Send
Close Add comments:
(status displays here)
Got it! This site "robinsnyder.com" uses cookies. You consent to this by clicking on "Got it!" or by continuing to use this website. Note: This appears on each machine/browser from which this site is accessed.
Computer literacy competency exams
1. Cost-value
How valuable is a certification exam? How about a computer literacy competency test?
What is the cost of looking at a student to determine if a student is computer literate?
What is the benefit of determining if a student is computer literate?
Does the value exceed the cost? If not, why do it?
2. Test accuracy
How accurate should the competency test be in terms of identifying a student as being computer literate?
That is, what is the probability that the student passes the test given that the student is computer literate.
What is P(PT | CL)?
3. Computer competency
What is the approximate percentage of students that are computer literate?
That is, what is the probability that a student is computer literate, given that we have no prior information about that student.
What is P(CL | PT)?
4. Problem
A student, who may or may not be computer literate, takes and passes a computer literacy competency exam.
Suppose that this is the only information available, as might be the case with a potential employer. What is the probability that the student is computer literate?
5. Computer literacy
A student is either computer literate or is not computer literate.
Let CL be the event that a student is computer literate, whatever that means.
The sets
CL and
CLc are mutually exclusive and collectively exhaustive.
6. Competency exam
A student either passes the computer literacy test or does not pass the computer literacy test.
Let PT be the event that a student passes a computer literacy test (i.e., a certification).
The sets
PT and
PTc are mutually exclusive and collectively exhaustive.
7. Possibilities
A student can pass the competency exam and be computer literate, a true-positive.
It is possible for a student to be computer literate, but not be able to pass the competency exam, a false-negative.
It is also possible for a student to pass the competency exam, but not be computer literate, a false-positive.
A student can fail the competency exam and not be computer literate, a true-negative.
8. Decision tree
9. Problem
What is the probability that a student is computer literate given that the student has passed a computer literacy test?
What is P(CL | PT)?
10. Knowns
The probability that can be measured is the probability that a student passes the computer literacy test given that they are computer literate.
P(PT | CL)
11. Conditional probability
From conditional probability, we have the following result.
P(CL | PT) = P(CL and PT) / P(PT)
We also know the following.
P(PT | CL) = (CL and PT) / P(CL)
12. Refinement
P(CL | PT)
= P(CL and PT) / P(PT)
= P(PT | CL) * P(CL) / (P(CL and PT) + P(CLc and PT))
= P(PT | CL) * P(CL) / (P(PT | CL) * P(CL) + P(PT | CLc) * P(CLc))
= P(PT | CL) * P(CL) / (P(PT | CL) * P(CL) + P(PT | CLc) * P(CLc))
= P(PT | CL) * P(CL) / (P(PT | CL) * P(CL) + (1 - P(PT | CL)) * (1 - P(CL)))
13. Variables
P(CL | PT) = P(PT | CL) * P(CL) /
(P(PT | CL) * P(CL) + (1 - P(PT | CL)) * (1 - P(CL)))
The dependent variable is P(CL | PT).
The independent variables are P(PT | CL) and P(CL).
The dependent variable
P(CL | PT) can be plotted as a 3-D chart in terms of the two independent variables
P(PT | CL) and
P(CL).
14. Some calculated results
If P(CL) = 10.0%, then even if P(PT | CL) is 80.0%, P(CL | PT) is only 30.0%.
If P(CL) = 10.0%, then even if P(PT | CL) is 50.0%, P(CL | PT) is only 10.0%.
15. 2-D sensitivity analysis
16. 3-D sensitivity analysis
17. End of page
