College and Research Libraries


Research Notes 
Attribute Sampling: 
A Library Management Tool 
Jack E. Kiger and Kenneth Wise 

Attribute sampling is a .tool that librarians may use to estimate characteristics 
of their collection, such as the portion of books needing repair, the accuracy of 
the circulation records, or the accuracy of cataloging activities. Because sam-
pling always results in risk that the sample is not an accurate indicator of true 
conditions, one can establish the risk of an incorrect inference. This article 
describes the nature of attribute sampling and presents the process a librarian 
might use to make a defensible inference. 

ibrarians may need to esti-
mate the maximum rate of oc-
currence of some specific 
quality or attribute for a par-

ticular function within their library. 
Making these estimates can be difficult 
since libraries tend to be rather large 
operations having some functions 
that are cumbersome to analyze. 
Making inferences about the number 
of books missing from the collection, 
or the accuracy of the circulation sys-
tem, or the percentage of items in the 
collection that is not properly bar-
coded would be intimidating tasks 
indeed if the librarian had to review all 
items or records before drawing any 
conclusions. 

Library management literature (Drott, 
1969; Dougherty, et al., 1982; Simpson, 
1988; and Powell, 1991) has discussed 
the use of attribute sampling to estimate 

attributes such as the average number of 
patrons served per day or the average 
age of patrons. These approaches in-
volve the use of equations, which makes 
the process unnecessarily complex. 
Certified public accountants often em-
ploy the techniques discussed in this ar-
ticle to estimate the maximum occurrence 
rate of a phenomenon, such as the max-
imum portion of the books reflected in 
the records as being on the shelf that 
are not. Advantages of the technique 
are that by using a table to determine 
sample size and another table to eval-
uate results, one can draw measurably 
precise conclusions based on an exami-
nation of relatively few items. In the fol-
lowing discussion, we will describe the 
nature of attribute sampling and illustrate 
how the librarian may use attribute sam-
pling techniques in managing library 
operations. 

Jack E. Kiger is Warren L. Slagle Professor of Accounting, College of Business Administration, and 
Kenneth Wise is Business Manager of the University Libraries at the University of Tennessee, Knoxville, 
Tennessee 37996. 

537 



538 College & Research Libraries 

Examination X 
ofsample / 

4% or less 

indicates 
that the 
occurrence 
rate is ~ . 

November 1993 

True State of Population 
Occurrence Rate is 

4% or less Higher than 4% 

Type II 
Error 

Correct 
Decision Risk of concluding the 

occurrence rate is 
lower than it actually is 

Type I 
Error 

Risk of concluding the Correct 
Decision 

Higher than 4% 

occurrence rate is 
higher than it actually is 

FIGUREl 
Sampling Risk in Attribute Testing 

THE NATURE OF 
STATISTICAL SAMPUNG 

Statistical sampling involves applying 
procedures to fewer than all items com-
posing a population. A population is all 
items about which one wishes to make 
an inference, such as all the books on 
reserve, all rare books, all books currently 
circulating, or all bound volumes. Sam-
pl~g is based on th~ premise that a sample 
Will be representative of the population. 
After examining the sample, one makes an 
inference about the population. 

Attribute sampling, a statistical tech-
nique, estimates the rate or percentage of 
occurrence of a specific characteristic or 
attribute in a population. Attribute sam-
pling is concerned with a rate of occur-
rence. For example, attribute sampling 
may be used to estimate the maximum 
percentageofbooks not on the shelf that the 
catalog record indicates are on the shelf. 
When using such sampling, one evaluates 
whether a characteristic or attribute is pres-
ent with a yes or no answer. 

Sampling Risk 

When selecting a statistical sample from 
a population, the objective is to obtain a 
sample that has the same characteristics as 

the enfue population. For example, if an 
examination of a sample indicates that 2 
percent of the books that should have 
been on the shelf were not there, one 
would expect that2 percent of all the books 
in the population would not be on the shelf. 
However, one must accept the risk that the 
co_nclusi<?n based on examining a sample 
Will be different from the conclusion if the 
entire population were examined. This 
risk is referred to as sampling risk. Sam-
pling risk is the risk that the projected 
characteristics will be different from the 
true characteristics of the population be-
cause all items in the population were 
not examined. When one is unwilling to 
accept any sampling risk, one must ex-
amine every item in the population. 

