Indiana University of Pennsylvania
Test Scoring Service
An Explanation of the Reports
IT Support Center
G35 Delany Hall
Indiana University of PA
724-357-4000
it-support-center@iup.edu
Test Scoring – Report Explanation
Table of Contents
REPORT HEADINGS ................................................................................................................................. 3
INDIVIDUAL TEST RESULTS REPORT ................................................................................................ 4
INDIVIDUAL ITEM RESPONSE REPORT............................................................................................. 6
ITEM ANALYSIS REPORT ....................................................................................................................... 8
RELATIVE FREQUENCY DISTRIBUTION REPORT........................................................................ 10
ABSOLUTE FREQUENCY DISTRIBUTION REPORT....................................................................... 12
TEST SCORE DISTRIBUTION REPORT ............................................................................................. 14
APPENDIX A.............................................................................................................................................. 16
GLOSSARY ................................................................................................................................................. 16
Average (Mean) Score .......................................................................................................................... 16
Batch..................................................................................................................................................... 16
Difficulty Factor ................................................................................................................................... 16
Discrimination Index ............................................................................................................................ 16
Formula Scoring................................................................................................................................... 16
Key Sheet .............................................................................................................................................. 17
Kuder Richardson 20 ............................................................................................................................ 17
Kuder Richardson 21 ............................................................................................................................ 17
Local Percentile.................................................................................................................................... 17
Median Score ........................................................................................................................................ 18
Raw Score ............................................................................................................................................. 18
Standard Deviation............................................................................................................................... 18
Stanine .................................................................................................................................................. 18
Subtest .................................................................................................................................................. 19
T-Score ................................................................................................................................................. 19
Z-Score ................................................................................................................................................. 19
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Test Scoring – Report Explanation
Report Headings
The heading is identical on all reports. The following is an example of a heading:

Report Name is the name of the type of report. You select this in the Report Information on the
front of the Test Score envelope. Example: Individual Test Results.

Date Run is the date the report was generated. The format is mm/dd/yyyy.

Test Date is the date that the test was administered as entered in the Test Date field on the Test
Header sheet.

Page x of y is the report page number and the total number of pages in the report.

Test Name is the Name entered in the “Subject/Course/Section” on the Test Header sheet. The
example is MATH.

Test ID is the Test ID number given to the test as entered on the Test Header sheet.
The example is 101100.

Sort is the order in which students are listed on the report as selected in the Report Information
on the front of the Test Score envelope: 1 student per pate, Omit names, Sort by (Name, ID No.
and Score) and Do not sort. Only the Individual Test Results Report and Individual Item
Response Report use Sort.

Instructor is Instructor’s name as entered on the Test Header sheet. If the Test Header sheet has
no instructor name, then the Instructor on the report will be blank. The example is BROWN,
KATRINA.

Grade is the Grade/Group being reported as entered on the Test Header sheet. This is an optional
item; if the Test Header contains no grade/group, this entry is blank. The example is 007.

Class is the Class/Subgroup being reported as entered on the Test Header sheet. This is an optional
item; if the Test Header does not include a class/subgroup, this entry will be blank. The example is
101.

Scoring is either Raw Score or Formula, Factor of #. If Formula Scoring is not selected on the
Test Header, then Raw Score appears. If it is selected, Formula, Factor of # appears, (# is the
number entered under Factor).

Select will always be displayed as All Students. Select applies only to the Individual Test
Results Report.
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Individual Test Results Report
The main body of the Individual Test Results Report contains the following items:

Identification # is the ID of the respondent as entered on the answer sheet.

Name is the name of the person taking the test. You may choose not to print the names by selecting
the Omit Names option box on the Test Scoring Envelope.

Subtest identifies the number of the subtest (up to 10). The report displays only the columns of data
for the subsets administered. A test not divided into subsets is itself considered a sub test; the report
will contain one column with the "1" heading.

