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Statistics_Overall_Key.tex
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reworded, changing from passivve to active voice, added commas, fixed a few typos.CVS: ----------------------------------------------------------------------
1: \label{Statistics_Key}
2:
3: The \textbf{Overall Problem Statistics} page displays the following
4: data about the problems currently in the course:
5:
6: \begin{description}
7:
8: \item{\textbf{\#Stdnts}}: Total number of students attempting the problem.
9:
10: \item{\textbf{Tries}}: Total number of attempts to solve the problem.
11:
12: \item{\textbf{Max Tries}}: Largest number of attempts to solve the problem by a student.
13:
14: \item{\textbf{Mean Tries}}: Average number of attempts.
15:
16: \item{\textbf{S.D. tries}}: Standard Deviation of the tries.
17:
18: \item{\textbf{Skew Tries}} Skewness of the students' tries.
19: \[ \frac{\sqrt{ \sum{(Xi - Mean)^3} / \#Stdnts}}{\sigma^3} \]
20:
21: \item{\textbf{\#YES}}: Number of students who solved the problem correctly.
22:
23: \item{\textbf{\#yes}}: Number of students who solved the problem by override.
24:
25: \item{\textbf{\%Wrng}}: Percentage of students who tried to solve the problem but were unable to.
26:
27: \item{\textbf{DoDiff}}: Degree of Difficulty of the problem.
28:
29: This statistics give a measure of how many attempts it took the
30: students to get the problem correct. Those students who did not get
31: the problem correct are not counted. A value close to 0 indicates
32: most students who got the problem correct did so on the first attempt.
33: A value close to 1 indicates many attempts were required for students
34: to get the problem correct. A negative value indicates students were
35: given points without attempting the problem. A value of 'nan' means
36: there were no attempts made on the problem.
37:
38: \[ 1 - \frac{\#YES+\#yes}{Tries} \]
39:
40: \item{\textbf{DoDisc}}: Degree of Discrimination of the problem.
41:
42: The students are grouped based on their scores on the sequence which
43: contains the homework problem. The percent score of the bottom 25\% of
44: the students is subtracted from the percent score the to top 25\% of
45: the students. This yields a number from -1 to 1. 1.0 indicates
46: all of the good students answered the problem correctly and none of the
47: poor students answered it correctly. Conversely, a score of -1.0 indicates
48: all of the good students got the problem wrong and the bad students did
49: well.
50:
51: \item{\textbf{weight}}: The weight of the problem in the course (``points'').
52: The value shown is the weight of the problem for the individual computing the
53: statistics. Individual student or section variations are not shown.
54:
55: \end{description}
56:
57: \textbf{Sequence Statistics}: Compiled statistics on problems based on
58: their containing sequence, are also shown. The following data are shown:
59:
60: \begin{description}
61:
62: \item{\textbf{\#Items}}: The number of problem parts in the sequence.
63:
64: \item{\textbf{Score Mean}, \textbf{Score STD}, \textbf{Score Max} \textbf{Score Min}}
65: The mean, standard deviation, maximum, and minimum of the scores of
66: the selected students on the given sequence.
67:
68: \item{\textbf{Score N}} The number of the selected students who submitted answers to problem parts in the sequence.
69:
70: \item \textbf{Count Mean}, \textbf{Count STD}, \textbf{Count Max}, \textbf{Count Min}:
71: The mean, standard deviation, maximum, and minimum count of correct
72: problem parts of the selected students on the given sequence.
73:
74: \item \textbf{Count N} The number of the selected students who submitted answers to problem parts in the sequence.
75:
76: \item \textbf{KR-21} The KR-21 reliability statistic measures the internal reliability of a test or exam.
77:
78: To compute the KR-21 reliability statistic the following formula is used:
79:
80: \[KR-21 = \frac{K}{K-1} \cdot \frac{1-(M \cdot (K-M))}{K \cdot s^{2}}\]
81:
82: Where
83: \begin{description}
84: \item{$K$} is the number of items in your test
85: \item{$M$} the mean score on the test
86: \item{$s$} the standard deviation of the scores on your test
87: \end{description}
88:
89: \end{description}
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