{"id":15,"date":"2019-04-10T13:27:49","date_gmt":"2019-04-10T13:27:49","guid":{"rendered":"https:\/\/wp.media.unc.edu\/biostatistics\/?page_id=15"},"modified":"2021-07-19T19:18:12","modified_gmt":"2021-07-19T19:18:12","slug":"lesson-2-descriptive-statistics","status":"publish","type":"page","link":"https:\/\/wp.media.unc.edu\/biostatistics\/lesson-2-descriptive-statistics\/","title":{"rendered":"Lesson 2: Descriptive Statistics"},"content":{"rendered":"<div class=\"\"><ul class=\"nav nav-tabs\" id=\"oscitas-tabs-0\"><li class=\"active\"><a class=\"\" href=\"#pane-0-0\" data-toggle=\"tab\">Introduction<\/a><\/li><li class=\"\"><a class=\"\" href=\"#pane-0-1\" data-toggle=\"tab\">Terminology<\/a><\/li><li class=\"\"><a class=\"\" href=\"#pane-0-2\" data-toggle=\"tab\">Basic Concepts<\/a><\/li><li class=\"\"><a class=\"\" href=\"#pane-0-3\" data-toggle=\"tab\">Reported Results<\/a><\/li><li class=\"\"><a class=\"\" href=\"#pane-0-4\" data-toggle=\"tab\">Assessment<\/a><\/li><\/ul><div class=\"tab-content\"><div class=\"tab-pane active\" id=\"pane-0-0\"><div id=\"quicktabs-tabpage-lesson_2_diagnosing_delirium-0\" class=\"quicktabs-tabpage \">\n<article id=\"node-8\" class=\"node node-book clearfix\">\n<header><\/header>\n<div class=\"field field-name-body field-type-text-with-summary field-label-hidden\">\n<div class=\"field-items\">\n<div class=\"field-item even\">\n<div class=\"tex2jax\">\n<div class=\"intro\">\n<div class=\"introtopper\">\n<p>This lesson reviews descriptive statistics. At the end of this lesson, you will be able to:<\/p>\n<\/div>\n<ol>\n<li>Define population and sample<\/li>\n<li>Differentiate between descriptive and inferential statistics<\/li>\n<li>Define basic measures of central tendency (mean, median, mode) and dispersion (standard deviation, interquartile range, range)<\/li>\n<li>Define frequency and probability<\/li>\n<li>Describe the characteristics of a normal distribution and a binomial distribution<\/li>\n<li>Describe what a 95% confidence interval represents<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n<\/div><\/div><div class=\"tab-pane \" id=\"pane-0-1\"><div id=\"quicktabs-tabpage-lesson_2_diagnosing_delirium-1\" class=\"quicktabs-tabpage quicktabs-hide\">\n<article id=\"node-9\" class=\"node node-book clearfix\">\n<header><\/header>\n<div class=\"field field-name-body field-type-text-with-summary field-label-hidden\">\n<div class=\"field-items\">\n<div class=\"field-item even\">\n<div class=\"tex2jax\">\n<div class=\"terminology\">\n<p>Terms that appear frequently throughout this lesson are defined below:<\/p>\n<table>\n<tbody>\n<tr>\n<td class=\"termdef\"><strong>Term<\/strong><\/td>\n<td class=\"termdef\"><strong>Definition<\/strong><\/td>\n<\/tr>\n<tr>\n<td class=\"tableseparator\"><strong>Population<\/strong><\/td>\n<td class=\"tableseparator\">The entire collection of people, animals, cells, or other things from which we collect data<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">\n<p style=\"margin-left: 40px;\"><strong>Parameter<\/strong><\/p>\n<\/td>\n<td style=\"vertical-align: top;\">A number that is calculated from an entire population<\/td>\n<\/tr>\n<tr>\n<td class=\"tableseparator\"><strong>Sample<\/strong><\/td>\n<td class=\"tableseparator\">A subset or group drawn from the population<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">\n<p style=\"margin-left: 40px;\"><strong>Statistic<\/strong><\/p>\n<\/td>\n<td style=\"vertical-align: top;\">A number or quantity that is calculated from a sample of data<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">\n<p style=\"margin-left: 40px;\"><strong>Descriptive statistics<\/strong><\/p>\n<\/td>\n<td style=\"vertical-align: top;\">Statistics that describe the sample without attempting to generalize the results to other groups or the population<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">\n<p style=\"margin-left: 40px;\"><strong>Inferential statistics<\/strong><\/p>\n<\/td>\n<td style=\"vertical-align: top;\">Statistics that infer the likelihood that the results can be generalized to the population<\/td>\n<\/tr>\n<tr>\n<td class=\"tableseparator\"><strong>Measure of central tendency<\/strong><\/td>\n<td class=\"tableseparator\">A single value that attempts to describe the central position of a set of