We have a test for some condition, say it is the dreaded Lurgi, and are testing some sample of the population, say 10,000 folks.
We have reason to believe that the prevalence of Lurgi is 1% of our population. That means that 99% do not have the condition.
We have an estimate that this test correctly identifies 99% of the people with Lurgi where the condition exists, missing 1%. This former percentage is called the sensitivity of the test.
We also have an estimate that it correctly identifies 99% of the people without Lurgi where the condition does not exist, giving false alarms for 1%. This former percentage is called the specificity or selectivity of the test.
Higher sensitivity or selectivity or both reduce the rate of errors. We can call this the power of the test.
If we test the 1% of the people with Lurgi, we can expect to identify 99% of that 1% or 0.99% of the sample correctly as having the condition, missing 1% of that 1% or 0.01% of the sample.
This also means that if we test the 99% of the people without Lurgi, we can expect to identify 99% of that 99% or 98.01% of the sample correctly as not having the condition, with false alarms of 1% of that 99% or 0.99% of the sample.
Since our sample is 10,000 people, we get the following results:
Prevalence  With Condition (1%)  Without Condition (99%)  Totals 
Tests Positive  Hits = 99
(10,000 X .99 X .01) 
False Alarms = 99
(10,000 X .01 X .99) 
198 
Tests Negative  Misses = 1
(10,000 X .01 X .01) 
Correct Rejections = 9,801
(10,000 X .99 X .99) 
9,802 
Totals  100  9,900  10,000 
You can see that for this population and test power, the number of false alarms is as great as the number of hits. That is, the number of hits is overstated by a factor of two, since we do not know from the test which ones are the false alarms, only their expected frequency.
The misses are not a problem. If you reverse the prevalence numbers, so that 99% have the condition, the false alarm problem goes away, and the miss problem becomes significant. For prevalence figures in the middle, the problems with errors become smaller.
With poor tests, less power, we get more errors. With even lower prevalence, we get more false alarms.
In medicine and statistics in general:
You may encounter these terms. The language I have used is both more intuitively understood, and is also the language of the formal methods underlying this type of analysis, Signal Detection Theory. You can relate it to smoke detectors, fire alarms, or many common situations, once you understand it.
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With respect to medical testing in general, the prevalence of a condition in the population has a huge effect on the number of false alarms and misses. Depending on the prevalence of the condition, and the performance of the test, the number of false alarms can exceed the number of hits. It is simple arithmetic, but a bit confusing.
If there is 0% infection in the population, any report of infection logically has to be a false alarm; there can be no hits. If there is 100% infection in the population, every report of infection logically has to be a hit; there can be no false alarms. The number of estimated false alarms drops as the percent infection rises.
If there is 0% infection in the population, logically there can be no misses. If there is 100% infection in the population, any report of no infection logically must be a miss. The number of estimated misses rises as the percent infection rises.
This is true even with a test of high sensitivity (detects infections if infection exists, with not too many misses) and high selectivity/specificity (detection of no infection if no infection exists, with not too many false alarms).
As sensitivity increases the number of hits increases and number of misses decreases. With a sensitivity of 100%, which does not happen, there would be no misses. See the graph below for a visual explanation of this.
As selectivity/specificity increases the number of correct rejections increases and the number of false alarms decreases. With a selectivity/specificity of 100%, which does not happen, there would be no false alarms. See the graph below for a visual explanation of this.
If selectivity/specificity is low, you get more false alarms. Combine this with a low prevalence, and the false alarms outshine the hits. This overstates the prevalence of the infection.
If the sensitivity is low, you get more misses. Combine this with a high prevalence, and the misses outshine the correct rejections. This understates the prevalence of the infection.
An Example
Use the calculations:
Sensitivity  Selectivity/
specificity 
Test Cases  Prevalence  Hits  False Alarms  Misses  Correct Rejections 
95%  85%  10000  0.00%  0  1500  0  8500 
95%  85%  10000  10.00%  950  1350  50  7650 
95%  85%  10000  20.00%  1900  1200  100  6800 
95%  85%  10000  30.00%  2850  1050  150  5950 
95%  85%  10000  40.00%  3800  900  200  5100 
95%  85%  10000  50.00%  4750  750  250  4250 
95%  85%  10000  60.00%  5700  600  300  3400 
95%  85%  10000  70.00%  6650  450  350  2550 
95%  85%  10000  80.00%  7600  300  400  1700 
95%  85%  10000  90.00%  8550  150  450  850 
95%  85%  10000  100.00%  9500  0  500  0 
Note the changes in 1) false alarms to hits, and 2) misses to correct rejections, as the prevalence increases.
Another Example Showing Ratios of Incorrect to Correct
For a selectivity/specificity of 99%, a sensitivity of 99%, and a prevalence of 1%, 50% of positives will be false alarms. It gets better as the prevalence increases (table below).
For a selectivity/specificity of 99%, a sensitivity of 99%, and a prevalence of 99%, 50% of negatives will be misses. It gets better as the prevalence decreases (table below).
Prevalence
0.00%  1.00%  2.00%  50.00%  98.00%  99.00%  100.00%  
False Positive to True Positive (FP/TP)  Infinite  1.00  0.49  0.01  0.00  0.00  0.00 
False Negative to True Negative Ratio (FN/TN)  0.00  0.00  0.00  0.01  0.49  1.00  Infinite 
False Positive to All Positive (FP/(TP + FP))  100.00%  50.00%  33.11%  1.00%  0.02%  0.01%  0.00% 
False Negative to All Negative (FN/(TN + FN))  0.00%  0.01%  0.02%  1.00%  33.11%  50.00%  100.00% 
In medical testing, we need to establish some test measure, some quantification of the condition of interest. We then need some method of assessment for determining this measurement, the values for that condition of interest. We need a consistent and reliable protocol for administering and scoring the test.
We can look at the measure as the signal. We can look at spurious signals as noise, extraneous information which will make it hard to detect the signal.
We need some method to discriminate the signal from the noise. Different tests have different abilities to differentiate the signal from random noise. That is to say not all tests give the same level of performance.
In signal detection theory, there are two ways to be wrong: false alarms and misses, and there are two ways to be right: hits and correct rejections.
Sensitivity, given as a fraction or a percent, is the ability of a test to correctly identify those who have the condition. It can only be assessed against the percentage of those who have the condition, the prevalence. It gives a rate for hits, and when the one’s complement is taken, a rate for misses.
Selectivity/specificity, given as a fraction or a percent, is the ability of a test to correctly identify those who do not have the condition. It can only be assessed against the percentage of those who do not have the condition, the infrequency. It gives a rate of correct rejections, and when the one’s complement is taken, a rate for false alarms.
For a given test method we establish a threshold, some cutoff value, for our measurement. We use this to determine if we are getting a signal, or just noise. Above the threshold a measure will be deemed to be a detected signal, below the threshold will be no detected signal. We can set the threshold to bias the detection one way or another. The resulting differences in type of error will be dependent upon the threshold setting.
