W2 - Lecture Summary
Type 1 and Type 2 Errors There are 4 different combinations when considering the potential outcomes of a scenario. We can see this if we examine the case of a doctors diagnosis of a patient:
The patient is sick, and the doctor’s diagnosis is positive
The patient is not sick, and the doctor’s diagnosis is negative
The patient is sick and the doctor’s diagnosis is negative
The patient is not sick and the doctor’s diagnosis is positive
As shown, the bottom two cases provide scenarios when the doctor is incorrect about his diagnosis of the patient; in case 3 (type 1 error), where something true claimed as false, and case 4 (type 2 error), where something false is claimed as true. One error may hold less consequence than the other, if continuing the scenario and saying the patient could have a life-threatening illness with the prescribed treatment holding little side-effect, we can see that receiving treatment and being subject to minor side effects holds much lesser consequence than not being treated and dying. Thus situations of similar nature are often implemented to favor the less detrimental outcome in case of error.
Coincidence Index To assist with cryptoanalysis we can determine how likely some text matches the frequency distribution of a set of data through the use of a coincidence index. This can be done as follows:
This allows us to provide a quantification of the likelihood of our text matching, and also provides information on effective (and ineffective) decryption methods to apply through testing. There are also other unreliable techniques which can be applied such a shifting the letters of the encrypted text, and seeing the recurrence of a letter between the the original and shifted versions.