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[[Filehttps:Accuracy and Precision 2//i0.wp.com/xpslibrary.gif|none|400px]]Accuracy in <math>x<com/math>wp-axis, Precision in <math>y<content/uploads/math>-axis <nowiki>*<2019/07/nowiki>In this example, μ is sample mean, not the population meanAccuracyvs.PrecisionABCDHighAccuracyHighPrecision.jpg
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==Disease frequency measurement==
{{#mermaid:
==Difference between Population and Sample==
===Accuracy =Validity and Precision=Reliability===
{|class="wikitable"
|+Definition
|-
!Accuracy!!Validity
|
*Closeness of observed values '''to true population values'''
**AKA 'Trueness'
|-
!Precision!!Reliability
|
*Closeness of observed values '''to each other among sample'''
|}
<div style="display:inline; vertical-align:bottom;">[[File:Accuracy and Precision 2.gif|thumb|left|500px|Accuracy in <math>x</math>-axis, Precision in <math>y</math>-axis<br><nowiki>*</nowiki>In this example, μ is sample mean, not the population mean]][[File:Accuracy and Precision 1.webp|thumb|none|400px]]300px|Precision in <math>x</math>-axis, Accuracy in <math>y</math>-axis]]
</div>
<div style="clear:both;"></div>
==Tips in Case-control design==
node3 -- "NO, unfeasible" --> yesR([MH adjusted estimate should<br>still include residual confounding])
}}
==Sampling==
===Simple random sampling (SRS)===
====Standard Error with Finite Population Correction in SRS====
The formula <math>SE = \frac{\sigma}{\sqrt{N}}</math> assume that samples are selected from ''infinite'' population ''with replacement'' (allowing repetitive sampling of the same individuals).
In reality, sampling is made from '''finite''' population '''without replacement''' (not allowing repetitive sampling of the same individuals).
When sampling from '''finite''' population '''without replacement''', if fraction <math>\frac{n}{N}</math> > 5% (0.05), <math>SE</math> will be too large.
<blockquote>
Repeating sampling from finite population of size of <math>N</math> by sample size of <math>n_i</math> decreases population size at every sampling:
population size at <math>m</math><sup>th</sup> sampling = <math>N - \sum_{i=1}^m {n_i}</math>
</blockquote>
If the fraction <math>\frac{n}{N}</math> > 5% (0.05), <math>SE</math> should be corrected by '''Finite Population Correction'''.
{|class="wikitable"
|-
!Standard Error corrected by Finite Population Correction when <math>\frac{n}{N}</math> > 5% (0.05)
|-
|<math>Finite\ Population\ Correction\ (FPC) = \sqrt{\frac{N-n}{N-1}}</math>
|-
|<math>Corrected\ SE = FPC \times SE = \sqrt{\frac{N-n}{N-1}} \cdot \frac{\sigma}{\sqrt{N}}</math>
|}
===Two-stage (multi-stage) sampling===
In case of two-stage sampling:
#Randomly sample primary sampling units (PSUs) (clusters) with '''probability proportional to size (PPS)'''
##larger size of PSUs (clusters) are more likely to be selected
#Randomly sample second-stage units (SSUs) (individuals) with the '''same number''' of individuals within PSUs (clusters)
##individuals in smaller size of PSUs are more likely to be selected
##final individual probability to be sampled is equivalent in entire population because of balancing probabilities between PSUs and SSUs
===Stratified random sampling===
To increase precision of estimates in heterogeneous groups in sample, separated (stratified) random sampling from each group in population can be chosen.
In stratified random sampling, sampling fractions in strata can be varied, e.g., sample size of minority groups can be larger than majority groups.