The ratio of hits to misses depends on the threshold, as does the ratio of correct rejections to false alarms. A decreased threshold shifts the bias towards more hits and fewer misses. At the same time, it shifts the bias towards more false alarms and fewer correct rejections. So hits and false alarms rise and fall in the same direction according to the bias.
A better test gives better discrimination of correct versus incorrect results, that is, better accuracy. This can be accomplished by changing the test, or changing the test protocols.
We may have statistics on expected performance for our test, but we also want to calculate estimated statistics for some given number of tests. We will want to count the number of independent tests performed and use those numbers in our calculations.
Prevalence is the estimated measure of the percent of the total population who have the condition.
Infrequency is the complement of prevalence, and is the estimated measure of the percent of the total population who do not have the condition.
Note that I use the word infrequency, as an antonym to frequency, which itself is a synonym for prevalence. There may be another term in common use, but I did not discover such.
We can compute a simple measure of accuracy by taking the total errors and dividing by the total of correct plus erroneous observations. With a better test, more discriminatory power, more accuracy, the error rate decreases.
With decreasing prevalence, the number of false alarms increases, and the number of misses decreases.
With an increasing prevalence, the number of false alarms decreases, and the number of misses increases.
The ratio of false alarms to hits is found by taking the infrequency rate multiplied by the expected false alarm percentage and then dividing this quantity by the prevalence multiplied by the expected hit percentage.
The ratio of misses to correct rejections is found by taking the prevalence rate multiplied by the expected miss rate and then dividing this quantity by the infrequency rate multiplied by the expected correct rejection percentage.
Let me work through an example:
I’m going to put these figures in the table below:
Does The Condition Exist?
Testing 1000 for Lurgi with Sensitivity of 90% and Selectivity/specificity of 90% 

Condition Exists
2% Estimated Prevalence = 20 
Condition Is Absent
98% Estimated Infrequency = 980 

Was the Effect Observed?  Effect Observed  90% x 20 = 18 Hits  10% x 980 = 98 False Alarms 
Effect Not Observed  10% x 20 = 2 Misses  90% x 980 = 882 Correct Rejections  
Estimated Counts
Based on Test Performance, Prevalence, and Number of Tests 
1 https://gladbloke.wordpress.com/2009/06/04/thedreadedlurgi/
See also:
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Because of the high false positive rate and the low prevalence, almost every positive test, a socalled case, identified by Pillar 2 since May of this year has been a FALSE POSITIVE. Not just a few percent. Not a quarter or even a half of the positives are FALSE, but around 90% of them. Put simply, the number of people Mr Hancock sombrely tells us about is an overestimate by a factor of about tenfold. Earlier in the summer, it was an overestimate by about 20fold.” — Dr Michael Yeadon, https://lockdownsceptics.org/liesdamnedliesandhealthstatisticsthedeadlydangeroffalsepositives/
This is a write up on false positive, false negative, true positive, true negative thinking. It is nice to now have those words, “specificity” (true negative) and “sensitivity” (true positive) which I lacked before.
I realize this fits within the framework of signal detection theory. When I studied signal detection, I had no idea why it was considered important, particularly in Psychology, but over the years, I have often gone back to it, since it comes up routinely in a number of guises. It has to be statistical signal detection, which would be an obvious extension to binary, deterministic signal detection. This also fits within the framework of fuzzy logic, which I have looked at in years past.
Medical testing makes use of the ideas on signal detection and upon reflection, is no different than the consideration of any other sort of evidence – it has to be obtained, assessed for quality, and interpreted to understand the implications.
Anybody who tells you that such and such a test is any given percentage effective is misleading you, unintentionally or perhaps even deliberately.
There are four quadrants in the “gold standard” detection matrix: true positive, false positive, true negative, and false negative. There are at least two percentages to be considered, and they vary independently according to the bias in your test, the detection threshold decided upon. You can bias so that you find all the cases, with the consequence that you get a lot of false positives (false alarms). You can bias so that you get few false positives, and as a result, get a lot of false negatives (miss the fire). In addition, the baseline must be considered, with respect to a Bayesian statistical analysis. So, the prior information on general infection rates will make the percentages change. Low base rate of infection gives a high number of false positives. High base rate of infection gives a low number of false positives.
Bayesian reasoning: start with prior probabilities (assessed somehow) and see how probabilities change with new evidence.
If you do not have much noise masking the signal, results are easier to interpret. If you have large numbers and effects that are strong with respect to variability, the statistics should bear you out. Potentially confounding factors can be accounted for.
It is routine for medical tests to be used to determine the health status of people. The simple view of a test is that it returns a true or false result, using some measure, some test instrument, and some testing protocol. Of course anyone reflecting on the issue even a little bit will realize that this is a much oversimplified view of things. For one thing, what threshold, what cutoff point, is being used to make the decision of true or false? What is the measure being used, and what is the measuring instrument? Most things we measure involve some sort of continuous scale. Are the measurements continuous or is it yes and no? What are the typical values that are used to make the judgement? What are the health implications? How are the numbers to be interpreted as a screening device or diagnostic tool? All of these considerations are important for understanding the test.
In this discussion I draw on ratios and proportions, odds, signal detection theory, statistics including Bayesian statistics, and simple arithmetic. I use these tools to examine the accuracy of testing.
Medical tests are not perfect; they give erroneous results along with correct results. We can estimate the accuracy of a test using scientific investigation. We can estimate how likely the test is to find that there is some condition (a hit). We can estimate how likely the test is to find there is not some condition (correct rejection). We can bias the test by changing the threshold, the cutoff value. We can increase hits and false alarms together, or reduce both together. In addition a low prevalence of the condition will give a lot of false alarms. A high prevalence of the condition will give a lot of misses. Also, a highly selective test will reduce the number of false alarms whereas a highly sensitive test will reduce the number of misses.
Here is a diagram which shows testing with no allowance for error.
Does the Condition Exist?  
Is the Effect Observed?  Effect Observed  Condition exists 
Effect Not Observed  Condition is absent  
True or false – assuming no errors 
The above chart shows:
As a result, we have two cases for the test result:
With a bit of thought, the question of errors for the test will come up. Is the test perfect? This would seem highly unlikely.
In testing, there are two ways for the results to be true, and two ways for the results to be false.
Does The Condition Exist?  
Condition Exists  Condition Is Absent  
Was the Effect Observed?  Effect Observed  Condition Is Correctly Considered To Exist
(HIT) (TRUE POSITIVE) 
Condition Is Falsely Considered To Exist
(FALSE ALARM) (FALSE POSITIVE) 
Effect Not Observed  Condition Is Falsely Considered To Be Absent
(MISS) (FALSE NEGATIVE) 
Condition Is Correctly Consider To Be Absent
(TRUE REJECTION) (TRUE NEGATIVE) 

True or false – Assuming Errors 
Synonyms for these terms are:
I will use the abbreviations TP, FP, FN, TN in most of the discussion, although the meanings are probably not as easily grasped.