data<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">\n<p style=\"margin-left: 40px;\"><strong>Mean<\/strong><\/p>\n<\/td>\n<td style=\"vertical-align: top;\">The average value<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">\n<p style=\"margin-left: 40px;\"><strong>Median<\/strong><\/p>\n<\/td>\n<td style=\"vertical-align: top;\">The middle value<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">\n<p style=\"margin-left: 40px;\"><strong>Mode<\/strong><\/p>\n<\/td>\n<td style=\"vertical-align: top;\">The most frequent value<\/td>\n<\/tr>\n<tr>\n<td class=\"tableseparator\"><strong>Measure of dispersion\/variation<\/strong><\/td>\n<td class=\"tableseparator\">A value that describes how the data are dispersed around the measure of central tendency, or the extent to which individual values differ from the mean, median, or mode<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">\n<p style=\"margin-left: 40px;\"><strong>Standard deviation<\/strong><\/p>\n<\/td>\n<td style=\"vertical-align: top;\">On average, how much individual values differ from the mean; the square root of the variance<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">\n<p style=\"margin-left: 40px;\"><strong>Variance<\/strong><\/p>\n<\/td>\n<td style=\"vertical-align: top;\">How far a set of numbers is spread out from the mean; the sum of the squared differences between each value and the mean, divided by the number of values minus one<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">\n<p style=\"margin-left: 40px;\"><strong>Range<\/strong><\/p>\n<\/td>\n<td style=\"vertical-align: top;\">The difference between the largest and smallest value in the data set<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">\n<p style=\"margin-left: 40px;\"><strong>Interquartile range<\/strong><\/p>\n<\/td>\n<td style=\"vertical-align: top;\">A measure of the &#8220;middle fifty&#8221; in the data set; where the bulk of the values exist<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">\n<p style=\"margin-left: 40px;\"><strong>Outlier<\/strong><\/p>\n<\/td>\n<td style=\"vertical-align: top;\">An observation point that is distant from other observations<sup id=\"cite_ref-1\" class=\"reference\"> <\/sup><\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">\n<p style=\"margin-left: 40px;\"><strong>Frequency<\/strong><\/p>\n<\/td>\n<td style=\"vertical-align: top;\">The number of times a value appears in the data set<\/td>\n<\/tr>\n<tr>\n<td class=\"tableseparator\"><strong>Frequency distribution<\/strong><\/td>\n<td class=\"tableseparator\">A table or graph that illustrates how frequently each value appears in the data set<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">\n<p style=\"margin-left: 40px;\"><strong>Normal distribution<\/strong><\/p>\n<\/td>\n<td style=\"vertical-align: top;\">A symmetric, bell-shaped distribution for a continuous variable; 68% of observations fall within 1 standard deviation of the mean, 95% fall within 2 standard deviations of the mean, and 99.7% fall within 3 standard deviations of the mean<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">\n<p style=\"margin-left: 40px;\"><strong>Binomial distribution<\/strong><\/p>\n<\/td>\n<td style=\"vertical-align: top;\">The probability distribution for a binomial variable (i.e. a variable that has only two possible values) with fixed probabilities that add up to one<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">\n<p style=\"margin-left: 40px;\"><strong>Confidence interval<\/strong><\/p>\n<\/td>\n<td style=\"vertical-align: top;\">An estimate of the population parameter that will contain the population mean a specified proportion of the time, typically either 95% or 99% of the time<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">\n<p style=\"margin-left: 40px;\"><strong>Probability<\/strong><\/p>\n<\/td>\n<td style=\"vertical-align: top;\">The likelihood that an event will occur<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n<\/div><\/div><div class=\"tab-pane \" id=\"pane-0-2\"><div id=\"quicktabs-tabpage-lesson_2_diagnosing_delirium-2\" class=\"quicktabs-tabpage quicktabs-hide\">\n<article id=\"node-10\" class=\"node node-book clearfix\">\n<header><\/header>\n<div class=\"field field-name-body field-type-text-with-summary field-label-hidden\">\n<div class=\"field-items\">\n<div class=\"field-item even\">\n<div class=\"tex2jax\">\n<p>A <strong>sample<\/strong> is the subset or group (e.g., individuals, cells, animals, machines) drawn from the<strong> population<\/strong> for data collection. <strong>Descriptive statistics<\/strong> describe the sample from which data is collected and communicate the results without attempting to generalize beyond the individuals included in the sample. The goal of <strong>inferential statistics<\/strong> is to determine the likelihood that the observed results can be generalized to other samples.