var presentation = ["<word>population<\/word>","<word>sample<\/word>","<word>same characteristics<\/word>","<word>representing<\/word>","<phrase>Sampling\nGathering information about an entire <strong data-readahead=\"population\">population<\/strong> often costs too much or is virtually impossible. Instead, we use a <strong data-readahead=\"sample\">sample<\/strong>\nof the <strong data-readahead=\"population\">population<\/strong>. A <strong data-readahead=\"sample\">sample<\/strong> should have the <strong data-readahead=\"same characteristics\">same characteristics<\/strong> as the <strong data-readahead=\"population\">population<\/strong> it is <strong data-readahead=\"representing\">representing<\/strong>.<\/phrase>","<word>random sampling<\/word>","<phrase>Most statisticians use various methods of <strong data-readahead=\"random sampling\">random sampling<\/strong> in an attempt to achieve this goal. This section will describe a few of the most common methods. There are several different methods of <strong data-readahead=\"random sampling\">random sampling<\/strong>. In each form of <strong data-readahead=\"random sampling\">random sampling<\/strong>, each\nmember of a <strong data-readahead=\"population\">population<\/strong> initially has an equal chance of being selected for the <strong data-readahead=\"sample\">sample<\/strong>. Each method has pros and cons.<\/phrase>","<word>simple random sample<\/word>","<phrase>The easiest method to describe is called a <strong data-readahead=\"simple random sample\">simple random sample<\/strong>. Any group of n individuals is equally likely to be chosen by\nany other group of n individuals if the simple <strong data-readahead=\"random sampling\">random sampling<\/strong> technique is used. In other words, each <strong data-readahead=\"sample\">sample<\/strong> of the same\nsize has an equal chance of being selected.<\/phrase>","<word>names in a hat<\/word>","<word>table of random numbers<\/word>","<word>computer<\/word>","<phrase>For example, suppose Lisa wants to form a four-person study group (herself and three other people) from her pre-calculus class, which has 31 members not including Lisa. To choose a <strong data-readahead=\"simple random sample\">simple random sample<\/strong> of size three from the other members of her class, Lisa could put all 31 <strong data-readahead=\"names in a hat\">names in a hat<\/strong>, shake the hat, close her eyes, and pick out three names. Lisa can use a <strong data-readahead=\"table of random numbers\">table of random numbers<\/strong> (found in many statistics books and mathematical handbooks), a calculator, or a <strong data-readahead=\"computer\">computer<\/strong> to generate random numbers.<\/phrase>","<word>stratified sample<\/word>","<word>cluster sample<\/word>","<word>systematic sample<\/word>","<word>divide<\/word>","<word>groups called strata<\/word>","<phrase>Besides simple <strong data-readahead=\"random sampling\">random sampling<\/strong>, there are other forms of sampling that involve a chance process for getting the <strong data-readahead=\"sample\">sample<\/strong>. Other well-known <strong data-readahead=\"random sampling\">random sampling<\/strong> methods are the <strong data-readahead=\"stratified sample\">stratified sample<\/strong>, the <strong data-readahead=\"cluster sample\">cluster sample<\/strong>, and the <strong data-readahead=\"systematic sample\">systematic sample<\/strong>. To choose a\n<strong data-readahead=\"stratified sample\">stratified sample<\/strong>, <strong data-readahead=\"divide\">divide<\/strong> the <strong data-readahead=\"population\">population<\/strong> into <strong data-readahead=\"groups called strata\">groups called strata<\/strong> and then take a proportionate number from each stratum.<\/phrase>","<phrase>For example, you could stratify (group) your college <strong data-readahead=\"population\">population<\/strong> by department and then choose a\nproportionate <strong data-readahead=\"simple random sample\">simple random sample<\/strong> from each stratum (each department) to get a stratified random <strong data-readahead=\"sample\">sample<\/strong>. To choose\na <strong data-readahead=\"simple random sample\">simple random sample<\/strong> from each department, number each member of the first department, number each member of\nthe second department, and do the same for the remaining departments. Then use simple <strong data-readahead=\"random sampling\">random sampling<\/strong> to choose\nproportionate numbers from the first department and do the same for each of the remaining departments. Those numbers\npicked from the first department, picked from the second department, and so on represent the members who make up the\n<strong data-readahead=\"stratified sample\">stratified sample<\/strong>.