The above matrix may be used to show more than one thing. It can be used to show proportions, expected percentages, the odds, for each cell of the matrix for some testing scenario. It may also be used to show the expected counts for each cell, given that we have an overall count for the number of tests.
In assigning proportions to these categories, these ratios can be expressed as fractions, decimal fractions or percentages. We have the following proportions of interest:
We will make this a binary split, not allowing for degrees of infection. That latter is important, but it is not important for this discussion.
Since you don’t know the percentage of infections, you must make an estimate. How this should be done is problematic in many cases. There may be little data, and the data may be suspect.
How we arrive at these estimated percentages is complex: scientific, statistical, and not without error. It should be done independently of the test being evaluated. We call these percentages prior odds, priors, or baseline values.
We also need to look at the performance of a given test for classifying the results.
At first glance, you might think that you can apply these percentages against the whole matrix, assuming that the matrix represents 100%, and each of the four cells has some fraction, all adding up to 100%. Things don’t work that way.
The test performance, the percentages, for separating false positives from true negatives only applies to those who are uninfected. Remember, this information on overall infection rates is obtained in some other manner, including other studies, some wildassed guess, or a deity told you.
On the other side of the matrix, the test performance, the percentages, for separating false negatives from true positives only applies to those who are infected. Remember the sources of this information laid out above.
Here is a diagram adapted from a very good tutorial on this topic. See “Confused by The Confusion Matrix: What’s the difference between Hit Rate, True Positive Rate, Sensitivity, Recall and Statistical Power?” by The Curious Learner, https://learncuriously.wordpress.com/2018/10/21/confusedbytheconfusionmatrix/
Does the Effect Exist?  
Effect Exists  Effect Doesn’t Exist  
Was the Effect Observed?  Effect Observed  · Hit Rate
· True Positive Rate · Sensitivity · Statistical Power · (1 – Beta) 
· False Alarm Rate
· False Positive Rate · Statistical Significance · Type I Error Rate (Alpha) 
Effect Not Observed  · Miss Rate
· False Negative Rate · Type II Error Rate (Beta) 
· Correct Rejection Rate
· True Negative Rate 
Tests provide evidence. Evidence must be:
Tests can be given scores based on sensitivity (true positives) and selectivity (true negatives). As shown above, true positives and false negatives are complements of one and other, and also, true negatives and false positives are also complements of one and other.
Testing must take the priors into account when the calculations are done. It makes no sense to apply percentages for false positives and true negatives against the category of estimated infected. Likewise, it makes no sense to apply percentage for true positives and false negatives against the category of estimated uninfected. The false positives and true negative test percentages are based on the uninfected. The true positives and false negative test percentages are based on the infected.
We can work with percentages, but for analysis, we really want to see actual counts. We make use of the overall number of independent tests, the priors, and the test performance to make a two by two matrix of estimated test performance.
You can set a threshold for a test score, setting the bias point. If you set the threshold, the sensitivity, to give more hits, you will get more false alarms and miss less often. If you set the threshold, the sensitivity, to give fewer hits, you will get fewer false alarms and miss more often.
With a low prior rate of infection, the number of false positives can be much greater than the number of true positives, even with an accurate test.
Estimated or actual values for a given test can be plotted, putting False Positives (X) against True Positives (Y) to give a curve. This plot is called the receiver operating characteristic (ROC) curve. Any point along the curve can be selected to give a cutoff point, a threshold. If this threshold is set to detect more cases, you also get more false positives. If this threshold is set to exclude more cases, you also get fewer false positives.
The area under the ROC curve also gives a measure of accuracy. The greater the area is, the more accurate the test. Since the axis both go from 0 to 1, the maximum area is 1 squared. A diagonal line for the ROC curve gives performance at chance levels.
Not all tests are equal. Some have much better accuracy overall. The more bowed the ROC curve is above the diagonal, the better the test.
See http://www.rad.jhmi.edu/jeng/javarad/roc/JROCFITi.html
False Positive Fraction (FPF)  True Positive Fraction (TPF)  Lower  Upper 
0.0000  0.0000  0.0000  0.0000 
0.0050  0.2301  0.0169  0.7407 
0.0100  0.3135  0.0430  0.7718 
0.0200  0.4168  0.0996  0.8061 
0.0300  0.4860  0.1545  0.8282 
0.0400  0.5384  0.2056  0.8449 
0.0500  0.5807  0.2523  0.8587 
0.0600  0.6159  0.2949  0.8705 
0.0700  0.6461  0.3337  0.8808 
0.0800  0.6723  0.3690  0.8901 
0.0900  0.6955  0.4012  0.8985 
0.1000  0.7161  0.4306  0.9062 
0.1100  0.7347  0.4575  0.9132 
0.1200  0.7515  0.4821  0.9198 
0.1300  0.7668  0.5047  0.9258 
0.1400  0.7809  0.5255  0.9314 
0.1500  0.7938  0.5447  0.9366 
0.2000  0.8454  0.6214  0.9577 
0.2500  0.8822  0.6757  0.9723 
0.3000  0.9096  0.7160  0.9824 
0.4000  0.9466  0.7727  0.9934 
0.5000  0.9691  0.8119  0.9978 
0.6000  0.9832  0.8424  0.9994 
0.7000  0.9918  0.8684  0.9999 
0.8000  0.9967  0.8927  1.0000 
0.9000  0.9992  0.9189  1.0000 
0.9500  0.9998  0.9357  1.0000 
1.0000  1.0000  1.0000  1.0000 
Number of Cases: 50
Number Correct: 42
Accuracy: 84%
Sensitivity: 88%
Specificity: 80%
Positive Cases Missed: 3
Negative Cases Missed: 5
(A rating of 3 or greater is considered positive.)
Fitted ROC Area: 0.905
Empiric ROC Area: 0.892
ROC Curve Type: Fitted
Key for the ROC Plot
RED symbols and BLUE line: Fitted ROC curve.
GRAY lines: 95% confidence interval of the fitted ROC curve.
BLACK symbols ± GREEN line: Points making up the empirical ROC curve (does not apply to Format 5).
The test can be viewed as the measure plus the measuring method. It can also include the procedures, the protocol for conducting the test. Differing protocols can change and confound the test results. Tests can be very accurate and still give a large number of false positives when the estimate of infection rates is low.
The test results require interpretation by a skilled clinician. Sometimes, tests are used for screening, and sometimes for actual diagnosis. One test alone should not be relied upon. Tests should be repeated.
Test results for the same individual can vary because of “noise” masking the “signal.” By noise we mean fluctuations in the measurement of interest that are based on other factors than the condition of interest, perhaps random factors.
