664 lines
32 KiB
HTML
664 lines
32 KiB
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href="#" role="button" data-bs-toggle="dropdown" id="navbarDropdown-1" aria-haspopup="true" aria-expanded="false">
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1. About Health Statistics
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<li><a class="dropdown-item" href="01-000.html">Overview</a></li>
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<li><a class="dropdown-item" href="01-100.html">Correlates</a></li>
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<li><a class="dropdown-item" href="01-200.html">Conditions</a></li>
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<li><a class="dropdown-item" href="01-300.html">Care</a></li>
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<li><a class="dropdown-item" href="01-400.html">Costs</a></li>
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<li><a class="dropdown-item" href="01-500.html">Correlates, Conditions, Care, and Costs</a></li>
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<li><a class="dropdown-item" href="01-600.html">Knowledge Check</a></li>
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href="#" role="button" data-bs-toggle="dropdown" id="navbarDropdown-2" aria-haspopup="true" aria-expanded="true">
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2. Common Terms and Equations
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</a>
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<ul class="dropdown-menu show" aria-labelledby="navbarDropdown-2">
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<li><a class="dropdown-item" href="02-000.html">Overview</a></li>
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<li><a class="dropdown-item" href="02-100.html">Sampling</a></li>
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<li><a class="dropdown-item" href="02-200.html">Dependent and Independent Variables</a></li>
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<li><a class="dropdown-item" href="02-300.html">Correlation</a></li>
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<li><a class="dropdown-item" href="02-400.html">Causation</a></li>
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<li><a class="dropdown-item" href="02-500.html">Validity</a></li>
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<li><a class="dropdown-item" href="02-600.html">Age-Adjustment</a></li>
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<li><a class="dropdown-item" href="02-700.html">Hypotheses</a></li>
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<li><a class="dropdown-item" href="02-800.html">Distribution</a></li>
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<li><a class="dropdown-item active" href="02-900.html">Standard Deviation</a></li>
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<li><a class="dropdown-item" href="02-910.html">z-score</a></li>
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<li><a class="dropdown-item" href="02-920.html">t-test</a></li>
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<li><a class="dropdown-item" href="02-930.html">Significance Level</a></li>
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<li><a class="dropdown-item" href="02-940.html">p-value</a></li>
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<li><a class="dropdown-item" href="02-950.html">Confidence Intervals</a></li>
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<li><a class="dropdown-item" href="02-960.html">Incorporation into Health Subjects</a></li>
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<li><a class="dropdown-item" href="02-970.html">Knowledge Check</a></li>
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href="#" role="button" data-bs-toggle="dropdown" id="navbarDropdown-3" aria-haspopup="true" aria-expanded="false">
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3. Health Data Sources
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</a>
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<ul class="dropdown-menu" aria-labelledby="navbarDropdown-3">
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<li><a class="dropdown-item" href="03-000.html">Overview</a></li>
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<li><a class="dropdown-item" href="03-100.html">Surveys</a></li>
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<li><a class="dropdown-item" href="03-200.html">Medical Records</a></li>
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<li><a class="dropdown-item" href="03-300.html">Claims Data</a></li>
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<li><a class="dropdown-item" href="03-400.html">Vital Records</a></li>
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<li><a class="dropdown-item" href="03-500.html">Surveillance</a></li>
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<li><a class="dropdown-item" href="03-600.html">(Other) Grey Literature</a></li>
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<li><a class="dropdown-item" href="03-700.html">Peer-Reviewed Literature</a></li>
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<li><a class="dropdown-item" href="03-800.html">Knowledge Check</a></li>
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href="#" role="button" data-bs-toggle="dropdown" id="navbarDropdown-4" aria-haspopup="true" aria-expanded="false">
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4. Finding Health Statistics Exercises
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</a>
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<ul class="dropdown-menu" aria-labelledby="navbarDropdown-4">
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<li><a class="dropdown-item" href="04-000.html">Overview</a></li>
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<li><a class="dropdown-item" href="04-100.html">National Center for Health Statistics (NCHS)</a></li>
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<li><a class="dropdown-item" href="04-200.html">World Health Organization (WHO)</a></li>
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<li><a class="dropdown-item" href="04-300.html">Agency for Healthcare Research and Quality (AHRQ)</a></li>
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<li><a class="dropdown-item" href="04-400.html">Centers for Disease Control and Prevention (CDC)</a></li>
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<li><a class="dropdown-item" href="04-500.html">Robert Wood Johnson Foundation: County Health Rankings & Roadmaps</a></li>
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<li><a class="dropdown-item" href="04-600.html">Centers for Medicare and Medicaid Services (CMS)</a></li>
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<li><a class="dropdown-item" href="04-700.html">Kaiser Family Foundation (KFF)</a></li>
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<li><a class="dropdown-item" href="04-800.html">United States Census Bureau</a></li>
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<li><a class="dropdown-item" href="04-900.html">HealthData.gov</a></li>
