Performance Overview

The First Hourly

Spring 2008

 

Score Distribution

 

There were 94 tests taken.

The mean score among the 94 tests was approximately 75.8%.

The lowest scores among the 94 tests was 0%.

Approximately 95% of the scores were at 21% or more.

Approximately 90% of the scores were at 40% or more.

Approximately 75% of the scores were at 68% or more.

Approximately 70% of the scores were at 72% or more.

Approximately 60% of the scores were at 76% or more.

Approximately 50% of the scores were at 83% or more.

Approximately 40% of the scores were at 88% or more.

Approximately 30% of the scores were at 92% or more.

Approximately 25% of the scores were at 94% or more.

Approximately 20% of the scores were at 96% or more.

Approximately 10% of the scores were at 97% or more.

Approximately   5% of the scores were at 98% or more.

The highest scores among the 94 tests were at 100%.

 

Tabular Summaries

 

HR1

Frequency

Percent

[0,40)

9

9.57

[40,50)

4

4.26

[50,60)

4

4.26

[60,70)

10

10.64

[70,80)

16

17.02

[80,90)

17

18.09

[90,100)

32

34.04

100

2

2.13

 

 

HR1

Frequency

Percent

[0,50)

13

13.83

[50,60)

4

4.26

[60,70)

10

10.64

[70,80)

16

17.02

[80,90)

17

18.09

[90,100)

32

34.04

100

2

2.13

 

 

HR1

Frequency

Percent

[0,60)

17

18.09

[60,70)

10

10.64

[70,80)

16

17.02

[80,90)

17

18.09

[90,100)

32

34.04

100

2

2.13

 

 

HR1

Frequency

Percent

[0,60)

17

18.09

[60,70)

10

10.64

[70,80)

16

17.02

[80,90)

17

18.09

[90,100]

34

36.17

 

 

HR1

Frequency

Percent

[0,70)

27

28.72

[70,90)

33

35.11

[90,100]

34

36.17

 

 

 

 

 

 

Detail

 

I checked for full detail in your work, and docked points for deficient detail. The process is the point, the correct answer(s) naturally flow from the correct process.

 

Algebra and Arithmetic

 

Clean up your work, and watch the details. Clean up the arithmetic: “(1/4)*(1/2)” is not “1/6”; “(1/8)+(1/8)” is not “1/16”. If your algebra and arithmetic are deficient, get the required remediation.

 

Formatting

 

Space out your work and use one side only of the provided work sheets. I have provided extensive examples of acceptable and preferred formatting.

 

Interpretation and Discussion

 

This was a clear problem for some students – I view this as a matter of work ethic and attention to detail. Writing is a regular part of test work, and continued neglect will draw additional loss of points. Study the test banks, pay attention to case summaries, and provide the required writing.

 

Case Type Comments

 

Long Run Argument / Perfect Samples

 

We begin with a model, typically specified as a list of events (F) and their corresponding probabilities (Pr{F}=PF). The Long Run Argument is a way of describing the meaning of the model probabilities. The Long Run Argument indicates hoe the probabilities PF predict the prevalence of the events F in long runs of sampling – each long run is an indefinitely large hypothetical random sample, that is, a very large random sample of unstated size.

 

Next, a sample size (n) is provided, and a perfect sample is constructed – one count per event is computed as EF = n*Pr{F} = n*PF. The likely behavior of random samples of size n is predicted by the perfect sample of the same size.  

 

Dice / Random Variables

 

We list the 12 triplets by fixing the 1st die and then working with the other two dice. Fix D1 at 1, then: (1,2,3), (1,2,4), (1,3,3) and (1,3,4). Fix D1 at 2, then: (2,2,3), (2,2,4), (2,3,3) and (2,3,4). Fix D1 at 4, then (4,2,3), (4,2,4), (4,3,3) and (4,3,4). Then, for example, Pr{(2,3,4)} = Pr{2 from D1}*Pr{3 from D2}*Pr{4 from D3} = (1/3)*(1/2)*(1/2) = 1/12.

Show details for each triplet.

 

Conditional Probability by Formula

 

The definition of conditional probability is based on the formula Pr{A|B} = Pr{A and B}/Pr{B}. A number of students did not understand the definition of conditional probability and used variants like Pr{A|B} = Pr{A}/Pr{B}. Other students computed Pr{A and B} and Pr{B}, but did not compute Pr{A|B}.

 

Probability Computation Rules

 

Probabilities P are between 0 and 1: 0 £ P £ 1 - a number of students presented probabilities outside this range. Additionally, a number of students did not demonstrate the Complementary Rule as indicated.

 

Further Comments

 

Follow the protocol: show your work and details, write on one side of the sheets.

Attention to detail: Clean up your work, and watch the details. Clean up the arithmetic: “(1/4)*(1/2)” is not “1/6”; “(1/8)+(1/8)” is not “1/16”.

 

Major issues include:

 

Deficient knowledge of the definition of conditional probability;

Deficient knowledge of the definitions for the long run argument and for perfect samples;

Deficient knowledge of the computation of random variables;

Insufficient familiarity with the material in general.

 

If your first score is low: Remember the grading policy – if you don’t, look it up. The worst of the three test scores drop.

 

Remediation: the standard for performance is my keys – and not your neighbors’ tests. Do not shop for points with me. If your points do not add up, let me know. Compare your test work to my key – note where and why you lost points. Note the cases in which you lost the most points. Think of a revised tool-sheet, one that would prevent these problems form re-occurring. Write that tool-sheet.

 

Self Audit, Patterns of Point Loss, Revision of Analytic Narratives

 

Find patterns in your losses – why did you lose points? Did you lose most points in a case or two, or were your losses spread out over all of the cases? Did you lose points over algebra? Detail? List your cases in order of point loss, from most to fewest. For each case with point loss, determine the reasons for the losses. Check your analytic narratives and modify them to avoid these losses.