Test results can vary for the same individual because the underlying conditions can change from one time to the next. Levels of any condition can fluctuate over time: hourly, daily, weekly, … . With heath conditions: you get infected, you get sick, you get better, you die, … .
The simple calculations of false positive expected rates:
Multiply them together to get the expected count of false positives. False positives are only evaluated against the uninfected cases, not all test cases.
Calculate the false negative expected rates
Multiply them together to get the expected count of false negatives. False negatives are only evaluated against the infected cases, not all test cases.
Calculate the true positive expected rates
Multiply them together to get the expected count of true positives. True positives are only evaluated against the infected cases, not all test cases.
Calculate the true negatives expected rates
Multiply them together to get the expected count of true negatives. True negatives are only evaluated against the uninfected cases, not all test cases.
In the example below, I set the following parameters:
Number of Tests  1,000.00 
Population Baseline Estimates  
Prior Baseline Infection Rate Estimate  2 % 
Baseline True Positives = Prior Baseline X Number of Tests 
20 
Baseline True Negatives = (1 – Prior Baseline) X Number of Tests 
980 
Testing Method Performance  
Hit Rate (Sensitivity)  95% 
Miss Rate = One’s Complement of Hit Rate 
5% 
False Alarm Rate  10% 
Correct Rejection Rate (Specificity) = One’s Complement of False Alarm Rate 
90% 
Using these parameters, I calculate expected counts:
Expected Counts  
True Positives (TP) = Baseline True Positives X Hit Rate 
19 
False Positives (FP) = Baseline True Negatives X False Alarm Rate 
98 
False Negatives (FN) = Baseline True Positives X Miss Rate 
1 
True Negatives (TN) = Baseline True Negatives X Correct Rejection Rate 
882 
I summarize the calculated values in the matrix below. You can see that the number of false positives, under these assumptions, is 5 times the amount of true positives, i.e., very high. Also, the false negative rate is very low for this test and the prior infection rates. This is with a test selectivity of 90%, a test sensitivity of 95%, and an estimated infection rate of 2%.
Does The Condition Exist?  
Condition Exists  Condition Is Absent  
Was the Effect Observed?  Effect Observed  TP = 19  FP = 98 
Effect Not Observed  FN = 1  TN = 882  
Estimated Counts
Based on Test Performance, Priors, and Number of Tests 
Below are various measures of test performance, test quality. They use the previous data from the previous example. The calculations presented here are simple. The interpretation takes more skill.
Measures of Test Performance  
Diagnostic Accuracy = (TP + TN) / TP + TN + FP + FN 
0.90 
Sensitivity = (TP) / (TP + FN) 
0.95 
Specificity = (TN) / (TN +FP) 
0.90 
Positive Predictive Value (PPV) = (TP) / (TP + FP) 
0.16 
Negative Predictive Value (NPV) = (TN) / (TN + FN) 
1.00 
The Positive Predictive Value (PPV) and the Negative Predictive Value (NPV) give the probabilities based on whether of not the effect was observed. This contrasts with the sensitivity and selectivity that give probabilities based on the estimated existence of the effect.
Does the Effect Exist?  
Effect Exists  Effect Doesn’t Exist  
Was the Effect Observed?  Effect Observed  True Discovery Rate
Positive Predictive Value Precision 
False Discovery Rate 
Effect Not Observed  False Omission Rate  True Omission Rate
Negative Predictive Value 
Adapted from “Confused by The Confusion Matrix: What’s the difference between Hit Rate, True Positive Rate, Sensitivity, Recall and Statistical Power?” by The Curious Learner, https://learncuriously.wordpress.com/2018/10/21/confusedbytheconfusionmatrix/
Here are test estimates based upon five differing population baseline estimates, that is, differing estimates of priors. I vary the priors from 0.1 percent to 99.9 percent.
N.B. In order to avoid division by 0, I did not use 0.0 percent and 100 percent.
Number of Tests  1,000  1,000  1,000  1,000  1,000 
Testing Method  
Hit Rate (Sensitivity)  95%  95%  95%  95%  95% 
Miss Rate = Ones Complement of Hit Rate 
5%  5%  5%  5%  5% 
False Alarm Rate  10%  10%  10%  10%  10% 
Correct Rejection Rate (Specificity) = Ones Complement of False Alarm Rate 
90%  90%  90%  90%  90% 
Population Baseline Estimates  
Prior Baseline  0.10%  2%  50%  98%  99.90% 
Baseline True Positives = Prior Baseline X Number of Tests 
1  20  500  980  999 
Baseline True Negatives = (1 – Prior Baseline) X Number of Tests 
999  980  500  20  1 
Expected Counts  
True Positives (TP) = Baseline True Positives X Hit Rate 
0.95  19  475  931  949.05 
False Positives (FP) = Baseline True Negatives X False Alarm Rate 
99.9  98  50  2  0.1 
False Negatives (FN) = Baseline True Positives X Miss Rate 
0.05  1  25  49  49.95 
True Negatives (TN) = Baseline True Negatives X Correct Rejection Rate 
899.1  882  450  18  0.90 
Quality Tests  
Diagnostic Accuracy = (TP + TN) / TP + TN + FP + FN 
0.90  0.90  0.93  0.95  0.95 
Sensitivity = (TP) / (TP + FN) 
0.95  0.95  0.95  0.95  0.95 
Specificity = (TN) / (TN +FP) 
0.90  0.90  0.90  0.90  0.90 
Positive Predictive Value (PPV) = (TP) / (TP + FP) 
0.01  0.16  0.90  1.00  1.00 
Negative Predictive Value (NPV) = (TN) / (TN + FN) 
1.00  1.00  0.95  0.27  0.02 
Positive Predictive Likelihood Ratios = Sensitivity / (1 – Specificity) 
9.50  9.50  9.50  9.50  9.50 
Negative Predictive Likelihood Ratios = (1 – Sensitivity) / Specificity 
0.06  0.06  0.06  0.06  0.06 
Youden’s Index = (Sensitivity + Specificity) – 1 
0.85  0.85  0.85  0.85  0.85 
Diagnostic Odds Ratio (DOR) = (TP / FN) / (FP / TN) 
171.00  171.00  171.00  171.00  171.00 
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This is a write up on false positive, false negative, true positive, true negative thinking in testing for some condition, trying to detect if it is there or not. It is useful for discussing medical tests, but it applies to any sort of testing where decisions must be made.
I said I would write up testing, so I did. It always comes out seeming more complex than it seems at first glance, even though the calculations are simple arithmetic. I have another one in draft, hitting the material from a different angle, but unfortunately not making it simpler.
This fits within the framework of signal detection theory. When I studied signal detection, I had no idea why it was considered important, particularly in Psychology, but over the years, I have often gone back to it, since it comes up routinely in a number of guises. It has to be statistical signal detection, which would be an obvious extension to binary, deterministic signal detection. This also fits within the framework of fuzzy logic, which I have looked at in years past.