<\/p>\n<p style=\"text-align: center;\"><a class=\"colorbox-load init-colorbox-load-processed cboxElement\" href=\"\/biostatistics\/wp-content\/uploads\/sites\/2\/2019\/04\/inferentialStatistics_lesson1-01.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" style=\"max-width: 701px; width: 70%;\" src=\"\/biostatistics\/wp-content\/uploads\/sites\/2\/2019\/04\/inferentialStatistics_lesson1-01.png\" alt=\"Diagram representing a sample as a subset of the population, with inferential statistics being the study of that sample's generalizability\" width=\"701\" height=\"281\" \/><\/a><\/p>\n<p>Descriptive statistics represent large amounts of data in an aggregate form. There are three basic descriptive characteristics for a single variable:<\/p>\n<ol type=\"1\">\n<li><strong>Central tendency:<\/strong> An estimate of the &#8220;center&#8221; of a distribution of values for continuous variables.\n<ol type=\"a\">\n<li>The<strong> mean<\/strong>, or average, is calculated by adding up all the values and dividing by the number of the values.<\/li>\n<li>The <strong>median <\/strong>is the value found in the exact middle of the set of values. If there are an even number of values and the middle values differ, the median is interpolated.<\/li>\n<li>The <strong>mode <\/strong>is the most frequently occurring value.<\/li>\n<\/ol>\n<\/li>\n<li><strong>Dispersion:<\/strong> Represents the spread of the data round the measure of central tendency.\n<ol type=\"a\">\n<li>The <strong>standard deviation<\/strong> (SD) shows the relation of the values to the mean and is most commonly reported with the mean. It is the square root of the <strong>variance<\/strong>, which is calculated by summing the squares of the difference between each value and the mean and dividing the sum of squares by the number of values minus 1. Large standard deviations suggest that the data are generally spread out far from the mean. Small standard deviations suggest that the values are tightly clustered around the mean.<\/li>\n<li>The <strong>range <\/strong>is the difference between the highest value and the lowest value. <em>Note <\/em>that it is sensitive to outliers, as an outlier can greatly exaggerate the range.<\/li>\n<li>The <strong>interquartile range<\/strong> (IQR), also called <em>middle fifty <\/em>or <em>midspread<\/em>, is the difference between the first quartile and the third quartile of the data. The median is the corresponding measure of central tendency.<\/li>\n<\/ol>\n<table class=\"table-centered\" style=\"width: 500px;\">\n<thead>\n<tr>\n<th scope=\"col\">Consider These Numbers<\/th>\n<th scope=\"col\">Mean, SD<\/th>\n<th scope=\"col\">Median, Range<\/th>\n<th scope=\"col\">Mode<\/th>\n<th scope=\"col\">IQR<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>2, 4, 5, 6, 7, 1, 3, 5, 4 ,3, 2, 2<\/td>\n<td style=\"text-align: center;\">3.7, 1.8<\/td>\n<td style=\"text-align: center;\">3.5, 6<\/td>\n<td style=\"text-align: center;\">2<\/td>\n<td style=\"text-align: center;\">3<\/td>\n<\/tr>\n<tr>\n<td>10, 14, 34, 25, 92, 34, 54, 20, 34<\/td>\n<td style=\"text-align: center;\">35.2, 25.0<\/td>\n<td style=\"text-align: center;\">34, 82<\/td>\n<td style=\"text-align: center;\">34<\/td>\n<td style=\"text-align: center;\">27<\/td>\n<\/tr>\n<tr>\n<td>6, 6, 7, 5, 7, 5, 4, 6, 8, 6<\/td>\n<td style=\"text-align: center;\">6.0, 1.2<\/td>\n<td style=\"text-align: center;\">6, 4<\/td>\n<td style=\"text-align: center;\">6<\/td>\n<td style=\"text-align: center;\">2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li><strong>Frequency distribution<\/strong>: Summary of the frequency of individual values or ranges of values for a variable. Frequency distributions are usually represented in one of two ways: as a table or as a graph.