<\/phrase>","<word>divide the population into clusters<\/word>","<phrase>To choose a <strong data-readahead=\"cluster sample\">cluster sample<\/strong>, <strong data-readahead=\"divide the population into clusters\">divide the population into clusters<\/strong> (groups) and then randomly select some of the clusters.\nAll the members from these clusters are in the <strong data-readahead=\"cluster sample\">cluster sample<\/strong>. For example, if you randomly <strong data-readahead=\"sample\">sample<\/strong> four departments\nfrom your college <strong data-readahead=\"population\">population<\/strong>, the four departments make up the <strong data-readahead=\"cluster sample\">cluster sample<\/strong>. <strong data-readahead=\"Divide\">Divide<\/strong> your college faculty by department.\nThe departments are the clusters. Number each department, and then choose four different numbers using simple random\nsampling. All members of the four departments with those numbers are the <strong data-readahead=\"cluster sample\">cluster sample<\/strong>.<\/phrase>","<word>randomly select a starting point<\/word>","<word>take every nth piece of data<\/word>","<phrase>To choose a <strong data-readahead=\"systematic sample\">systematic sample<\/strong>, <strong data-readahead=\"randomly select a starting point\">randomly select a starting point<\/strong> and <strong data-readahead=\"take every nth piece of data\">take every nth piece of data<\/strong> from a listing of the\n<strong data-readahead=\"population\">population<\/strong>. For example, suppose you have to do a phone survey. Your phone book contains 20,000 residence listings. You\nmust choose 400 names for the <strong data-readahead=\"sample\">sample<\/strong>. Number the <strong data-readahead=\"population\">population<\/strong> 1-20,000 and then use a <strong data-readahead=\"simple random sample\">simple random sample<\/strong> to pick a\nnumber that represents the first name in the <strong data-readahead=\"sample\">sample<\/strong>. Then choose every fiftieth name thereafter until you have a total of 400\nnames (you might have to go back to the beginning of your phone list). Systematic sampling is frequently chosen because\nit is a simple method.<\/phrase>","<word>non-random<\/word>","<word>convenience sampling<\/word>","<phrase>A type of sampling that is <strong data-readahead=\"non-random\">non-random<\/strong> is <strong data-readahead=\"convenience sampling\">convenience sampling<\/strong>. <strong data-readahead=\"Convenience sampling\">Convenience sampling<\/strong> involves using results that are\nreadily available. For example, a <strong data-readahead=\"computer\">computer<\/strong> software store conducts a marketing study by interviewing potential customers\nwho happen to be in the store browsing through the available software. The results of <strong data-readahead=\"convenience sampling\">convenience sampling<\/strong> may be very\ngood in some cases and highly biased (favor certain outcomes) in others.<\/phrase>","<word>Sampling data should be done very carefully<\/word>","<phrase><strong data-readahead=\"Sampling data should be done very carefully\">Sampling data should be done very carefully<\/strong>. Collecting data carelessly can have devastating results. Surveys mailed to\nhouseholds and then returned may be very biased (they may favor a certain group). It is better for the person conducting the\nsurvey to select the <strong data-readahead=\"sample\">sample<\/strong> respondents.<\/phrase>","<word>True random sampling<\/word>","<word>done with replacement<\/word>","<word>Surveys are typically done without replacement<\/word>","<word>sampling without replacement<\/word>","<phrase><strong data-readahead=\"True random sampling\">True random sampling<\/strong> is <strong data-readahead=\"done with replacement\">done with replacement<\/strong>\n-That is, once a member is picked, that member goes back into the <strong data-readahead=\"population\">population<\/strong> and thus may be chosen more than once. However for practical reasons, in most populations, simple <strong data-readahead=\"random sampling\">random sampling<\/strong> is done without replacement.\n-<strong data-readahead=\"Surveys are typically done without replacement\">Surveys are typically done without replacement<\/strong>. That is, a member of the <strong data-readahead=\"population\">population<\/strong> may be chosen only once. Most samples are taken from large populations and the <strong data-readahead=\"sample\">sample<\/strong> tends to be small in comparison to the <strong data-readahead=\"population\">population<\/strong>. Since this is the case, <strong data-readahead=\"sampling without replacement\">sampling without replacement<\/strong> is approximately the same as sampling with replacement because the chance of picking the same individual more than once with replacement is very low.<\/phrase>","<phrase>In a college <strong data-readahead=\"population\">population<\/strong> of 10,000 people, suppose you want to pick a <strong data-readahead=\"sample\">sample<\/strong> of 1,000 randomly for a survey.