Specificity And Sensitivity - Revision history

Carver: /* Something to be aware of */

2016-08-01T20:18:47Z

‎Something to be aware of

Carver: /* Something to be aware of */

2016-08-01T20:17:53Z

‎Something to be aware of

Carver at 20:14, 1 August 2016

2016-08-01T20:14:12Z

Carver at 19:39, 1 August 2016

2016-08-01T19:39:28Z

Carver at 19:36, 1 August 2016

2016-08-01T19:36:53Z

Carver at 19:35, 1 August 2016

2016-08-01T19:35:56Z

Carver at 19:29, 1 August 2016

2016-08-01T19:29:49Z

Carver at 19:23, 1 August 2016

2016-08-01T19:23:36Z

Carver at 19:21, 1 August 2016

2016-08-01T19:21:42Z

Carver at 19:16, 1 August 2016

2016-08-01T19:16:21Z

@@ Line 27: / Line 27: @@
 * Knowing the se'''N'''sitivity, and applying the last formula, you can figure out the probability of a False '''N'''egative.
-== Something to be aware of ==
+== Something to be aware of with imperfect tests ==
 You get a test for some terrible rare disease.  How terrible?  Let your imagination run with this.  How rare?  Only 1 in a million people have the disease.  Let's say the test has a seemingly decent specificity and sensitivity, 0.90 for each.

@@ Line 29: / Line 29: @@
 == Something to be aware of ==
-You get a test for some terrible rare disease.  How terrible?  Let your imagination run with this.  How rare?  Only 1 in a million people have the disease.  Let's say the test has a seemingly decent specificity and sensitivity, 0.90 for each.  You test positive for the disease!  Should you be worried?
+You get a test for some terrible rare disease.  How terrible?  Let your imagination run with this.  How rare?  Only 1 in a million people have the disease.  Let's say the test has a seemingly decent specificity and sensitivity, 0.90 for each.
-The answer is no, you should not be worried, if the disease is that rare.
+Uh oh, you test positive for the disease!  Should you be worried?
 If the disease were common, then yes, you should be worried.  (Not that worrying is going to help.)
@@ Line 41: / Line 43: @@
 So if you are one of the crowd who has a positive test result, your odds are only 9 in 100,000 of having the disease.  Pretty good odds!
-Moral: don't test for rare conditions, unless there are other indications that the disease is present.
+Moral: don't test for rare conditions, unless your test is perfect, or unless there are other indications that the disease is present.
-What if the condition were common?  If you 1 in 10 people had the disease, how would that change things?
+If you 1 in 10 people had the disease, how would that change things?
 There would be 1,000,000 with the disease, with 900,000 true positive and 100,000 false negatives.

← Older revision		Revision as of 20:14, 1 August 2016
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	* Knowing the se'''N'''sitivity, and applying the last formula, you can figure out the probability of a False '''N'''egative.		* Knowing the se'''N'''sitivity, and applying the last formula, you can figure out the probability of a False '''N'''egative.
		+
		+	== Something to be aware of ==
		+
		+	You get a test for some terrible rare disease. How terrible? Let your imagination run with this. How rare? Only 1 in a million people have the disease. Let's say the test has a seemingly decent specificity and sensitivity, 0.90 for each. You test positive for the disease! Should you be worried?
		+
		+	The answer is no, you should not be worried, if the disease is that rare.
		+
		+	If the disease were common, then yes, you should be worried. (Not that worrying is going to help.)
		+
		+	Let's say you run the test on all 10 million inhabitants of a large city. Only 10, or so, will have the disease; 9 of them will get a true positive whereas only 1 of them will get a false negative. There is of course some statistical uncertainty here, so the numbers may come out slightly different each time, in practice.
		+
		+	Of the approximately 10 million people that don't have the disease, 900,000 get true negative results where as 100,000 get false positives.
		+
		+	So if you are one of the crowd who has a positive test result, your odds are only 9 in 100,000 of having the disease. Pretty good odds!
		+
		+	Moral: don't test for rare conditions, unless there are other indications that the disease is present.
		+
		+	What if the condition were common? If you 1 in 10 people had the disease, how would that change things?
		+
		+	There would be 1,000,000 with the disease, with 900,000 true positive and 100,000 false negatives.
		+
		+	There would be 9,000,000 disease-free with 8,100,000 true negatives and 900,000 false positives.
		+
		+	You have a 50-50 chance of having the disease! Much worse odds. But still a worthless test. You want the specificity to be much higher.