Considering the relationship between 
risk and reliability makes the nature of 
risk clearer. Reliability, a measure of the 
dependability of an estimate based on a 
sample, is the complement of risk (1 
minus risk). One can specify a level of 
reliability and determine the number of 
items that must be examined to achieve 
it. The degree of reliability of an estimate 
~ased on a s~mple _increases as the por-
tion. <?f th~ Items m the population is 
exammed mcreases. Examining a rela-
tively small number of items can provide 



a high degree of reliability beyond 
which additional testing will improve 
reliability only in very small incre-
ments. Also one can have complete con-
fidence in an estimate by examining the 
whole population. 

A librarian who examines a sample 
and concludes that the occurrence rate of 
a specific characteristic is 4 percent or 
less when the population's occurrence 
rate is 4 percent or less makes a correct 
decision (see figure 1 ). Similarly, when a 
librarian examines a sample containing 
a 4 percent or greater occurrence rate 
and the occurrence rate in the popula-
tion is 4 percent or greater, the librarian 
makes a correct decision. 

Attribute sampling, a statistical 
technique, estimates the rate or 
percentage of occurrence of a specific 
characteristic or attribute in a 
population. 

However, when sampling, one may 
make either of two mistakes. One may 
conclude that the occurrence rate is 
higher than 4 percent when it is not. In 
such a situation, the occurrence rate is 
estimated to be higher than it actually is. 
Making such an error is generally re-
ferred to as a Type I error and the risk of 
making such an error is referred to as 
Alpha risk. Alternatively, one may ex-
amine a sample and conclude that the 
occurrence rate is 4 percent or less when 
it actually is not. This type of error is 
referred to as a Type II error and the risk 
of making such an error is referred to as 
a Beta risk. In such a situation, the librar-
ian concludes the occurrence rate to be 
lower than it actually is. 

When sampling results cause a librar-
ian to conclude that the occurrence rate 
is higher than it actually is, the librarian 
may incur additional costs by assigning 
staff to check and correct all of the re-
cords. When a librarian concludes that 
the occurrence rate is lower than it is, the 
librarian accepts the occurrence rate as 
satisfactory when it is really not. Hence, 
the records continue to be in error. 

Attribute Sampling 539 

Should a librarian conclude that the oc-
currence rate is less than it actually is, the 
librarian would assume that the records are 
correct. Hence, when sampling, librarians 
are concerned with the risk of concluding 
the occurrence rate is lower than it actually 
is. This risk (Beta) may be reduced by in-
creasing the sample size. Sampling risk 
varies inversely with the sample size: the 
greater the sample size, the smaller the 
sampling risk. Increasing the sample size to 
include all items in the population would 
eliminate all sampling risk. 

Nonsampling Risk 

In addition to the sampling risk, 
librarians incur the nonsampling risk, 
which results from human error such as 
failure to recognize an occurrence when 
performing a procedure or use of an in-
effective procedure. For example, an ex-
hausted or inadequately trained person 
might misread a call number when ex-
amining a book. An example of using an 
ineffective procedure is comparing only 
the title of a book to the catalog record 
rather than comparing all of the details. 
Nonsampling risk does not result from 
failure to examine all items in the popu-
lation. Nonsampling risk is not ordi-
narily quantified. Librarians may mini-
mize nonsampling risk by providing 
adequate training and supervision to 
persons examining sample items. 

Statistical versus 
Nonstatistical Sampling 

Statistical sampling requires using ran-
dom techniques for selecting a sample and 
using the laws of probability to evaluate 
results of the sampling process. Nonstatis-
tical sampling refers to selecting a sample 
without using random selection tech-
niques or making an inference from a 
sample without using the laws of proba-
bility. When using statistical sampling, a 
librarian can use probability theory to 
make statements or generalizations 
about a population and to measure the 
risk that the sample is not representative 
of the population (sampling risk). Statis-
tical sampling also assists the librarian in 
setting an efficient sample size and in 
evaluating sample results. 



540 College & Research Libraries 

Sampling is not always appropriate. 
For example, a librarian wishing to cor-
rect all of the errors in the circulation sys-
tem may identify errors but would not 
detect all of them by sampling. The rare 
book librarian may choose not to verify 
every item in the listing while the news-
paper librarian may verify no items. 