\n<p style=\"text-align: center;\"><a class=\"colorbox-load init-colorbox-load-processed cboxElement\" href=\"\/biostatistics\/wp-content\/uploads\/sites\/2\/2019\/04\/StandardDeviations_lesson1_0.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" style=\"max-width: 700px; width: 70%;\" src=\"\/biostatistics\/wp-content\/uploads\/sites\/2\/2019\/04\/StandardDeviations_lesson1_0.png\" alt=\"A bell curve, with standard deviations on the X-axis and corresponding percentages represented on the Y-axis. Definition provided below.\" width=\"700\" height=\"280\" \/><\/a><\/p>\n<ol type=\"a\">\n<li><strong>Normal distribution: <\/strong>The Gaussian or bell curve, in which 50% of the values occur above and below the mean, 68% of values fall within 1 standard deviation, 95% of values fall within 2 standard deviations, 99% of the values fall within 3 standard deviations, and the mean = median = mode.<\/li>\n<li><strong>Binomial distribution:<\/strong>\u00a0The probability distribution for a binomial variable that is tested in repeated trials (e.g., flipping a coin for heads\/tails 100 times); fixed probabilities add up to one.<\/li>\n<li><strong>Confidence Interval:<\/strong>\u00a0Provides an estimated range of values in which the population parameter is likely to fall a specified proportion of the time, typically either 95% or 99% of the time. In other words, a 95% confidence interval means that the confidence interval should contain the population parameter 95 times if the study is repeated 100 times.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<div class=\"alert alert-warning\"><span class=\"glyphicon glyphicon-exclamation-sign red\">\u00a0<\/span><strong> BEWARE! Approximately normal data.<\/strong> If the sample size is large enough, continuous data that is not normally distributed is sometimes used with statistical tests that are developed for normally distributed data. Debate surrounds how large the sample size must be to relax the normality assumption but some use the following rule of thumb:<\/p>\n<table class=\"table-striped\" style=\"width: 500px; position: relative; margin: 0 auto;\">\n<thead>\n<tr>\n<th scope=\"col\">If:<\/th>\n<th scope=\"col\">THEN:<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>n &gt;= 100<\/td>\n<td>It is always safe to relax the normality assumption<\/td>\n<\/tr>\n<tr>\n<td>50 &lt;= n &lt; 100<\/td>\n<td>It is almost always safe<\/td>\n<\/tr>\n<tr>\n<td>30 &lt;= n &lt; 50<\/td>\n<td>It is probably safe<\/td>\n<\/tr>\n<tr>\n<td>n &lt; 30<\/td>\n<td>It is not safe<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n<\/div><\/div><div class=\"tab-pane \" id=\"pane-0-3\"><div id=\"quicktabs-tabpage-lesson_2_diagnosing_delirium-3\" class=\"quicktabs-tabpage quicktabs-hide\">\n<article id=\"node-11\" class=\"node node-book clearfix\">\n<div class=\"field field-name-body field-type-text-with-summary field-label-hidden\">\n<div class=\"field-items\">\n<div class=\"field-item even\">\n<div class=\"tex2jax\">\n<p style=\"text-align: left;\">When descriptive data is computed, the following guidelines are generally followed:<\/p>\n<div class=\"table-responsive\">\n<table class=\"table table-centered\" style=\"width: 500px; position: relative; margin: 0 auto;\">\n<thead>\n<tr>\n<th style=\"text-align: left;\" scope=\"col\"><em>OK TO COMPUTE<\/em><\/th>\n<th scope=\"col\">NOMINAL<\/th>\n<th scope=\"col\">ORDINAL<\/th>\n<th scope=\"col\">INTERVAL<\/th>\n<th scope=\"col\">RATIO<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Frequency distribution<\/td>\n<td style=\"text-align: center;\">Yes<\/td>\n<td style=\"text-align: center;\">Yes<\/td>\n<td style=\"text-align: center;\">Yes<\/td>\n<td style=\"text-align: center;\">Yes<\/td>\n<\/tr>\n<tr>\n<td>Mode<\/td>\n<td style=\"text-align: center;\">Yes<\/td>\n<td style=\"text-align: center;\">Yes (categorical)<\/td>\n<td style=\"text-align: center;\">Yes (uncommon)<\/td>\n<td style=\"text-align: center;\">Yes (uncommon)<\/td>\n<\/tr>\n<tr>\n<td>Median, range<\/td>\n<td style=\"text-align: center;\"><span style=\"color: #a9a9a9;\">No<\/span><\/td>\n<td style=\"text-align: center;\">Yes (categorical)<\/td>\n<td style=\"text-align: center;\">Yes<\/td>\n<td style=\"text-align: center;\">Yes<\/td>\n<\/tr>\n<tr>\n<td>Mean, standard deviation<\/td>\n<td