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<li><a class="dropdown-item" href="04-910.html">Dartmouth Atlas of Health Care (DAHC)</a></li>
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<li><a class="dropdown-item" href="04-920.html">Academic Journal Databases</a></li>
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<li><a class="dropdown-item" href="04-930.html">Search Engines</a></li>
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</ul>
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<a class="nav-link" href="05-000.html">Closing</a>
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<a class="nav-link" href="06-000.html">Glossary</a>
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<a class="nav-link" href="nav.html">How to Navigate This Course</a>
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<div class="row">
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<header class="bg-secondary p-3 truncate shadow" style="border-bottom: 1px solid #eee;">
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<strong>Finding and Using Health Statistics</strong>
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<a href="https://www.nlm.nih.gov/training.html" id="anch_29" target="_blank">Training & Outreach</a>
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<a href="https://learn.nlm.nih.gov/" id="anch_30" target="_blank">Learning Resources</a>
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<a class="nav-link" href="index.html">Course Home</a>
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</li>
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<li class="nav-item">
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<a class="nav-link" data-bs-toggle="collapse" href="#collapse-item-1">1. About Health Statistics</a>
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<div id="collapse-item-1" class="collapse">
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<ul class="nav flex-column ps-3">
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<a class="nav-link" href="01-000.html">Overview</a>
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<li class="nav-item">
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<a class="nav-link" href="01-100.html">Correlates</a>
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</li>
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<li class="nav-item">
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<a class="nav-link" href="01-200.html">Conditions</a>
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</li>
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<li class="nav-item">
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<a class="nav-link" href="01-300.html">Care</a>
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</li>
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<li class="nav-item">
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<a class="nav-link" href="01-400.html">Costs</a>
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</li>
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<li class="nav-item">
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<a class="nav-link" href="01-500.html">Correlates, Conditions, Care, and Costs</a>
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</li>
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<li class="nav-item">
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<a class="nav-link" href="01-600.html">Knowledge Check</a>
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</ul>
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</li>
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<li class="nav-item">
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<a class="nav-link" data-bs-toggle="collapse" href="#collapse-item-2">2. Common Terms and Equations</a>
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<ul class="nav flex-column ps-3">
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<li class="nav-item">
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<a class="nav-link" href="02-000.html">Overview</a>
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</li>
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<li class="nav-item">
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<a class="nav-link" href="02-100.html">Sampling</a>
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</li>
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<li class="nav-item">
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<a class="nav-link" href="02-200.html">Dependent and Independent Variables</a>
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</li>
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<li class="nav-item">
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<a class="nav-link" href="02-300.html">Correlation</a>
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</li>
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<li class="nav-item">
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<a class="nav-link" href="02-400.html">Causation</a>
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</li>
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<li class="nav-item">
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<a class="nav-link" href="02-500.html">Validity</a>
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</li>
|
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<li class="nav-item">
|
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<a class="nav-link" href="02-600.html">Age-Adjustment</a>
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</li>
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<li class="nav-item">
|
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<a class="nav-link" href="02-700.html">Hypotheses</a>
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</li>
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<li class="nav-item">
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<a class="nav-link" href="02-800.html">Distribution</a>
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</li>
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<li class="nav-item">
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<a class="nav-link active" href="02-900.html">Standard Deviation</a>
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</li>
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||
<li class="nav-item">
|
||
<a class="nav-link" href="02-910.html">z-score</a>
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||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="02-920.html">t-test</a>
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||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="02-930.html">Significance Level</a>
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||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="02-940.html">p-value</a>
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||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="02-950.html">Confidence Intervals</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="02-960.html">Incorporation into Health Subjects</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="02-970.html">Knowledge Check</a>