MAKING A 
STATISTICAL INFERENCE 

Statistical sampling provides a frame-
work for making a statistical inference. 
Below, we will discuss the steps in 
making a statistical inference: 

1. Determine the objective of the 
statistical inference. 

2. Define the population and the sam-
pling unit. 

3. Determine the acceptable risk of 
concluding that the occurrence rate 
is lower than it actually is. 

4. Set the tolerable occurrence rate. 
5. Determine the expected population 

occurrence rate. 
6. Using a statistical sample size 

table, determine the initial sample 
size. 

7. Using random sampling techniques, 
identify the actual items to examine. 

8. Examine the selected items and 
identify occurrences of deviations. 

9. Make conclusions about the fre-
quency of occurrences. . 

To illustrate these steps, we wdl as-
sume that a librarian wants to estimate 
the portion of books missing from a 
specified range of the collection; for ex-
ample, all books in the LC classification 
PR, generally the English literature col-
lection. The collection consists of 15,000 
items readily identifiable in the catalog 
record. The librarian is willing to accept 
a 5 percent risk of concluding that the 
occurrence rate is lower that it actually 
is and that the records are accurate 
enough if they contain a 4 percent error 
rate. The librarian expects that only .5 
percent of the books are missing. 

Determine the Objective 
of the Statistical Inference 

Attribute sampling is used to estimate 
the rate of occurrence or percentage 9f 

November1993 

items with a specific quality or attribute 
within a population. An attribute is a 
characteristic of an item being examined. 
When the characteristic is not present, a 
deviation exists. For example, a librarian 
may be concerned about the reliability of 
the catalog records of the English litera-
ture collection. On the basis of pro-
fessional judgment, the librarian would 
like to be able to determine that 4 percent 
or fewer of the books which the catalog 

One must identify the population in 
such a way as to ascertain that all 
items in the population are subject to 
being included in the sample. 

records show as being on the shelf are 
missing. Rather than determining the ac-
curacy of every item in the catalog record 
the librarian establishes the hypothesis 
that the occurrence rate of the deviation 
is 4 percent or less. The attribute being 
examined is whether a book that should 
be on the shelf according to the catalog 
record is in fact on the shelf. When the 
librarian examines the shelf, the book is 
either there or it is not. When the librar-
ian looks on the shelf for a book and it is 
not there, a deviation exists. 

Define the Population 
and Sampling Unit 

A population is all the items about 
which one wishes to make an inference. 
The population one examines is gener-
ally dictated by the objective of using 
attribute sampling. For example, if one 
is evaluating whether the catalog re-
cords include all English literature books 
actually on the shelf, the population is all 
of the English literature books on the 
shelf at a particular point in time. If one 
is evaluating the accuracy of the cata-
log records, the population is all the 
catalog records of English literature 
books at a particular point in time. A 
population consists of sampling units. 
A sampling unit is an individual item 
such as a book or an entry in a record 
of the population (such as the catalog 
record) that is examined. 



One must identify the population in 
such a way as to ascertain that all items 
in the population are subject to being 
included in the sample. For example, if 
one wants to make an inference about 
the entire collection of English literature 
books, all books in the collection must be 
subject to selection, not just those cur-
rently on the shelves. 

Population size has little impact on the 
sample size for populations of less than 
5,000 items, and no effect on sample size 
for populations of 5,000 or more items. 

Specify Acceptable Risk of 
Concluding that the Occurrence 
Rate Is Lower Than It Actually Is 

When sampling, one must accept 
some risk that his or her conclusion 
about the population occurrence rate of 
a characteristic is incorrect. The risk of 
concluding that the occurrence rate is 
lower than it actually is refers to the 
probability of accepting an attribute as 
satisfactory because of the tolerable oc-
currence rate specified when the occur-
rence rate actually is higher. When 
specifying a 5 percent risk of concluding 
that the occurrence rate is lower than it 
actually is, one accepts a 5 percent 
chance of concluding that an ·occurrence 
rate is lower than the tolerable rate when 
it is not. Looking at it another way, one 
has a 95 percent reliability level or a 95 
percent chance of being right. 