style=\"text-align: center;\"><span style=\"color: #a9a9a9;\">No<\/span><\/td>\n<td>\n<p style=\"text-align: center;\"><span style=\"color: #a9a9a9;\">No (categorical)<\/span><\/p>\n<p style=\"text-align: center;\">Yes (continuous)<\/p>\n<\/td>\n<td style=\"text-align: center;\">Yes<\/td>\n<td style=\"text-align: center;\">Yes<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p style=\"text-align: center;\">\n<h2>Example 1: Patient Characteristics<\/h2>\n<p style=\"text-align: left;\">In the following table, <strong>m<\/strong><strong>ean and standard deviation<\/strong> are reported for continuous variables (e.g., age, number of medications per patient) and <strong>frequency<\/strong> for nominal (e.g., gender, ethnicity, race) and ordinal variables (e.g., number of past pharmacist-managed clinic visits):<\/p>\n<p style=\"text-align: center;\"><strong>Patient Demographics<\/strong><\/p>\n<div class=\"table-responsive\">\n<table class=\"table-condensed\">\n<tbody>\n<tr>\n<td><strong>Average age in years (SD)<\/strong><\/td>\n<td style=\"text-align: center;\">56 (12)<\/td>\n<\/tr>\n<tr>\n<td><strong>Gender<\/strong><\/td>\n<td style=\"text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">Male<\/p>\n<\/td>\n<td style=\"text-align: center;\">36 (50.7%)<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">Female<\/p>\n<\/td>\n<td style=\"text-align: center;\">35 (49.3%)<\/td>\n<\/tr>\n<tr>\n<td><strong>Ethnicity<\/strong><\/td>\n<td style=\"text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">Hispanic or Latino<\/p>\n<\/td>\n<td style=\"text-align: center;\">1 (1.4%)<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">Not Hispanic or Latino<\/p>\n<\/td>\n<td style=\"text-align: center;\">70 (98.6%)<\/td>\n<\/tr>\n<tr>\n<td><strong>Race<\/strong><\/td>\n<td style=\"text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">American Indian\/Alaska Native<\/p>\n<\/td>\n<td style=\"text-align: center;\">3 (4%)<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">Asian<\/p>\n<\/td>\n<td style=\"text-align: center;\">1 (1.4%)<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">Black\/African American<\/p>\n<\/td>\n<td style=\"text-align: center;\">26 (37.1%)<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">Native Hawaiian\/Pacific Islander<\/p>\n<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">White\/Caucasian<\/p>\n<\/td>\n<td style=\"text-align: center;\">40 (57.1%)<\/td>\n<\/tr>\n<tr>\n<td><strong>No. of past pharmacist-managed clinic visits<\/strong><\/td>\n<td style=\"text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">2<\/p>\n<\/td>\n<td style=\"text-align: center;\">14 (34.1%)<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">3 &#8211; 4<\/p>\n<\/td>\n<td style=\"text-align: center;\">21 (29.6%)<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">5 &#8211; 7<\/p>\n<\/td>\n<td style=\"text-align: center;\">11 (15.5%)<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">8 &#8211; 10<\/p>\n<\/td>\n<td style=\"text-align: center;\">13 (18.3%)<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">&gt; 10<\/p>\n<\/td>\n<td style=\"text-align: center;\">12 (16.9%)<\/td>\n<\/tr>\n<tr>\n<td><strong>Prescription drug coverage<\/strong><\/td>\n<td style=\"text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">Institution specific<\/p>\n<\/td>\n<td style=\"text-align: center;\">32 (47.8%)<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">Medicaid\/Medicare<\/p>\n<\/td>\n<td style=\"text-align: center;\">21 (31.3%)<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">Private<\/p>\n<\/td>\n<td style=\"text-align: center;\">6 (9.0%)<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">Cash\/no third party<\/p>\n<\/td>\n<td style=\"text-align: center;\">7 (10.4%)<\/td>\n<\/tr>\n<tr>\n<td><strong>Total average no. of medications per patient (SD)<\/strong><\/td>\n<td style=\"text-align: center;\">8.1 (5.3)<\/td>\n<\/tr>\n<tr>\n<td><strong>Average no. of medications managed by pharmacist per patient (SD)<\/strong><\/td>\n<td style=\"text-align: center;\">4.2 (3.6)<\/td>\n<\/tr>\n<tr>\n<td><strong>Pharmacist-managed disease state<\/strong><\/td>\n<td style=\"text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">Diabetes<\/p>\n<\/td>\n<td style=\"text-align: center;\">34 (47.9%)<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">Warfarin (Coumadin) management<\/p>\n<\/td>\n<td style=\"text-align: center;\">19 (26.7%)<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">High blood pressure<\/p>\n<\/td>\n<td style=\"text-align: center;\">30 (42.2%)<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">Quitting smoking<\/p>\n<\/td>\n<td style=\"text-align: center;\">3 (4.2%)<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">High cholesterol<\/p>\n<\/td>\n<td style=\"text-align: center;\">42 (59.2%)<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left: 40px;\">Other<\/p>\n<\/td>\n<td style=\"text-align: center;\">3 (4.2%)*<\/td>\n<\/tr>\n<tr>\n<td><strong>Duration of pharmacist-managed disease state in years (SD)<\/strong><\/td>\n<td style=\"text-align: center;\">6.5 (7.4)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p class=\"note\">*Total is greater than 100% due to patients having multiple pharmacist-managed disease states&gt;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n<\/div>\n<div id=\"quicktabs-tabpage-lesson_2_diagnosing_delirium-4\" class=\"quicktabs-tabpage quicktabs-hide\">\n<article id=\"node-11\" class=\"node node-book clearfix\">\n<div class=\"field field-name-body field-type-text-with-summary field-label-hidden\">\n<div class=\"field-items\">\n<div class=\"field-item even\">\n<div class=\"tex2jax\">\n<h2>Example 2: Survey Responses<\/h2>\n<p style=\"text-align: left;\">The following table reports the <strong>median<\/strong> and <strong>range<\/strong> for ordinal data measured on a Likert scale survey. This table also reports the <strong>totals<\/strong> for each response, which provides the frequency distribution for each of the <em>Reasons<\/em>:<\/p>\n<p style=\"text-align: center;\"><strong>Ranking of the Importance of the Reasons\/Motivation to Study Pharmacy<\/strong><br \/>\n(ranked on 5 Likert scale ranging from 1=not important to 5=very important)<\/p>\n<div class=\"table-responsive\">\n<table class=\"table-condensed\">\n<tbody>\n<tr>\n<th colspan=\"1\" rowspan=\"2\" scope=\"col\">Reasons<\/th>\n<th style=\"text-align: center;\" colspan=\"5\" rowspan=\"1\" scope=\"colgroup\">Number of Students Choosing the Importance of Each Reason<\/th>\n<th style=\"text-align: center;\" colspan=\"1\" rowspan=\"2\" scope=\"col\">Interpolated Median<\/th>\n<\/tr>\n<tr>\n<th style=\"text-align: center;\" scope=\"col\">1<\/th>\n<th style=\"text-align: center;\" scope=\"col\">2<\/th>\n<th style=\"text-align: center;\" scope=\"col\">3<\/th>\n<th style=\"text-align: center;\" scope=\"col\">4<\/th>\n<th style=\"text-align: center;\" scope=\"col\">5<\/th>\n<\/tr>\n<tr>\n<td>Interested in health and medicine<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">12<\/td>\n<td style=\"text-align: center;\">5<\/td>\n<td style=\"text-align: center;\">97<\/td>\n<td style=\"text-align: center;\">123<\/td>\n<td style=\"text-align: center;\">4.5<\/td>\n<\/tr>\n<tr>\n<td>Felt that health-related disciplines are good professions<\/td>\n<td style=\"text-align: center;\">3<\/td>\n<td style=\"text-align: center;\">11<\/td>\n<td style=\"text-align: center;\">15<\/td>\n<td style=\"text-align: center;\">135<\/td>\n<td style=\"text-align: center;\">74<\/td>\n<td style=\"text-align: center;\">4.2<\/td>\n<\/tr>\n<tr>\n<td>Felt that pharmacy is a good profession<\/td>\n<td style=\"text-align: center;\">7<\/td>\n<td style=\"text-align: center;\">23<\/td>\n<td style=\"text-align: center;\">27<\/td>\n<td style=\"text-align: center;\">133<\/td>\n<td style=\"text-align: center;\">48<\/td>\n<td style=\"text-align: center;\">4.0<\/td>\n<\/tr>\n<tr>\n<td>Felt that pharmacy has a good job prospect<\/td>\n<td style=\"text-align: center;\">14<\/td>\n<td style=\"text-align: center;\">19<\/td>\n<td style=\"text-align: center;\">40<\/td>\n<td style=\"text-align: center;\">111<\/td>\n<td style=\"text-align: center;\">54<\/td>\n<td style=\"text-align: center;\">3.9<\/td>\n<\/tr>\n<tr>\n<td>Did well at chemistry\/biology in higher school certificate<\/td>\n<td style=\"text-align: center;\">30<\/td>\n<td style=\"text-align: center;\">28<\/td>\n<td style=\"text-align: center;\">32<\/td>\n<td style=\"text-align: center;\">95<\/td>\n<td style=\"text-align: center;\">53<\/td>\n<td style=\"text-align: center;\">3.8<\/td>\n<\/tr>\n<tr>\n<td>Am