|
||
</li>
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</ul>
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</div>
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</li>
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||
|
||
<li class="nav-item">
|
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<a class="nav-link" data-bs-toggle="collapse" href="#collapse-item-3">3. Health Data Sources</a>
|
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<div id="collapse-item-3" class="collapse">
|
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<ul class="nav flex-column ps-3">
|
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<li class="nav-item">
|
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<a class="nav-link" href="03-000.html">Overview</a>
|
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</li>
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<li class="nav-item">
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<a class="nav-link" href="03-100.html">Surveys</a>
|
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</li>
|
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<li class="nav-item">
|
||
<a class="nav-link" href="03-200.html">Medical Records</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="03-300.html">Claims Data</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="03-400.html">Vital Records</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="03-500.html">Surveillance</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="03-600.html">(Other) Grey Literature</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="03-700.html">Peer-Reviewed Literature</a>
|
||
</li>
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||
<li class="nav-item">
|
||
<a class="nav-link" href="03-800.html">Knowledge Check</a>
|
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</li>
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</ul>
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</div>
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</li>
|
||
|
||
|
||
<li class="nav-item">
|
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<a class="nav-link" data-bs-toggle="collapse" href="#collapse-item-4">4. Finding Health Statistics Exercises</a>
|
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<div id="collapse-item-4" class="collapse">
|
||
<ul class="nav flex-column ps-3">
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="04-000.html">Overview</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="04-100.html">National Center for Health Statistics (NCHS)</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="04-200.html">World Health Organization (WHO)</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="04-300.html">Agency for Healthcare Research and Quality (AHRQ)</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="04-400.html">Centers for Disease Control and Prevention (CDC)</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="04-500.html">Robert Wood Johnson Foundation: County Health Rankings & Roadmaps</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="04-600.html">Centers for Medicare and Medicaid Services (CMS)</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="04-700.html">Kaiser Family Foundation (KFF)</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="04-800.html">United States Census Bureau</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="04-900.html">HealthData.gov</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="04-910.html">Dartmouth Atlas of Health Care (DAHC)</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="04-920.html">Academic Journal Databases</a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="04-930.html">Search Engines</a>
|
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</li>
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</ul>
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</div>
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</li>
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<li class="nav-item">
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<a class="nav-link" href="05-000.html">Closing</a>
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<li style="height: auto; line-height: 0;"><hr></li>
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<li class="nav-item">
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<a class="nav-link" href="06-000.html">Glossary</a>
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<a class="nav-link" data-bs-toggle="modal" data-bs-target="#navModal">How to Navigate This Course</a>
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There are a variety of ways you can navigate this course. You can:</p>
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<!-- Header -->
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<h2>2. Common Terms and Equations
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<hr>
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<h3>Standard Deviation</h3>
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<p>A <strong>standard deviation</strong> (or σ) is a measure of how dispersed the data is in relation to the mean. Low, or small, standard deviation indicates data are clustered tightly around the mean, and high, or large, standard deviation indicates data are more spread out. A standard deviation close to zero indicates that data points are very close to the mean, whereas a larger standard deviation indicates data points are spread further away from the mean.</p>
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<p>In the image, the curve on top is more spread out and therefore has a higher standard deviation, while the curve below is more clustered around the mean and therefore has a lower standard deviation.<sup><a href="#fn1" id="anch_1">1</a></sup></p>
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<a href="img/StandardDeviation.png" target="_blank"><img class="img-fluid" src="img/StandardDeviation.png" alt="A graphic showing high and low standard deviation curves."></a>
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<p>
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<em><small>Example Standard Deviation Curves</small></em>
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<p>To calculate the standard deviation, use the following formula:</p>
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<a href="img/SDFormula.png" target="_blank"><img class="img-fluid" src="img/SDFormula.png" alt="In this formula, σ is the standard deviation, x1 is the data point we are solving for in the set, µ is the mean, and N is the total number of data points."></a>
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<p>In this formula, σ is the standard deviation, x<sub>i</sub> is each individual data point in the set, µ is the mean, and N is the total number of data points. In the equation, x<sub>i</sub>, represents each individual data point, so if you have 10 data points, subtract x<sub>1</sub> (first data point) from the mean and then square the absolute value. This process is continued all the way through x<sub>10</sub> (last data point). The results are then summed (symbolized as Σ), which is the numerator of the fraction from the equation.</p>
