because each individual was measured. Also, the average birth weight would be a useful summary of this data.</p>
</div>
</div>
<div id="price" class="section level6">
<h6>Price</h6>
<div class="conceptparagraph">
<p>A student records the price of different kinds of cereal in dollars.</p>
<p>This is quantitative data because each type of cereal was measured by its price. The average price of cereals from a certain store could be computed for this data.</p>
</div>
</div>
<div id="gpa" class="section level6">
<h6>GPA</h6>
<div class="conceptparagraph">
<p>A university records the GPA of each student on a scale from 0.000 to 4.000.</p>
<p>This is quantitative data because each student receives a measurement and the average GPA of the university could be determined from this data.</p>
</div>
</div>
</div>
<div id="categorical-data" class="section level5 tabset tabset-fade tabset-pills">
<h5>Categorical Data</h5>
<div id="gender" class="section level6">
<h6>Gender</h6>
<div class="conceptparagraph">
<p>A researcher samples fish from a river and counts up how many male fish and how many female fish were in the sample.</p>
<p>This is categorical data because each fish is categorized into one of two groups based on its gender. Computing the average gender would not make sense.</p>
</div>
<hr class=conceptsplit>
<p><br /></p>
</div>
<div id="nationality" class="section level6">
<h6>Nationality</h6>
<div class="conceptparagraph">
<p>A survey asks participants to select their nationality from a list of several options.</p>
<p>This is categorical data because each individual will be categorized into a certain type of nationality based on their response. It would not make sense to compute the average nationality.</p>
</div>
<hr class=conceptsplit>
<p><br /></p>
</div>
<div id="job-title" class="section level6">
<h6>Job Title</h6>
<div class="conceptparagraph">
<p>A recent publication shows average job satisfaction ratings from various job titles like plumber, doctor, statistician, accountant and lawyer.</p>
<p>Job title is a categorical variable that allowed researchers to group individuals into their occupations. It wouldn’t make sense to report the average job title. However, notice that job satisfaction rating is a quantitative variable, and by first categorizing individuals by job title, the researchers could then report the average job satisfaction rating for each category.</p>
</div>
<hr class=conceptsplit>
<p><br /></p>
</div>
<div id="area-code" class="section level6">
<h6>Area Code</h6>
<div class="conceptparagraph">
<p>Note that phone numbers of themselves are just unique identification numbers, they are not data. However, the area code of a phone number does contain information that categorizes individuals into areas or regions of the U.S. according to where their phone number is originally located.</p>
</div>
<hr class=conceptsplit>
<p><br /></p>
</div>
</div>
</div>
<div id="explanation-1" class="section level4">
<h4>Explanation</h4>
<p>For a <strong>quantitative variable</strong>, it makes sense to apply arithmetic operations to the data, like calculating an average.</p>
<p><strong>Categorical variables</strong> are labels and it does not make sense to do arithmetic with them. They simply categorize each observation into a distinct category.</p>
<p><strong>Note</strong>: some variables, like shoe size, can be considered as either quantitative or categorical variables. The researcher must decide if they wish to compute the “average shoe size” or if they want to “categorize people into groups based on their shoe size.”</p>
<hr class=conceptsplit>
<p><br /></p>
<hr />
</div>
</div>
<div id="populations-parameters-samples-statistics" class="section level3 tabset">
<h3>Populations, Parameters, Samples, & Statistics</h3>
<div id="overview-2" class="section level4">
<h4>Overview</h4>
<table>
<colgroup>
<col width="52%" />
<col width="47%" />
</colgroup>
<thead>
<tr class="header">
<th><strong>Population</strong></th>
<th><strong>Parameter</strong></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>The entire collection of individuals (or items) of interest.</td>
<td>A characteristic of the population. Typically unknown.</td>
</tr>
</tbody>
</table>
<table>
<colgroup>
<col width="52%" />
<col width="47%" />
</colgroup>
<thead>
<tr class="header">
<th><strong>Sample</strong></th>
<th><strong>Statistic</strong></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>A subset of individuals (or items) from the population.</td>
<td>A characteristic of the sample.</td>
</tr>
</tbody>
</table>
<strong>Sample Statistics</strong> allow us to estimate the unknown <strong>Population Parameters</strong>.