Medical testing makes use of the ideas on signal detection and upon reflection, is no different than the consideration of any other sort of evidence – it has to be obtained, assessed for quality, and interpreted to understand the implications.
The take away is that for low prevalence of a condition (e.g. infection), you can get a lot of false positives (false alarms), even with a fairly specific test. For a high prevalence of a condition, you can get a lot of false negatives (misses). In addition, for a highly selective test, you get fewer false positives (false alarms), and for a highly sensitive test, you get fewer false negatives (misses).
In the example below, I show how false positives can be far greater than true positives, even for a fairly well performing test, when the prevalence is low:
Parameters 
Complement of Parameters 
Selectivity = .95  1 – selectivity = .05 
Sensitivity = .99  1 – sensitivity = .01 
Prevalence = .01  1 – prevalence = .99 
We have this formula: Ratio of false positives (FP) to true positives (TP) = ( (1selectivity) x (1prevalence) ) / ((sensitivity) x (prevalence) ) .
False positives to true positives = ((.05) x (.99))/(.99) x (.01)) = 5
Using the formula, we get a 5 fold increase of false positives over true positives, for a test that has quite good performance. Below I will show how for any test with error rates, both low prevalence and high prevalence give more false results.
It is nice to now have those words, “specificity” (true negative) and “sensitivity” (true positive) for test performance which I lacked before. I give more explanation below.
Anybody who tells you that such and such a test is any given percentage effective is misleading you somewhat, unintentionally or perhaps even deliberately.
There are four quadrants in the “gold standard” detection matrix: true positive, false positive, true negative, and false negative. There are at least two percentages to be considered, and they vary independently according to the bias in your test, the detection threshold decided upon. You can bias so that you find all the cases, with the consequence that you get a lot of false positives (false alarms). You can bias so that you get few false positives, and as a result, get a lot of false negatives (miss the fire). In addition, the baseline must be considered, with respect to a Bayesian statistical analysis. So, the prior information on general infection rates will make the percentages change. Low base rate of infection gives a high number of false positives. High base rate of infection gives a low number of false positives.
Bayesian reasoning: start with prior probabilities (assessed somehow) and see how probabilities change with new evidence.
If you do not have much noise masking the signal, results are easier to interpret. If you have large numbers and effects that are strong with respect to variability, the statistics should bear you out. Potentially confounding factors can be accounted for.
See http://ephektikoi.ca/blog/2020/10/11/bibliographyontestinganduncertainty/ for more information.
It is routine for medical tests to be used to determine the health status of people. The simple view of a test is that it returns a true or false result, using some measure, some test instrument, and some testing protocol. Of course anyone reflecting on the issue even a little bit will realize that this is a much oversimplified view of things. For one thing, what threshold, what cutoff point, is being used to make the decision of true or false? What is the measure being used, and what is the measuring instrument? Most things we measure involve some sort of continuous scale. Are the measurements continuous or is it yes and no? What are the typical values that are used to make the judgement? What are the health implications? How are the numbers to be interpreted as a screening device or diagnostic tool? All of these considerations are important for understanding the test.
Here is a diagram of a test which does not consider that there might be some error.
Does the Condition Exist?  
Is the Effect Observed?  Observed  Condition exists 
Not observed  Condition is absent  
True or false – assuming no errors 
With a bit of thought, the question of errors for the test will come up. Is the test perfect? This would seem highly unlikely.
In testing, there are two ways for the results to be true, and two ways for the results to be false.
Does The Condition Exist?  
Condition Exists  Condition Is Absent  
Is The Effect Observed?  Observed  Condition Is Correctly Considered To Exist
(HIT) (TRUE POSITIVE) 
Condition Is Falsely Considered To Exist
(FALSE ALARM) (FALSE POSITIVE) 
Not Observed  Condition Is Falsely Considered To Be Absent
(MISS) (FALSE NEGATIVE) 
Condition Is Correctly Consider To Be Absent
(TRUE REJECTION) (TRUE NEGATIVE) 

True Or False – Assuming Errors

Synonyms for these terms are:
I will use the abbreviations TP, FP, FN, TN in most of the discussion, although the meanings are probably not as easily grasped.
Three factors for calculations:
Performance of a test: selectivity and sensitivity
Sensitivity applies to a population that all truly have the condition. It is the ratio of hits to misses, usually as a percentage of hits to overall tests. Percentage is calculated (hits / (hits + misses) x 100). Sensitivity gives the percent hits. The one’s complement of sensitivity gives the percent misses. With poorer sensitivity tests, the number of misses gets larger.
Selectivity applies to a population were none have the condition. It is the ratio of correct rejections to false alarms, usually as a percentage of rejections to overall tests. Percentage is calculated as (rejections / (rejections + false alarms) x 100). Selectivity gives the percent correct rejections. The one’s complement of selectivity gives the false alarm percent. With poorer selectivity tests, the number of false alarms gets larger.
Prevalence gives the estimated number where the condition is present. The one’s complement of prevalence gives the estimated number where the condition is absent.
Lower prevalence gives more false positives or false alarms and also lower prevalence gives fewer false negatives or misses.
Higher prevalence gives more false negatives or misses and also higher prevalence gives fewer false positives or false alarms.
False negatives are a function of sensitivity and prevalence whereas false positives are a function of selectivity and prevalence.
The number of tests done independently gives the counts.
In calculating expected values for a condition and errors, use performance, prevalence and the number of tests
Hits  False alarms 
Misses  Correct rejections 
Hits versus false alarms are a function of test performance and prevalence.
Considerations: It is a mistake to only use just performance and test count without taking prevalence into account – a big mistake
Given that you know the performance of a test, and the prevalence of the condition, you can calculate the ratios of:
Ratio of FP to TP ( (1selectivity) x (1prevalence) ) / ((sensitivity) x (prevalence) )
Ratio of FN to TN ( (1sensitivity) x (prevalence) ) / ((selectivity) x (1 – prevalence) )
Example 1
Parameters  Complement 
Selectivity = .95  1 – selectivity = .05 
Sensitivity = .99  1 – sensitivity = .01 
Prevalence = .01  1 – prevalence = .99 
False positives to true positives = ((.05) x (.99))/(.99) x (.01)) = 5
Using the formula, we get a 5 fold increase of false positives over true positives
Example 2
Parameters  Complement 
Selectivity = 1.00  1 – selectivity = 0.0 
Sensitivity = 1.00  1 – sensitivity = 0.0 
Prevalence = .50  1 – prevalence = .50 
False positives to true positives = ((0) x (.5))/(1) x (.5)) = 0
Using the formula, we get a no increase in false positives over true positives; in fact, there are no false positives or false negatives.