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<p>Let’s go back to the class example, but this time look at their height. To calculate the standard deviation of the class’s heights, first calculate the mean from each individual height. In this class, there are nine students with an average height of 75 inches. Now the standard deviation equation looks like this:</p>
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<a href="img/SDFormulaEx.png" target="_blank"><img class="img-fluid" src="img/SDFormulaEx.png" alt="To calculate the standard deviation of the class’s heights, first calculate the mean from each individual height. In this class there are nine students with an average height of 75 inches."></a>
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<p>The first step is to subtract the mean from each data point. Then square the value before adding them all together. Now divide by 9 (the total number of data points) and finally take the square root to reach the standard deviation of the data:</p>
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<table class="table table-bordered">
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<tbody>
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<tr>
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<th scope="col" style="text-align: center">Height in inches<br> <em>x<sub>i</sub></em></th>
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<th scope="col" style="text-align: center">Mean<br> µ</th>
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<th scope="col" style="text-align: center">Subtract mean from each data point<br><em>x</em> - µ</th>
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<th scope="col" style="text-align: center">Result<br><em>x</em></th>
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<th scope="col" style="text-align: center">Square each value<br><em>x<sup>2</sup></em></th>
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<th scope="col" style="text-align: center">Sum of Squares<br>∑ <sup>x</sup></th>
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<th scope="col" style="text-align: center">Variance<br><span style="text-decoration: underline;"><em>x</em></span><br>Ν</th>
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<th scope="col" style="text-align: center">Standard Deviation<br> σ=√<em>x</em></th>
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</tr>
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<tr>
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<td>56</td>
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<td style="vertical-align: top;" rowspan="9">75</td>
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<td>56 – 75</td>
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<td>-19</td>
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<td>361</td>
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<td style="vertical-align: top;" rowspan="9">784</td>
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<td style="vertical-align: top;" rowspan="9">87.1</td>
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<td style="vertical-align: top;" rowspan="9"><strong>9.3</strong></td>
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</tr>
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<tr>
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<td>65</td>
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<td>65 – 75</td>
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<td>-10</td>
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<td>100</td>
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</tr>
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<tr>
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<td>74</td>
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<td>74 – 75</td>
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<td>-1</td>
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<td>1</td>
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</tr>
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<tr>
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||
<td>75</td>
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<td>75 – 75</td>
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<td>0</td>
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||
<td>0</td>
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||
</tr>
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<tr>
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||
<td>76</td>
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<td>76 – 75</td>
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<td>1</td>
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<td>1</td>
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||
</tr>
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||
<tr>
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||
<td>77</td>
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||
<td>77 – 75 </td>
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||
<td>2</td>
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<td>4</td>
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||
</tr>
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||
<tr>
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||
<td>80</td>
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||
<td>80 – 75</td>
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||
<td>5</td>
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<td>25</td>
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||
</tr>
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<tr>
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||
<td>81</td>
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||
<td>81 – 75</td>
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||
<td>6</td>
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||
<td>36</td>
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||
</tr>
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||
<tr>
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||
<td>91</td>
|
||
<td>91 – 75</td>
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||
<td>16</td>
|
||
<td>256</td>
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||
</tr>
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</tbody>
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</table>
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<p>This data shows that 68% of heights were 75 inches plus or minus 9.3 inches (1 standard deviation away from the mean), 95% of heights were 75’’ plus or minus 18.6’’ (2 standard deviations away from the mean), and 99.7% of heights were 75’’ plus or minus 27.9’’ (3 standard deviations away from the mean).</p>
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||
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||
<hr>
|
||
<p class="small">
|
||
<a name="fn1" id="anch_101"></a>1. "Image 7: High and low standard deviation curves" <em>Density Curves and Normal Distributions</em>. University of North Carolina, 2012.</p>
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