a people person and wanted a career with high levels of patient contact<\/td>\n<td style=\"text-align: center;\">17<\/td>\n<td style=\"text-align: center;\">26<\/td>\n<td style=\"text-align: center;\">46<\/td>\n<td style=\"text-align: center;\">96<\/td>\n<td style=\"text-align: center;\">53<\/td>\n<td style=\"text-align: center;\">3.8<\/td>\n<\/tr>\n<tr>\n<td>Felt that pharmacy would have a high income<\/td>\n<td style=\"text-align: center;\">26<\/td>\n<td style=\"text-align: center;\">35<\/td>\n<td style=\"text-align: center;\">49<\/td>\n<td style=\"text-align: center;\">86<\/td>\n<td style=\"text-align: center;\">42<\/td>\n<td style=\"text-align: center;\">3.6<\/td>\n<\/tr>\n<tr>\n<td>Had family members who encouraged a health-related field of study<\/td>\n<td style=\"text-align: center;\">51<\/td>\n<td style=\"text-align: center;\">26<\/td>\n<td style=\"text-align: center;\">41<\/td>\n<td style=\"text-align: center;\">85<\/td>\n<td style=\"text-align: center;\">35<\/td>\n<td style=\"text-align: center;\">3.5<\/td>\n<\/tr>\n<tr>\n<td>Felt that pharmacy provides a diversity of options<\/td>\n<td style=\"text-align: center;\">27<\/td>\n<td style=\"text-align: center;\">35<\/td>\n<td style=\"text-align: center;\">77<\/td>\n<td style=\"text-align: center;\">65<\/td>\n<td style=\"text-align: center;\">34<\/td>\n<td style=\"text-align: center;\">3.2<\/td>\n<\/tr>\n<tr>\n<td>Wanted to own a pharmacy<\/td>\n<td style=\"text-align: center;\">62<\/td>\n<td style=\"text-align: center;\">34<\/td>\n<td style=\"text-align: center;\">60<\/td>\n<td style=\"text-align: center;\">53<\/td>\n<td style=\"text-align: center;\">29<\/td>\n<td style=\"text-align: center;\">2.9<\/td>\n<\/tr>\n<tr>\n<td>Had family members who encouraged pharmacy training<\/td>\n<td style=\"text-align: center;\">80<\/td>\n<td style=\"text-align: center;\">23<\/td>\n<td style=\"text-align: center;\">48<\/td>\n<td style=\"text-align: center;\">56<\/td>\n<td style=\"text-align: center;\">31<\/td>\n<td style=\"text-align: center;\">2.8<\/td>\n<\/tr>\n<tr>\n<td>Joined pharmacy as a gateway to dentistry\/medicine<\/td>\n<td style=\"text-align: center;\">102<\/td>\n<td style=\"text-align: center;\">27<\/td>\n<td style=\"text-align: center;\">52<\/td>\n<td style=\"text-align: center;\">35<\/td>\n<td style=\"text-align: center;\">22<\/td>\n<td style=\"text-align: center;\">2.1<\/td>\n<\/tr>\n<tr>\n<td>Joined pharmacy because I want to work for a pharmaceutical company<\/td>\n<td style=\"text-align: center;\">111<\/td>\n<td style=\"text-align: center;\">21<\/td>\n<td style=\"text-align: center;\">42<\/td>\n<td style=\"text-align: center;\">50<\/td>\n<td style=\"text-align: center;\">14<\/td>\n<td style=\"text-align: center;\">1.9<\/td>\n<\/tr>\n<tr>\n<td>Joined pharmacy because I wanted to undertake research in medicine<\/td>\n<td style=\"text-align: center;\">112<\/td>\n<td style=\"text-align: center;\">26<\/td>\n<td style=\"text-align: center;\">49<\/td>\n<td style=\"text-align: center;\">37<\/td>\n<td style=\"text-align: center;\">14<\/td>\n<td style=\"text-align: center;\">1.8<\/td>\n<\/tr>\n<tr>\n<td>Joined pharmacy because I want to join the government sector<\/td>\n<td style=\"text-align: center;\">112<\/td>\n<td style=\"text-align: center;\">27<\/td>\n<td style=\"text-align: center;\">57<\/td>\n<td style=\"text-align: center;\">34<\/td>\n<td style=\"text-align: center;\">8<\/td>\n<td style=\"text-align: center;\">1.8<\/td>\n<\/tr>\n<tr>\n<td>Family members own a pharmacy<\/td>\n<td style=\"text-align: center;\">158<\/td>\n<td style=\"text-align: center;\">13<\/td>\n<td style=\"text-align: center;\">48<\/td>\n<td style=\"text-align: center;\">9<\/td>\n<td style=\"text-align: center;\">10<\/td>\n<td style=\"text-align: center;\">1.3<\/td>\n<\/tr>\n<tr>\n<td>Joined pharmacy as my school friends were doing it<\/td>\n<td style=\"text-align: center;\">173<\/td>\n<td style=\"text-align: center;\">15<\/td>\n<td style=\"text-align: center;\">42<\/td>\n<td style=\"text-align: center;\">6<\/td>\n<td style=\"text-align: center;\">2<\/td>\n<td style=\"text-align: center;\">1.2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p style=\"text-align: left;\">\n<h2>Example 3: Periodontitis<\/h2>\n<p id=\"frequencydistribution\" style=\"text-align: left;\">The following figure represents a simple <strong>frequency distribution<\/strong> for the age of periodontitis patients, showing two peaks:<\/p>\n<p style=\"text-align: center;\"><a class=\"colorbox-load init-colorbox-load-processed cboxElement\" href=\"\/wp-content\/uploads\/sites\/2\/2019\/04\/frequency-age_0.png\"><img decoding=\"async\" style=\"width: 100%; max-width: 530px;\" src=\"\/wp-content\/uploads\/sites\/2\/2019\/04\/frequency-age_0.png\" alt=\"A frequency distribution for the age of periodontitis patients, showing two peaks.