Formulae Summarized
Test Count = number of tests
selectivity (fraction of correct rejections for those without condition)
complement of selectivity (fraction of false alarms for those without condition) = (1 – selectivity)
sensitivity (fraction of hits for those with condition)
complement of sensitivity (fraction of misses for those with condition) = (1 – sensitvity)
prevalence is actual incidence as percent of population with condition
complement of prevalance is percent of population without condition = (1 – prevalence)
Estimated True Positive (Hits, TP) = sensitivity x prevalence x case count
Estimated False Positive (False Alarms, FP) = (1 – selectivity) x (1 – prevalence) x (case count)
Estimated False Negatives (Misses, FN) = (1 – sensitivity) * (prevalence) x case count
Estimated True Negatives (Correct Rejections, TN) = (selectivity) x (1 – prevalence) x (case count)
Ratio of FP to TP ( (1selectivity) x (1prevalence) ) / ((sensitivity) x (prevalence) )
Ratio of FN to TN ( (1sensitivity) x (prevalence) ) / ((selectivity) x (1 – prevalence) )
The pattern for all is that the end regions of the curve get high inversely in proportion to the performance of the test. That is for low prevalence and high prevalence both, there are more errors. For low prevalence, the errors are false positives. For high prevalence, the errors are false negatives. The error rates for both types of errors are lower in the middle. High selectivity reduces false positive errors. High sensitivity reduces false negative errors. The ultimate high is the nonexistent perfectly performancing test with selectivity of 100% and sensitivity of 100%.
Selectivity 100%, Sensitivity 100%  
A Balanced Perfect Test  Counts  
Count  Selectivity  Sensitivity  Prevalence  Ratio FP to TP  Ratio FN to TN  TP  FP  FN  TN 
1000  1.00  1.00  0.00  0.00  0.00  0.00  0.00  0.00  1000.00 
1000  1.00  1.00  0.02  0.00  0.00  20.00  0.00  0.00  980.00 
1000  1.00  1.00  0.03  0.00  0.00  30.00  0.00  0.00  970.00 
1000  1.00  1.00  0.04  0.00  0.00  40.00  0.00  0.00  960.00 
1000  1.00  1.00  0.05  0.00  0.00  50.00  0.00  0.00  950.00 
1000  1.00  1.00  0.10  0.00  0.00  100.00  0.00  0.00  900.00 
1000  1.00  1.00  0.20  0.00  0.00  200.00  0.00  0.00  800.00 
1000  1.00  1.00  0.30  0.00  0.00  300.00  0.00  0.00  700.00 
1000  1.00  1.00  0.40  0.00  0.00  400.00  0.00  0.00  600.00 
1000  1.00  1.00  0.50  0.00  0.00  500.00  0.00  0.00  500.00 
1000  1.00  1.00  0.60  0.00  0.00  600.00  0.00  0.00  400.00 
1000  1.00  1.00  0.70  0.00  0.00  700.00  0.00  0.00  300.00 
1000  1.00  1.00  0.80  0.00  0.00  800.00  0.00  0.00  200.00 
1000  1.00  1.00  0.90  0.00  0.00  900.00  0.00  0.00  100.00 
1000  1.00  1.00  0.98  0.00  0.00  980.00  0.00  0.00  20.00 
1000  1.00  1.00  1.00  0.00  0.00  1000.00  0.00  0.00  0.00 
Selectivity 90%, Sensitivity 99%  
An Unbalanced Test with Reasonable Performance  Counts  
Count  Selectivity  Sensitivity  Prevalence  Ratio FP to TP  Ratio FN to TN  TP  FP  FN  TN 
1000  0.90  0.99  0.01  10.00  0.00  9.90  99.00  0.10  891.00 
1000  0.90  0.99  0.02  4.95  0.00  19.80  98.00  0.20  882.00 
1000  0.90  0.99  0.03  3.27  0.00  29.70  97.00  0.30  873.00 
1000  0.90  0.99  0.04  2.42  0.00  39.60  96.00  0.40  864.00 
1000  0.90  0.99  0.05  1.92  0.00  49.50  95.00  0.50  855.00 
1000  0.90  0.99  0.10  0.91  0.00  99.00  90.00  1.00  810.00 
1000  0.90  0.99  0.20  0.40  0.00  198.00  80.00  2.00  720.00 
1000  0.90  0.99  0.30  0.24  0.00  297.00  70.00  3.00  630.00 
1000  0.90  0.99  0.40  0.15  0.01  396.00  60.00  4.00  540.00 
1000  0.90  0.99  0.50  0.10  0.01  495.00  50.00  5.00  450.00 
1000  0.90  0.99  0.60  0.07  0.02  594.00  40.00  6.00  360.00 
1000  0.90  0.99  0.70  0.04  0.03  693.00  30.00  7.00  270.00 
1000  0.90  0.99  0.80  0.03  0.04  792.00  20.00  8.00  180.00 
1000  0.90  0.99  0.90  0.01  0.10  891.00  10.00  9.00  90.00 
1000  0.90  0.99  0.98  0.00  0.54  970.20  2.00  9.80  18.00 
1000  0.90  0.99  0.99  0.00  1.10  980.10  1.00  9.90  9.00 
Selectivity 99%, Sensitivity 90%  
An Unbalanced Test with Reasonable Performance 
Counts  
Count  Selectivity  Sensitivity  Prevalence  Ratio FP to TP  Ratio FN to TN  TP  FP  FN  TN 
1000  0.99  0.90  0.01  1.10  0.00  9.00  9.90  1.00  980.10 
1000  0.99  0.90  0.02  0.54  0.00  18.00  9.80  2.00  970.20 
1000  0.99  0.90  0.03  0.36  0.00  27.00  9.70  3.00  960.30 
1000  0.99  0.90  0.04  0.27  0.00  36.00  9.60  4.00  950.40 
1000  0.99  0.90  0.05  0.21  0.01  45.00  9.50  5.00  940.50 
1000  0.99  0.90  0.10  0.10  0.01  90.00  9.00  10.00  891.00 
1000  0.99  0.90  0.20  0.04  0.03  180.00  8.00  20.00  792.00 
1000  0.99  0.90  0.30  0.03  0.04  270.00  7.00  30.00  693.00 
1000  0.99  0.90  0.40  0.02  0.07  360.00  6.00  40.00  594.00 
1000  0.99  0.90  0.50  0.01  0.10  450.00  5.00  50.00  495.00 
1000  0.99  0.90  0.60  0.01  0.15  540.00  4.00  60.00  396.00 
1000  0.99  0.90  0.70  0.00  0.24  630.00  3.00  70.00  297.00 
1000  0.99  0.90  0.80  0.00  0.40  720.00  2.00  80.00  198.00 
1000  0.99  0.90  0.90  0.00  0.91  810.00  1.00  90.00  99.00 
1000  0.99  0.90  0.98  0.00  4.95  882.00  0.20  98.00  19.80 
1000  0.99  0.90  0.99  0.00  10.00  891.00  0.10  99.00  9.90 