<hr class=conceptsplit>
<p><br /></p>
</div>
<div id="examples-2" class="section level4 tabset tabset-fade tabset-pills">
<h4>Examples</h4>
<div id="example-1-2" class="section level5">
<h5>Example 1</h5>
<div class="conceptparagraph">
<p>A researcher wishes to know the average debt load of U.S. households. They take a sample of 1,000 households. They use the information they find in their sample of 1,000 U.S. households to make a claim about the average debt load of all U.S. households.</p>
<table>
<thead>
<tr class="header">
<th><strong>Population</strong></th>
<th><strong>Parameter</strong></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>U.S. Households</td>
<td>Average debt load of U.S. households. (Unknown.)</td>
</tr>
</tbody>
</table>
<table style="width:99%;">
<colgroup>
<col width="25%" />
<col width="73%" />
</colgroup>
<thead>
<tr class="header">
<th><strong>Sample</strong></th>
<th><strong>Statistic</strong></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>The 1,000 U.S. households contacted.</td>
<td>Average debt load of the 1,000 U.S. households contacted.</td>
</tr>
</tbody>
</table>
<p>The average debt load from the sample of 1,000 households is used to estimate the average debt load of all U.S. households.</p>
</div>
<hr class=conceptsplit>
<p><br /></p>
</div>
<div id="example-2-2" class="section level5">
<h5>Example 2</h5>
<div class="conceptparagraph">
<p>A business wants to determine the percentage of their customers that would be interested in a new service they are considering providing. They email out surveys to a sample of 100 recent customers, but only 70 customers respond. They find that a certain percentage of the sample is interested in the new service. They use this information to make a conclusion about the percentage of all their customers that are interested in the new service.</p>
<table style="width:97%;">
<colgroup>
<col width="25%" />
<col width="72%" />
</colgroup>
<thead>
<tr class="header">
<th><strong>Population</strong></th>
<th><strong>Parameter</strong></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>All customers of the business.</td>
<td>Percentage of customers of the business that are interested in the new service. (Unknown.)</td>
</tr>
</tbody>
</table>
<table style="width:97%;">
<colgroup>
<col width="25%" />
<col width="72%" />
</colgroup>
<thead>
<tr class="header">
<th><strong>Sample</strong></th>
<th><strong>Statistic</strong></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>The 70 customers of the business that were contacted and responded.</td>
<td>The percentage of the 70 customers that responsed that are interested in the new service.</td>
</tr>
</tbody>
</table>
<p>The percentage of 70 customers that are interested in the new service will be used to estimate the percentage of <em>all</em> the customers of the business that would be interested in the new service.</p>
</div>
<hr class=conceptsplit>
<p><br /></p>
</div>
</div>
<div id="explanation-2" class="section level4">
<h4>Explanation</h4>
<p>It is often impossible to conduct a census, which is an examination of the full population. Whenever a census is possible, the population parameter of interest can be known.</p>
<p>Instead, a more feasible approach is to select a sample from the population, which provides a more manageable group of items. The information gained from the sample, the sample statistic, is used to estimate the population parameter. This process of estimating the parameter from the statistic is called “making an inference,” i.e., a generalization from the sample to the population.</p>
<hr class=conceptsplit>
<p><br /> <br /></p>
<hr class=conceptsplit>
</div>
</div>
<div id="types-of-sampling-random-convenience" class="section level3 tabset">
<h3>Types of Sampling: Random & Convenience</h3>
<p>In statistics, the information from a sample is used to make inference about the population. Because of this, it is important that the <strong>sample</strong> that is obtained is found in an <strong>unbiased</strong> way.</p>
<p><em>Using random sampling is the best way to reduce bias.</em></p>
<div id="overview-3" class="section level4">
<h4>Overview</h4>
<table>
<colgroup>
<col width="41%" />
<col width="58%" />
</colgroup>
<thead>
<tr class="header">
<th>Random Sampling Methods</th>
<th>Definition</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>Simple Random Sampling (SRS)</td>
<td>Every group of size <span class="math inline">\(n\)</span> is given an equal chance of selection.</td>
</tr>
<tr class="even">
<td>Stratified Sampling</td>
<td>Simple random samples are drawn from each of separate homogeneous groups of the population called strata.</td>
</tr>
<tr class="odd">
<td>Systematic Sampling</td>
<td>Every <span class="math inline">\(k^{\text{th}}\)</span> item in the population is selected, beginning at a random starting point.</td>
</tr>
<tr class="even">
<td>Cluster Sampling</td>
<td>Consists of taking all items in one or more randomly selected clusters, or blocks.</td>
</tr>
</tbody>
</table>
<table>
<colgroup>
<col width="40%" />
<col width="59%" />
</colgroup>
<thead>
<tr class="header">
<th>Non-Random Sampling Methods</th>
<th></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>Convenience Sampling</td>
<td>Selecting items that are relatively easy to obtain without the use of random selection to choose the sample. <em>Should be avoided.</em></td>
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<p>Unfortunately, most samples are obtained by convenience sampling, which can result in a very biased sample. A biased sample will make us think the truth about the population is very different from what it actually is.</p>
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<p><br></p>
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<div id="examples-3" class="section level4">
<h4>Examples</h4>
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<th>Random Sampling Methods</th>