## 5/24/2009

### Popular Concepts in Error/Result Analysis

The following are some popular and also confusing terms used in error/result analysis:

I - False Positive/False Negative

- False Positive
- A result that is erroneously positive when a situation is normal.
[误判 是某种情况被判断为成立，但实际上并不成立]
- False Negative - A result that appears negative but fails to reveal a situation.
[漏判 是某种情况实际上成立，但被判断为不成立]

The following table may better describe these concepts:

Actual condition
Present Absent
Test
result
Positive Condition Present + Positive result = True Positive Condition absent + Positive result = False Positive
Type I error
Negative Condition present + Negative result = False (invalid) Negative
Type II error
Condition absent + Negative result = True (accurate) Negative
(from wikipedia)

What confues me often is what's positive, what's negative? It may depend on your definition on test result and actual condition.

II - Precision/Recall

- Precision can be seen as a measure of exactness or fidelity
[查准率 是用来衡量准确、逼真程度的度量]

- Recall
is a measure of completeness.
[查全率 是用来衡量完备程度的度量]

In Information Retrieve Context, these two concepts can be defined as:

$\mbox{Precision}=\frac{|\{\mbox{relevant documents}\}\cap\{\mbox{documents retrieved}\}|}{|\{\mbox{documents retrieved}\}|}$
$\mbox{Recall}=\frac{|\{\mbox{relevant documents}\}\cap\{\mbox{documents retrieved}\}|}{|\{\mbox{relevant documents}\}|}$

While in classification context, these two concepts can be defined as:

correct result / classification

E1 E2
obtained
result / classification
E1 tp
(true positive)
fp
(false positive)
E2 fn
(false negative)
tn
(true negative)

$\mbox{Precision}=\frac{tp}{tp+fp} \,$
$\mbox{Recall}=\frac{tp}{tp+fn} \,$
(from wikipedia)

[Reference]

http://en.wikipedia.org/wiki/Precision_and_recall
http://en.wikipedia.org/wiki/Type_I_and_type_II_errors