Prior to selecting a sample and per-
forming procedures to determine the 
presence or absence of an attribute, one 
must specify the acceptable risk of con-
cluding that the occurrence rate is lower 
than it actually is. The higher the risk of 
concluding that the occurrence rate is 
lower than it actually is, the smaller the 
required sample size. This is logical, be-
cause the higher the risk, the smaller the 
likelihood that the sample will be repre-
sentative of the population. In other 
words, the less evidence gathered, the 
higher the risk of concluding that the 
occurrence rate is lower than it actually 
is. As discussed below, the acceptable 
risk of concluding that the occurrence 
rate is lower than it actually is deter-
mines which sample size table to use. 

Attribute Sampling 541 

Set the Tolerable Occurrence Rate 

The tolerable occurrence rate is the 
maximum occurrence rate for a specific 
attribute that the librarian will permit. 
For example, consider a librarian's test of 
the catalog records for English literature 
books. When setting the tolerable occur-
rence rate at 4 percent, the librarian has 
decided that even if 4 percent of the 
English literature books included in the 
catalog records are not on the shelf, the 
assessment of the occurrence rate would 
not change. 

Setting the tolerable occurrence rate 
involves judgment. Tolerable occurrence 
rates vary with the importance of a par-
ticular attribute. The more critical the 
attribute, the lower the tolerable occur-
rence rate should be. 

Estimate the Expected 
Population Occurrence Rate 

The expected population occurrence 
rate or the frequency of the attribute also 
affects the initial sample size. An esti-
mate of the rate can be made from the 
previous year's occurrence rate, the oc-
currence rate in a preliminary random 
sample of the poP.ulation being ex-
amined, or an estimate based on one's 
experience with occurrence rates in similar 
situations. Estimating the occurrence rate 
incorrectly may cause the initial sample 
size to be incorrect and require selecting 
an additional sample. Fortunately, an in-
correct estimate does not increase the 
risk of concluding that the occurrence 
rate is lower than it actually is. 

The smaller the expected occurrence 
rate in relation to the tolerable occur-
rence rate, the smaller the required 
sample size. In other words, when the 
maximum tolerable occurrence rate is 4 
percent, and the estimate of the actual oc-
currence rate is .5 percent, the sample size 
will be smaller than if the estimate of the 
actual occurrence rate were 2 percent. The 
clo~r the expected population occurrence 
rate is to the tolerable occurrence rate, the 
larger the required sample size. 

Detennine the Initial Sample Size 

After estimating the expected popula-
tion occurrence rate, specifying a risk of 



542 College & Research Libraries November1993 

TABLEt 
DETERMINATION OF SAMPLE SIZE TABLE-10% RISK OF CONCLUDING THE 

OCCURRENCE RATE IS LOWER THAN IT ACTUALLY IS 
Expected Percent Tolerable Rate: % Rate of Occurrence 

Rate of 2 3 4 
Occurrence 

0.25 400 200 140 100 
0.50 800 200 140 100 
1.0 400 180 100 
1.5 .. 320 180 
2.0 600 200 
2.5 .. 360 
3.0 800 
3.5 .. 
4.0 
4.5 
5.0 
5.5 
6.0 
6.5 
7.0 
7.5 
8.0 
8.5 
9.0 
9.5 

• Sample size more than 1,000. 

concluding the occurrence rate is lower 
than it actually is, and setting a tolerable 
occurrence rate, one may use a sample 
size table such as that in table 1, 2, or 3 
to make an initial estimate of sample 
size. The sample size is called the initial 
sample size because the occurrence rate 
in the actual sample determines whether 
the sample size is large enough to reach 
the desired conclusion. 

The specified risk of concluding the 
occurrence rate is lower than it actually 
is determines which table to use. The 
sample size tables are one-sided tables 
because they present an upper occur-
rence rate (not an upper and lower) for a 
given risk of concluding that the occur-
rence rate is lower than it actually is. 
One-sided tables are used because of 
concern with knowing the maximum, 
not the minimum occurrence rate. 

The librarian is willing to accept a 5 per-
cent risk of concluding that the occur-

5 6 7 8 9 10 

80 70 60 50 50 40 
80 70 60 50 50 40 
80 70 60 50 50 40 

120 90 60 50 50 40 
140 90 80 50 50 40 
160 120 80 70 60 40 
260 160 100 90 60 60 
400 200 140 100 80 70 
900 300 200 100 90 70 

.. 550 220 160 120 80 .. 320 160 120 80 
.. 600 280 160 120 

.. 380 200 160 

.. 600 260 180 
.. 400 200 
.. 800 280 

.. 460 

.. 800 
.. 
.. 

renee rate is lower than it actually is, and 
is willing to assume that the catalog rec-
ords are accurate enough if they con-
tain a 4 percent error rate (tolerable 
occurrence rate), and expects the popu-
lation occurrence rate to be .5 percent. 
To determine the initial sample size, fol-
low these steps: 

1. Locate the table that corresponds to 
the acceptable risk of concluding 
that the error rate is lower than it 
actually is. 