Selectivity 99%, Sensitivity 99%  
A Balanced Test, with Excellent Performance 
Counts  
Count  Selectivity  Sensitivity  Prevalence  Ratio FP to TP  Ratio FN to TN  TP  FP  FN  TN 
1000  0.99  0.99  0.01  1.00  0.00  9.90  9.90  0.10  980.10 
1000  0.99  0.99  0.02  0.49  0.00  19.80  9.80  0.20  970.20 
1000  0.99  0.99  0.03  0.33  0.00  29.70  9.70  0.30  960.30 
1000  0.99  0.99  0.04  0.24  0.00  39.60  9.60  0.40  950.40 
1000  0.99  0.99  0.05  0.19  0.00  49.50  9.50  0.50  940.50 
1000  0.99  0.99  0.10  0.09  0.00  99.00  9.00  1.00  891.00 
1000  0.99  0.99  0.20  0.04  0.00  198.00  8.00  2.00  792.00 
1000  0.99  0.99  0.30  0.02  0.00  297.00  7.00  3.00  693.00 
1000  0.99  0.99  0.40  0.02  0.01  396.00  6.00  4.00  594.00 
1000  0.99  0.99  0.50  0.01  0.01  495.00  5.00  5.00  495.00 
1000  0.99  0.99  0.60  0.01  0.02  594.00  4.00  6.00  396.00 
1000  0.99  0.99  0.70  0.00  0.02  693.00  3.00  7.00  297.00 
1000  0.99  0.99  0.80  0.00  0.04  792.00  2.00  8.00  198.00 
1000  0.99  0.99  0.90  0.00  0.09  891.00  1.00  9.00  99.00 
1000  0.99  0.99  0.98  0.00  0.49  970.20  0.20  9.80  19.80 
1000  0.99  0.99  0.99  0.00  1.00  980.10  0.10  9.90  9.90 
Selectivity 95%, Sensitivity 95%  
A Balanced Test, with Decent Performance 
Counts  
Count  Selectivity  Sensitivity  Prevalence  Ratio FP to TP  Ratio FN to TN  TP  FP  FN  TN 
1000  0.95  0.95  0.01  5.21  0.00  9.50  49.50  0.50  940.50 
1000  0.95  0.95  0.02  2.58  0.00  19.00  49.00  1.00  931.00 
1000  0.95  0.95  0.03  1.70  0.00  28.50  48.50  1.50  921.50 
1000  0.95  0.95  0.04  1.26  0.00  38.00  48.00  2.00  912.00 
1000  0.95  0.95  0.05  1.00  0.00  47.50  47.50  2.50  902.50 
1000  0.95  0.95  0.10  0.47  0.01  95.00  45.00  5.00  855.00 
1000  0.95  0.95  0.20  0.21  0.01  190.00  40.00  10.00  760.00 
1000  0.95  0.95  0.30  0.12  0.02  285.00  35.00  15.00  665.00 
1000  0.95  0.95  0.40  0.08  0.04  380.00  30.00  20.00  570.00 
1000  0.95  0.95  0.50  0.05  0.05  475.00  25.00  25.00  475.00 
1000  0.95  0.95  0.60  0.04  0.08  570.00  20.00  30.00  380.00 
1000  0.95  0.95  0.70  0.02  0.12  665.00  15.00  35.00  285.00 
1000  0.95  0.95  0.80  0.01  0.21  760.00  10.00  40.00  190.00 
1000  0.95  0.95  0.90  0.01  0.47  855.00  5.00  45.00  95.00 
1000  0.95  0.95  0.98  0.00  2.58  931.00  1.00  49.00  19.00 
1000  0.95  0.95  0.99  0.00  5.21  940.50  0.50  49.50  9.50 
Selectivity 90%, Sensitivity 90%  
A Balanced Test, with OK Performance 
Counts  
Count  Selectivity  Sensitivity  Prevalence  Ratio FP to TP  Ratio FN to TN  TP  FP  FN  TN 
1000  0.90  0.90  0.01  11.00  0.00  9.00  99.00  1.00  891.00 
1000  0.90  0.90  0.02  5.44  0.00  18.00  98.00  2.00  882.00 
1000  0.90  0.90  0.03  3.59  0.00  27.00  97.00  3.00  873.00 
1000  0.90  0.90  0.04  2.67  0.00  36.00  96.00  4.00  864.00 
1000  0.90  0.90  0.05  2.11  0.01  45.00  95.00  5.00  855.00 
1000  0.90  0.90  0.10  1.00  0.01  90.00  90.00  10.00  810.00 
1000  0.90  0.90  0.20  0.44  0.03  180.00  80.00  20.00  720.00 
1000  0.90  0.90  0.30  0.26  0.05  270.00  70.00  30.00  630.00 
1000  0.90  0.90  0.40  0.17  0.07  360.00  60.00  40.00  540.00 
1000  0.90  0.90  0.50  0.11  0.11  450.00  50.00  50.00  450.00 
1000  0.90  0.90  0.60  0.07  0.17  540.00  40.00  60.00  360.00 
1000  0.90  0.90  0.70  0.05  0.26  630.00  30.00  70.00  270.00 
1000  0.90  0.90  0.80  0.03  0.44  720.00  20.00  80.00  180.00 
1000  0.90  0.90  0.90  0.01  1.00  810.00  10.00  90.00  90.00 
1000  0.90  0.90  0.98  0.00  5.44  882.00  2.00  98.00  18.00 
1000  0.90  0.90  0.99  0.00  11.00  891.00  1.00  99.00  9.00 
Selectivity 50%, Sensitivity 50%  
A Balanced Test, with Poor Performance 
Counts  
Count  Selectivity  Sensitivity  Prevalence  Ratio FP to TP  Ratio FN to TN  TP  FP  FN  TN 
1000  0.50  0.50  0.01  99.00  0.01  5.00  495.00  5.00  495.00 
1000  0.50  0.50  0.02  49.00  0.02  10.00  490.00  10.00  490.00 
1000  0.50  0.50  0.03  32.33  0.03  15.00  485.00  15.00  485.00 
1000  0.50  0.50  0.04  24.00  0.04  20.00  480.00  20.00  480.00 
1000  0.50  0.50  0.05  19.00  0.05  25.00  475.00  25.00  475.00 
1000  0.50  0.50  0.10  9.00  0.11  50.00  450.00  50.00  450.00 
1000  0.50  0.50  0.20  4.00  0.25  100.00  400.00  100.00  400.00 
1000  0.50  0.50  0.30  2.33  0.43  150.00  350.00  150.00  350.00 
1000  0.50  0.50  0.40  1.50  0.67  200.00  300.00  200.00  300.00 
1000  0.50  0.50  0.50  1.00  1.00  250.00  250.00  250.00  250.00 
1000  0.50  0.50  0.60  0.67  1.50  300.00  200.00  300.00  200.00 
1000  0.50  0.50  0.70  0.43  2.33  350.00  150.00  350.00  150.00 
1000  0.50  0.50  0.80  0.25  4.00  400.00  100.00  400.00  100.00 
1000  0.50  0.50  0.90  0.11  9.00  450.00  50.00  450.00  50.00 
1000  0.50  0.50  0.98  0.02  49.00  490.00  10.00  490.00  10.00 
1000  0.50  0.50  0.99  0.01  99.00  495.00  5.00  495.00  5.00 
]]>
The effectiveness of mask wearing is called into doubt by some people and by some studies. Although I believe the evidence shows that it is of value in controlling the spread of Covid19, both infectivity and viral load, all evidence is subject to interpretation. All evidence has a possibility of being incorrect. All findings are underdetermined.