Items is the number of items in each subtest and in the entire test. Because multiple subtests can
include the same question, the number of items in the Total column is not necessarily the sum of all
the subtest items.

RS (Raw Score) is the total number of questions correct for each subtest and the overall test.

% is the percent of correct responses for each subtest and the overall test.

Total is the overall totals for the Items, Raw Scores, and percentages for all the subtests. Because
multiple subtests can include the same question, the number of items in the Total column is not
necessarily the sum of all the subtest items.

%tile (local percentile) is the ranking of the individual within the test population. See the Glossary
for a description of Local Percentile.
The following summary information is printed at the bottom of each page of this report. Analysis data is
described later in this section.








Number of Respondents is the number of persons included in the report.
Number of Items is the total number of questions in the test. This value should match the first entry
under the Total column in the report body.
Average Score is the average score (mean) for the reported group.
Median Score is the median score for the reported group.
Std. Deviation (standard deviation) is the range above or below the average score where the majority
of the scores lie.
Highest Score is the highest score for the reported group.
Lowest Score is the lowest score for the reported group.
The subtest legend displays each subtest number and name.
A sample of the Individual Test Results Report follows.
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Individual Item Response Report
The Individual Item Response Report shows student responses for a subtest or total test. The following
data appears in the body of the report.
 Question Number is a line of numbers indicating the question numbers for the test or subtest.

Answer Key lists the correct answers for the test according to these rules:
o
When any response is correct, an asterisk (*) is shown.
o
When all responses are to be ignored, a space is shown.
o
When there is only one possible correct answer (normal test question), the answer is
indicated by a number from 1 thru 7 for 7-response test. The lines are labeled 1-, 51-,
101-, and so on. The number of lines shown depends on the number of test questions.
For example, a 60-question test will show two lines of answer key items. Q# is the same
information for respondent answers.

Student ID is the ID of the student taking the test as entered in the Identification # field of the
Student Answer Sheet.

Student Name is the name of the person taking the test as entered in the Student Answer Sheet.
You can choose to omit student names from the report by selecting the Omit Names box in the
Report Information area on the front of the Test Scoring Envelope.

Score is the raw score (total number of items correct) for the sub test or total test. Formula scoring
is included in the raw score calculation.

Item Responses are the answers selected by the student according to these rules:
o
1 thru 7 identifies a wrong answer on a 7-response test.
o
Correct answers are identified with a period (.)
o
Questions not answered are identified with a dash (-).
o
Multiple answers are identified with an asterisk (*).
o
A blank ( ) identifies questions not scored (as specified on answer key).
The following summary information is printed at the bottom of this report.
 Key Symbols identify the symbols used in the answer key.

Respondent Symbols identify the symbols (*,-, etc.) used for respondent answers.

Number of Respondents is the number of respondents included in the report.

Average/Median Score are the mean score and median score for the reported group.

Highest/Lowest Score are the highest and lowest scores for the reported group.

Standard Deviation is the range above or below the average score where the majority of the
scores lie.
A sample of the Individual Items Response report follows
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Item Analysis Report
The Item Analysis Report allows you to analyze each question of a selected test evaluating test difficulty.
The report contains the following information:

Question shows the question number (in bold) and possible answers to the test question. The row
marked Oth (other) is the number of students in each group who marked either no answer or
multiple answers. An asterisk to the right of an answer number indicates the correct answer to the
question.
o

A 7-response test will show rows 1 thru 7.
Upper Quartile shows the number of individuals in the upper quarter (75th percentile and up) of
the test group that selected each test item alternative.

Lower Quartile shows the number of individuals in the lower quarter (25th percentile and lower)
of the test group that selected each test item alternative.

Total Count shows the total number of students who responded to each alternative.

Total % shows the total percentage of students who responded to each alternative.

Discrimination Index is a measure of the ability of an item response to discriminate between
those individuals who attained a high score on the test and those who attained a low score. Refer
to the Glossary for a description of the formula used.