@@ Line 9: / Line 9: @@
 This is where it gets confusing: False Positive Results are related to True Negative results and False Negative results are related to True Positive results.  Huh?
-* A false positive result means the truth is ''negative.''  So the test might have been '''a true negative''' instead of being '''a false positive''', those events are disjoint, and if the truth is negative, the result can't be categorized any other way.
+* A false positive result means the truth is ''negative.''  So the test might have been '''a true negative''' instead of being '''a false positive''', those events are disjoint, and result couldn't possibly be categorized any other way (if the truth is negative).
-* If the truth is negative, the test could still be positive or negative, so PROBABILITY(False Positive) + PROBABILITY(True Negative) = 1
+* If the truth is negative, the test could still go either way, so PROBABILITY(False Positive) + PROBABILITY(True Negative) = 1
 * Knowing one probability you can find the other
@@ Line 21: / Line 21: @@
 Similarly...
-* If the truth is positive, the test could still be positive or negative, so PROBABILITY(False Negative) + PROBABILITY(True Positive) = 1.
+* If the truth is positive, the test could still go either way, so PROBABILITY(False Negative) + PROBABILITY(True Positive) = 1.
 * The '''Sensitivity''' is the '''Probability of a True Positive, assuming the truth is Positive'''.
 * Knowing the se'''N'''sitivity, and applying the last formula, you can figure out the probability of a False '''N'''egative.

@@ Line 15: / Line 15: @@
 * Knowing one probability you can find the other
-* The '''Specificity''' is the Probability of a True Negative, assuming the truth is Negative.
+* The '''Specificity''' is the '''Probability of a True Negative, assuming the truth is Negative'''.
 * Knowing the s'''P'''ecificity, and applying the formula, you can figure out the probability of a False '''P'''ositive.
@@ Line 23: / Line 23: @@
 * If the truth is positive, the test could still be positive or negative, so PROBABILITY(False Negative) + PROBABILITY(True Positive) = 1.
-* The '''Sensitivity''' is the Probability of a True Positive, assuming the truth is Positive.
+* The '''Sensitivity''' is the '''Probability of a True Positive, assuming the truth is Positive'''.
 * Knowing the se'''N'''sitivity, and applying the last formula, you can figure out the probability of a False '''N'''egative.

@@ Line 7: / Line 7: @@
 * Sensitivity or se'''N'''sitivity concerns the rate of false '''N'''egatives.
-This is where it gets confusing...
+This is where it gets confusing: False Positive Results are related to True Negative results and False Negative results are related to True Positive results.  Huh?
-* A false positive result means the truth is ''negative.''  So the test might have been '''a true negative''' instead of being '''a false positive''', those events are disjoint, and if the truth is negative, the result can't be anything else.
+* A false positive result means the truth is ''negative.''  So the test might have been '''a true negative''' instead of being '''a false positive''', those events are disjoint, and if the truth is negative, the result can't be categorized any other way.
 * If the truth is negative, PROBABILITY(False Positive) + PROBABILITY(True Negative) = 1
@@ Line 16: / Line 16: @@
 * The '''Specificity''' is the Probability of a True Negative, assuming the truth is Negative.
 Similarly...
@@ Line 22: / Line 24: @@
 * The '''Sensitivity''' is the Probability of a True Positive, assuming the truth is Positive.

← Older revision		Revision as of 19:23, 1 August 2016
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	Similarly...		Similarly...
		+
		+	* If the truth is positive, PROBABILITY(False Negative) + PROBABILITY(True Positive) = 1.

	* The '''Sensitivity''' is the Probability of a True Positive, assuming the truth is Positive.		* The '''Sensitivity''' is the Probability of a True Positive, assuming the truth is Positive.

← Older revision		Revision as of 19:21, 1 August 2016
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	* A false positive result means the truth is ''negative.'' So the test might have been '''a true negative''' instead of being '''a false positive''', those events are disjoint, and if the truth is negative, the result can't be anything else.		* A false positive result means the truth is ''negative.'' So the test might have been '''a true negative''' instead of being '''a false positive''', those events are disjoint, and if the truth is negative, the result can't be anything else.
		+
		+	* If the truth is negative, PROBABILITY(False Positive) + PROBABILITY(True Negative) = 1
		+
		+	* Knowing one probability you can find the other
		+
		+	* The '''Specificity''' is the Probability of a True Negative, assuming the truth is Negative.
		+
		+	Similarly...
		+
		+	* The '''Sensitivity''' is the Probability of a True Positive, assuming the truth is Positive.

← Older revision		Revision as of 19:16, 1 August 2016
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	* Sensitivity or se'''N'''sitivity concerns the rate of false '''N'''egatives.		* Sensitivity or se'''N'''sitivity concerns the rate of false '''N'''egatives.
		+
		+	This is where it gets confusing...
		+
		+	* A false positive result means the truth is ''negative.'' So the test might have been '''a true negative''' instead of being '''a false positive''', those events are disjoint, and if the truth is negative, the result can't be anything else.