\" longdesc=\"#frequencydistribution\" \/><\/a><\/p>\n<p style=\"text-align: left;\">A <strong>box plot diagram <\/strong>is a more robust approach to graphically representing the <strong>frequency distribution<\/strong>, along with central tendency and dispersion. The box plot below shows age distribution by gender in patients with chronic periodontitis and aggressive periodontitis. The box encompasses the interquartile range and the black line represents the median. The median was lower for patients with aggressive periodontitis than those with chronic periodontitis. Higher variability of age among females with aggressive periodontitis and lower variability among males in the same group were observed. Several outliers were observed in the aggressive form, as indicated by the stars and circles (i.e., data points that did not fall within the whiskers):<\/p>\n<p style=\"text-align: center;\"><a class=\"colorbox-load init-colorbox-load-processed cboxElement\" href=\"\/wp-content\/uploads\/sites\/2\/2019\/04\/whiskerPlot_noKey_0.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" style=\"width: 519px; max-width: 519px; height: 542px;\" src=\"\/wp-content\/uploads\/sites\/2\/2019\/04\/whiskerPlot_noKey_0.jpg\" alt=\"An example of a box plot diagram.\" width=\"519\" height=\"542\" data-wp-editing=\"1\" \/><\/a><\/p>\n<p style=\"text-align: left;\">\n<p style=\"text-align: left;\">\n<div class=\"well moreinformation\">\n<p>For more information<\/p>\n<ul>\n<li class=\"citation\" style=\"text-align: left;\">Table 1: Patient Demographics: Vincent AH, et al. <a href=\"http:\/\/scielo.isciii.es\/pdf\/pharmacin\/v11n4\/original4.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Survey of pharmacist-managed primary care clinics using healthcare failure mode and effect analysis. <\/a><cite>Pharmacy Practice<\/cite>. 2013; <cite>11<\/cite>(4): 196-202.<\/li>\n<li class=\"citation\" style=\"text-align: left;\">Table 4: Ranking the Importance: Shen G, et al. <a href=\"http:\/\/www.ncbi.nlm.nih.gov\/pubmed\/25035715\" target=\"_blank\" rel=\"noopener noreferrer\">Course experiences, satisfaction and career intent of final year pre-registration Australian pharmacy students. <\/a><cite>Pharmacy Practice<\/cite>. 2014;12(2).<\/li>\n<li class=\"citation\" style=\"text-align: left;\">Figures 1 and 2: Benoist HM, et al. <a href=\"https:\/\/synapse.koreamed.org\/articles\/1082298\" target=\"_blank\" rel=\"noopener noreferrer\">Profile of chronic and aggressive periodontitis among Sengalese. <\/a><cite>J Periodontal Implant Sci. <\/cite>2011;41(6):279-284.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n<\/div><\/div><div class=\"tab-pane \" id=\"pane-0-4\"><div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-1\" class=\"h5p-iframe\" data-content-id=\"1\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Assessment (for Lesson 2)\"><\/iframe><\/div><\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"_links":{"self":[{"href":"https:\/\/wp.media.unc.edu\/biostatistics\/wp-json\/wp\/v2\/pages\/15"}],"collection":[{"href":"https:\/\/wp.media.unc.edu\/biostatistics\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/wp.media.unc.edu\/biostatistics\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/wp.media.unc.edu\/biostatistics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.media.unc.edu\/biostatistics\/wp-json\/wp\/v2\/comments?post=15"}],"version-history":[{"count":59,"href":"https:\/\/wp.media.unc.edu\/biostatistics\/wp-json\/wp\/v2\/pages\/15\/revisions"}],"predecessor-version":[{"id":1421,"href":"https:\/\/wp.media.unc.edu\/biostatistics\/wp-json\/wp\/v2\/pages\/15\/revisions\/1421"}],"wp:attachment":[{"href":"https:\/\/wp.media.unc.edu\/biostatistics\/wp-json\/wp\/v2\/media?parent=15"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}