Difficulty Factor is a measure of how difficult the question was to answer correctly. The higher
the difficulty factor, the easier the question is. Refer to the Glossary for a description of the
formula used.
The following summary information is printed at the bottom of this report:
 Number of Respondents is the number of respondents included in the report.

Total in Upper/Lower Quartile is the number of students in the upper quarter and the number of
students in the lower quarter of the test group.

Number of Test Items is the number of test questions in this test.

Kuder Richardson 20 is a coefficient of reliability. Refer to the Glossary for a full description of
this term.

Kuder Richardson 21 is another coefficient of reliability. Refer to the Glossary for a description
of this term.
A sample of an Item Analysis Report follows
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Relative Frequency Distribution Report
The Relative Frequency Distribution Report, using a bar graph, allows you to quickly determine the
percentage of students that achieved all possible raw scores for a test. It lists the raw score, number of times
that score was achieved, and local percentile represented by that score.

Score lists all the possible number of correct answers for a subtest or total test starting with the
highest number. For example, for a 30-question test, the first line will be 30, the next line will be
29, and so on down to 0. If you are using formula scoring, there is the possibility of negative
scores (-1, -2, -3,...).

Frequency shows the number of times that the score was achieved.

%ile (percentile) is the local percentile ranking of a score within the test population.

A bar graph illustrates the relationship of a particular raw score frequency to the whole test
population in terms of a percentage. It shows the percent of the population receiving each
particular score. The percentage is graphically displayed using one or more asterisks (*). Each
asterisk represents 2% of the test group.
For example, if there are 100 respondents and 10 of them scored 25 on a 30-question test, then the
25 score row of this report will display 5 asterisks (*****) representing 10% of the test population.
The following summary information appears at the bottom of the page:

Number of Respondents is the number of persons in the group you have selected who took the
test or subtest and are included in the report.

Number of Items is the total number of questions in this subtest or total test.

A note reminds you that each "*" in the report represents 2% of respondents.

Average/Median Score is the average score (mean) and median score for the reported group.

Highest/Lowest Score is the highest and lowest scores for the reported group.

Standard Deviation is the range above or below the average score where the majority of the
scores lie.
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Absolute Frequency Distribution Report
The Absolute Frequency Distribution Report, using a bar graph, allows you to quickly determine the
number of students that achieved all possible raw scores for a test or subtest. It lists the raw score, and the
number of times that score was achieved.
Each respondent is designated by an asterisk (*) on one of the score lines.

Score lists all the possible number of correct answers for a subtest or total test starting with the highest
score. For example, for a 100-question test, the first line will be 100, the next line will be 99, and so
on. If you are using formula scoring, there is the possibility of negative scores (-1, -2, -3,...).

Frequency shows the number of respondents that achieved that score.

%ile (percentile) is the local percentile ranking of a score within the test population.

A bar graph illustrates the number of respondents that received each score. Each asterisk (*)
represents a single respondent. The headings count up to 50, so the graph can show up to 50
respondents that have achieved one of the scores of the test group.
For example, if four students received a score of 40 out of a possible 50, then four asterisks (****)
will appear in the Score 40 line of the report.
The following summary information appears at the bottom of the page:

Number of Respondents is the number of persons in the group you have selected who took the
test or subtest and are included in the report.

Number of Items is the total number of questions in this subtest or total test.

A note reminds you that each "*" = 1 of respondent.

Average/Median Score is the average score (mean) and median score for the reported group.

Highest/Lowest Score is the highest and lowest scores for the reported group.