\nFor any particular <strong data-readahead=\"sample\">sample<\/strong> of 1,000, if you are sampling with replacement,\n-the chance of picking the first person is 1,000 out of 10,000 (0.1000);\n-the chance of picking a different second person for this <strong data-readahead=\"sample\">sample<\/strong> is 999 out of 10,000 (0.0999);\n-the chance of picking the same person again is 1 out of 10,000 (very low).<\/phrase>","<phrase>If you are <strong data-readahead=\"sampling without replacement\">sampling without replacement<\/strong>,\n-the chance of picking the first person for any particular <strong data-readahead=\"sample\">sample<\/strong> is 1000 out of 10,000 (0.1000);\n-the chance of picking a different second person is 999 out of 9,999 (0.0999);\n-you do not replace the first person before picking the next person.<\/phrase>","<phrase>Compare the fractions 999\/10,000 and 999\/9,999. For accuracy, carry the decimal answers to four decimal places. To four\ndecimal places, these numbers are equivalent (0.0999).<\/phrase>","<word>becomes a mathematical issue<\/word>","<word>when the population is small<\/word>","<phrase><strong data-readahead=\"Sampling without replacement\">Sampling without replacement<\/strong> instead of sampling with replacement <strong data-readahead=\"becomes a mathematical issue\">becomes a mathematical issue<\/strong> only <strong data-readahead=\"when the population is small\">when the population is small<\/strong>. For example, if the <strong data-readahead=\"population\">population<\/strong> is 25 people, the <strong data-readahead=\"sample\">sample<\/strong> is ten, and you are sampling with replacement for any particular <strong data-readahead=\"sample\">sample<\/strong>, then the chance of picking the first person is ten out of 25, and the chance of picking a different second person is nine out of 25 (you replace the first person).<\/phrase>","<phrase>If you <strong data-readahead=\"sample\">sample<\/strong> without replacement, then the chance of picking the first person is ten out of 25, and then the chance of\npicking the second person (who is different) is nine out of 24 (you do not replace the first person).\nCompare the fractions 9\/25 and 9\/24. To four decimal places, 9\/25 = 0.3600 and 9\/24 = 0.3750. To four decimal places,\nthese numbers are not equivalent.<\/phrase>","<word>important to be aware<\/word>","<word>sampling errors<\/word>","<word>nonsampling errors<\/word>","<phrase>When you analyze data, it is <strong data-readahead=\"important to be aware\">important to be aware<\/strong> of <strong data-readahead=\"sampling errors\">sampling errors<\/strong> and <strong data-readahead=\"nonsampling errors\">nonsampling errors<\/strong>. The actual process of\nsampling causes <strong data-readahead=\"sampling errors\">sampling errors<\/strong>. For example, the <strong data-readahead=\"sample\">sample<\/strong> may not be large enough. Factors not related to the sampling\nprocess cause <strong data-readahead=\"nonsampling errors\">nonsampling errors<\/strong>. A defective counting device can cause a nonsampling error.<\/phrase>","<phrase>In reality, a <strong data-readahead=\"sample\">sample<\/strong> will never be exactly representative of the <strong data-readahead=\"population\">population<\/strong> so there will always be some sampling error. As a\nrule, the larger the <strong data-readahead=\"sample\">sample<\/strong>, the smaller the sampling error.<\/phrase>","<phrase>In statistics, a sampling bias is created when a <strong data-readahead=\"sample\">sample<\/strong> is collected from a <strong data-readahead=\"population\">population<\/strong> and some members of the <strong data-readahead=\"population\">population<\/strong>\nare not as likely to be chosen as others (remember, each member of the <strong data-readahead=\"population\">population<\/strong> should have an equally likely chance of\nbeing chosen). When a sampling bias happens, there can be incorrect conclusions drawn about the <strong data-readahead=\"population\">population<\/strong> that is being\nstudied.<\/phrase>","<phrase>Download for free at\nhttp:\/\/cnx.org\/content\/col11562\/latest\/<\/phrase>"];
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		action = action != undefined ? action.trim() : 'UNKNOWN';
		area = area != undefined ? area.trim() : '';
		details = details != undefined ? details : '';

		// If we are about to show a new word, increase the number of keywords
		// reinforced so we can log that for the Dashboard page.
		if (area == 'Word') {
			window.keywordCount++;
		}

		$.ajax({
			type:'POST',
			url:'/logging/logPlayerAction.php',
			data: { 'documentId':276,
					'userId':0,
					'playerAction':action,
					'playerArea':area,
					'details':details,
					'timestamp': t
				}
		})
		.done(function(results){
		})
		.fail(function( jqXHR, textStatus ) {
			alert( "Request failed: " + textStatus );
		});

	}