There is a great diversity of opinion about the wearing of masks for protection against Covid19 infection. Sometimes, the opinions are allegedly supported by studies and expertise. In other cases, they seem to be little more than the result of a game of “telephone,” conducted over the Internet and social media. The discussion is much politicized, and brings in issues going far beyond the efficacy of masks in slowing the spread of a virus. People with claimed relevant expertise have weighed in on various sides of the topic, each with their arguments, each with information presented as fact. A lot of the views seem to be springing from bias – confirmation and disconfirmation – and in general motivated reasoning. It is clear that motivated reasoning, beliefs and values, determine how we evaluate evidence.
I also have my biases, and these are towards the wearing of masks as a reasonable and somewhat effective infection control measure and risk management measure. I cite a metaanalysis published in the Lancet which I find reasonably convincing, although the statistical techniques are far more advanced than any that I have ever studied. It can be found here at Physical distancing, face masks, and eye protection to prevent persontoperson transmission of SARScov2 and COVID19: a systematic review and metaanalysis.
I also refer you to a presentation of the UCSF School of Medicine by three specialists in disease control speaking on infection control. It can be found here at Covid19: How the Virus Gets in and How to Block It: Aerosols, Droplets, Masks, Face Shields, & More.
You can undoubtedly locate contrary opinions with ease. These may or may not be sound. When opinions differ, and contradict one and other, at best one can be correct.
On the issue of masks for infection control and Covid19 there are factors ranging far beyond the medical case. Cultural, social and emotional thinking colour the opinions that people hold.
Here are some of the issues that I feel might be important. There are undoubtedly other aspects to this that I have not covered but I think this is a good set for thinking about the issues.
Disagreement about the infectivity and virulence of Covid 19 are rampant in various communities. Your belief that the virus is mild or it is only those with comorbidities who suffer will influence the way you think about masks. If you believe that it is a very mild infection and that you probably won’t be infected, you will certainly not see the wisdom of wearing masks.
The effectiveness of mask wearing is called into doubt by some people and by some studies. Although I believe the evidence shows that it is of value in controlling the spread of Covid19, both infectivity and viral load, all evidence is subject to interpretation. All evidence has a possibility of being incorrect. All findings are underdetermined.
A person’s attitudes towards personal freedom and control by the state will affect their view of the wisdom and the appropriateness of wearing masks. This seems to trump any notion that the masks might be useful for controlling infection. I strongly suspect that those who are concerned with personal freedom are also prone to denigrate the infectivity and virulence of the virus and to also downplay the effectiveness of mask wearing. This is confirmation bias at work.
The degree of one’s concern for others as opposed to concern for the self may well play a role in attitudes towards the wearing of masks. If you’re someone with low empathy, someone who basically feels it’s every man for himself, then you may well be biased toward saying masks are ineffective or that masks should not be worn; its not the function of the state to mandate them.
The identification with political factions and shared viewpoints about the advisability of mask wearing will bias those holding certain views. In general people on the right tend to be more antimask than people in the left but it is not as clearcut as all of that.
You may have a belief that masks have harmful social consequences because it is essential that we be able to see others face in order to function smoothly in society. Of course, there are no cultures where masks are routinely worn, are there?
You may have a belief that masks have harmful medical consequences. For instance you may believe that masks do not allow the adequate intake of oxygen and the exhalation of carbon dioxide. There are studies on both sides of this issue but in fact people do wear masks in society and in medicine for extended periods of time; there do not seem to routine and significant reported negative consequences.
In addition there is a school of thought that by wearing a mask you do not allow the virus to escape and it will recirculate in your own body and increase your viral load. I have to admit this makes very little sense to me.
It’s my thinking that if you are strongly libertarian, you may find reasons to downplay both the severity of the infection and the need to wear masks.
If you are deficient in concern about others, and believe that the mask just protects others, you will find reasons to disparage mask wearing.
Perhaps those who believe in wearing a mask think along these lines:
Perhaps those who do not believe in wearing a mask think along these lines:
So, if you believe that the seriousness of the infection is vastly overblown you will find reasons to downplay mask wearing is necessary. These opinions all interact to some unknown degree. They are not independent factors. Beliefs, values and biases are an aspect of motivated reasoning.
Paul Graham
March 2008
The web is turning writing into a conversation. Twenty years ago, writers wrote and readers read. The web lets readers respond, and increasingly they do—in comment threads, on forums, and in their own blog posts.
Many who respond to something disagree with it. That’s to be expected. Agreeing tends to motivate people less than disagreeing. And when you agree there’s less to say. You could expand on something the author said, but he has probably already explored the most interesting implications. When you disagree you’re entering territory he may not have explored.
The result is there’s a lot more disagreeing going on, especially measured by the word. That doesn’t mean people are getting angrier. The structural change in the way we communicate is enough to account for it. But though it’s not anger that’s driving the increase in disagreement, there’s a danger that the increase in disagreement will make people angrier. Particularly online, where it’s easy to say things you’d never say face to face.
If we’re all going to be disagreeing more, we should be careful to do it well. What does it mean to disagree well? Most readers can tell the difference between mere namecalling and a carefully reasoned refutation, but I think it would help to put names on the intermediate stages. So here’s an attempt at a disagreement hierarchy: … ” more How to Disgree
]]>I consider it prudent to wear a mask when in close contact with people not in your personal “bubble.” I do not feel it makes sense to wear one when outside in the fresh air while maintaining a couple of meters of distance from those who are not in my “bubble.” This is risk management 101. I also think that claims of harm, physical and psychological from the wearing of masks are overblown to the point of absurdity. The other issue, that of social control, seems possibly overblown as well, although I am aghast at some of the draconian steps taken by authorities is some places. There are also a number of illinformed interpretations of the research literature.
I am by most indicators some sort of socialist libertarian, so yes, a libertarian. I still am not sold on the idea of masks being some part of a plot to control us. I believe that a lot of conspiracist views are well founded, since there are clearly many deep state conspiracies. I am not so sure about this one.
See for instance: https://www.opednews.com/articles/MotivatedReasoningbyMikeZimmerBelief_Bias_Ideas_MotivatedReasoning200804599.html and https://www.opednews.com/articles/MasksandMotivatedReasonbyMikeZimmerBelief_Bias_Covid19_Empathy200805253.html
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