Standard Deviation is the range above or below the average score where the majority of the
scores lie.
A sample Absolute Frequency Distribution Report follows:
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Test Score Distribution Report
The Test Score Distribution Report allows you to compare raw scores to various types of standard scores
and distributions. It lists raw scores, percentiles, Z-scores, T-scores, and stanines for an individual subtest
or total test. Refer to Appendix A for a display of the formulas used.
The body of the Test Score Distribution Report contains the following:

Raw Score is the possible number of correct answers for a subtest or total test starting with the
highest score. For example, for a 50-question test, the first line will be 50, the next line will be 49,
and so on. If you are using formula scoring, there is the possibility of negative scores (-1, -2, -3,...).

Percentile is the local percentile ranking of a score within the test population.

Z-Score is a standard score based on raw scores, a standard deviation of 1, and a mean of zero. See
the Glossary for more details.

T-Score is a standard score based on raw scores, a standard deviation of 10, and a mean of 50. See
the Glossary for more details.

Stanine is the standard score based on a 9-point scale. See the Glossary for more details.
The following summary information appears at the bottom of the page:

Number of Respondents is the number of persons who took the test and are included in the report.

Number of Items is the total number of questions in this subtest or total test.

Average/Median Score is the average score (mean) and median score for the reported group.

Highest/Lowest Score is the highest and lowest scores for the reported group.

Standard Deviation is the range above or below the average score where the majority of the scores
lie.
A sample of the Test Score Distribution Report follows.
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Appendix A
Glossary
Average (Mean) Score
The average is the arithmetic mean of a set of scores. It is used in every report except the Item Analysis
Report.
Batch
A set of forms to be scanned as a group. A batch consists of a Test Header Sheet, one or more Key Sheets,
and a set of General Purpose Answer Sheets. Refer to the “Submitting exams to be scanned” on the back on
the Test Scoring Envelope.
Difficulty Factor
The difficulty factor of a question is the proportion of respondents selecting the right answer to that
question. It is used in the Item Analysis Report. The difficulty factor is calculated using the following
formula.
D=c/n
D - Difficulty factor
c - Number of correct answers
n - Number of respondents
Discrimination Index
The discrimination index measures the extent to which item responses can discriminate between individuals
who attain a high score on the test and those who attain a low score. This is calculated for each response
alterative. The discrimination index is used in the Item Analysis Report. This value is calculated using the
following formula.
DI
a
b
n
DI = (a - b) / n
- Discrimination index
- Response frequency of the upper quartile
- Response frequency of the lower quartile
- Number of respondents in the upper quartile
Formula Scoring
Formula scoring is intended to discourage guessing on tests. If formula scoring is selected, it is calculated
using the following formula.
R = c - (i/f)
R - Raw score
c - Number of correct answers
i - Number of incorrect answers (does NOT include answers left blank)
f - Formula scoring factor (selected on the Test Header). Normally, the factor should be one less than the
number of possible answers to each question. For example, if each question has 5 choices, the factor should
be 4. Scoring will deduct 1/4 of a point for each wrong answer.
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Test Scoring – Report Explanation
Example: In a test with 50 questions, there are 5 choices for the answer to each question. The scoring
factor is 4 (5-1). Assume 45 questions were answered, 5 left blank. Of the 45 answered, 40 were correct and
7 were incorrect. The score without formula scoring is 40. The total score calculated using formula scoring
is:
40 - (7 + 4) = 38.25
Because of rounding, the adjusted raw score is 38.
Key Sheet
A form that has been filled out that contains the correct answers to a test. There can be multiple key sheets
for a test, one key sheet per subtest. Generally, all key sheets for a test must follow a test header sheet, and
precede the student answer sheets. For details, see www.iup.edu/ats/helpdesk/tscore/key.shtm.
Kuder Richardson 20
This test reliability statistic measures inter-item consistency. A higher Kuder Richardson 20 value indicates
a strong relationship between items on the test. A lower value indicates a weaker relationship between test
items. This is a more accurate measure than the Kuder Richardson 21 statistic. The Kuder Richardson 20
value is used on the Item Analysis Report. This value is calculated using the following formula.
n
KR 
KIR
N
V
pi
qi
N
*
N 1
V   pi qi
i 1
V
- Kuder Richardson 20
- Number of items in the test
- Variance of raw scores or standard deviation squared (see Standard Deviation)
- Proportion of correct answers of item i (correct answers / number of answers)
- Proportion of incorrect answers of item i (incorrect answers - p)
Kuder Richardson 21
This test reliability statistic provides a rough approximation of inter-item consistency. A higher Kuder
Richardson 21 value indicates a strong relationship between items on the test. A lower value indicates a
weaker relationship between test items. The Kuder Richardson 21 value is used on the Item Analysis
Report. This value is calculated using the following formula.
KR 
KR
N
M
V
N
1  [ M ( N  M )]
*
N 1
N *V
- Kuder Richardson 21.
- Number of items in the test.
- Arithmetic mean of the test scores.
- Variance of the raw scores or the standard deviation squared (see Standard Deviation)
Local Percentile
The local percentile of a raw score shows a student’s percentile ranking within the local test population. A
high local percentile indicates a test score that is high compared to the test scores of the other respondents.
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Test Scoring – Report Explanation
Local percentile is used in these reports: Individual Test Results, Relative Frequency Distribution, Absolute
Frequency Distribution and Test Score Distribution. The value is calculated using the following formula:
L = ((0.5 * a) + b) / n
L – Local Percentile
a – Frequency of raw score
b – Frequency of lower than the raw score
n – Number of respondents
Median Score
The median is the middle score in a set of scores. If there are an even number of scores, the mean value of
the two closest to the middle is considered the median score. The Median score is part of every report
except the Item Analysis Report.
Raw Score
The raw score is the total number of correct responses.
In order to calculate the correct response for each question, the key sheet is used to define what is correct.
The correct answer can be indicated one for the following ways for a question on a key sheet:



Only one response is marked – this mark is the only correct answer. Any answer other than the one
marked is considered incorrect, including no response (blank), nothing is filled in) is considered
incorrect.
All responses are marked – any response marked for this question is acceptable and considered
correct. No response marked (blank, nothing filled in) is considered incorrect.
No response is marked – the question is ignored, the answer is not marked correct or incorrect, and
is not used to calculate the respondent’s raw score.
Standard Deviation
The standard deviation value is calculated using the following formula.
  ( a  b) 2

 n 1





The median score is part of every report except the Item Analysis Report.
A - Score for the nth respondent
b - Mean (average) score
n - Number of respondents
Stanine
A stanine is a standard score on a scale of 1 to 9. The stanine scale has a mean of 5 and a standard deviation
of 2. The stanine is part of the Test Score Distribution Report. Each stanine corresponds to the following
range of percentiles:
Stanine
Percentile
9
8
97-100
90-96
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Test Scoring – Report Explanation
7
6
5
4
3
2
1
78-89
61-77
40-60
23-39
11-22
4-10
0-3
Subtest
A subset of a test. A test can be divided into subtests so that individuals parts of an overall test can be
individually reported. For example, a math test can be divided into three subtests: Algebra, Trigonometry,
and Geometry. In a multiple subtest setup, a Key Sheet for each sub test must follow the Test Header.
On the Header Sheet, you can specify between zero (0) and ten (10) subtests.
T-Score
The T-score describes a score that falls within a normal distribution with a mean of 50 and a standard
deviation of 10. The T-score may be positive (+) or negative (-). T-score is part of the Test Score
Distribution Report. It is calculated as follows:
T= (Z* 10) + 50)
T - T-score
Z - Z-score
Z-Score
The Z-score describes a score that falls within a normal distribution with a mean of zero and a standard
deviation of 1. The Z-score may be positive (+) or negative (-). Z-score is part of the Test Score
Distribution Report. It is calculated as follows:
z = (a - b) / c
Z
a
b
c
-
Z-score
Raw score
Mean raw score
Standard deviation
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