2. Locate at the top of the table the 
tolerable occurrence rate. 

3. Locate the expected occurrence rate 
at the left of the table. 

4. Read the initial sample size from 
the intersection of the column (de-
termined in 2 above) and row (de-
termined in 3 above). 

Using table 2, the initial sample size is 
120. Table 4 shows the effect of the risk 
of concluding the occurrence rate is 



Attribute Sampling 543 

TABLE2 
DETERMINATION OF SAMPLE SIZE TABLE-S% RISK OF CONCLUDING THE 

OCCURRENCE RATE IS LOWER THAN IT ACTUALLY IS 
Expected Percent Tolerable Rate: % Rate of Occurrence 

Rate of 2 3 4 
Occurrence 

0.25 650 240 160 120 
0.50 .. 320 160 120 
1.0 600 260 160 
1.5 .. 400 200 
2.0 900 300 
2.5 .. 550 
3.0 .. 
3.5 .. 
4.0 
4.5 
5.0 
5.5 
6.0 
6.5 
7.0 
7.5 
8.0 
8.5 
9.0 
9.5 

• Sample size more than 1,000. 

lower than it actually is, tolerable occur-
rence rate, and expected population oc-
currence rate on the initial sample size. 
The relationship between sample size 
and these factors can be summarized in 
table 5. 

Select the Sample 

After determining the initial sample 
size, select a random sample from the 
population. A random sample is a 
sample in which every sampling unit in 
the population has an equal chance of 
being included in the sample. For the 
English literature collection example, a 
librarian would select 120 entries in the 
catalog record. While books including 
random number tables are available, 
using computer software to generate a 
listing of random numbers is much more 
efficient. Both Lotus and Excel have a 
feature for generating random numbers. 
Also, most computer programmers can 
easily incorporate random number 

5 6 7 8 9 10 

100 80 70 60 60 50 
100 80 70 60 60 50 
100 80 70 60 60 50 
160 120 90 60 60 50 
200 140 90 80 70 50 
240 160 120 80 70 70 
400 200 160 100 90 80 
650 280 200 140 100 80 

.. 500 240 180 100 90 

.. 800 360 200 160 120 .. 500 240 160 120 .. 900 360 200 160 
.. 550 280 180 
.. 1000 400 240 

.. 600 300 .. .. 460 
.. 650 
.. .. 

.. 

.. 

generators into programs they routinely 
run to select a random sample. 

Examine the Items in the Sample 

Next, the librarian performs pro-
cedures to determine whether devia-
tions occur. The procedures are the same 
whether one uses statistical sampling or 
examines all items in the population. As 
stated above, a deviation exists for any 
book that the record indicates is on the 
shelf if the book is not on the shelf. As-
sume that only one English literature 
book was not found on the shelf. 

Evaluate the Sample Results 

The librarian may calculate the occur-
rence rate of deviations in the sample 
and use it to estimate the population's 
upper occurrence rate. The sample oc-
currence rate is computed by dividing 
the occurrence rate for each attribute by 
the sample size. This rate is the best esti-



544 College & Research Libraries November 1993 

TABLE3 
DETERMINATION OF SAMPLE SIZE TABLE-1% RISK OF CONCLUDING THE 

OCCURRENCE RATE IS LOWER THAN IT ACTUALLY IS 
Expected Percent Tolerable Rate: % Rate of Occurrence 

Rate of 2 3 4 5 6 7 8 9 
Occurrence 

0.25 .. 340 240 180 140 120 100 90 80 
0.50 .. 500 280 180 140 120 100 90 80 
1.0 .. 400 260 180 140 100 90 80 
1.5 .. 800 360 200 180 120 120 100 
2.0 .. 500 300 200 140 140 100 
2.5 .. 1000 400 240 200 160 120 
3.0 .. 700 360 260 160 160 
3.5 .. .. 550 340 200 160 
4.0 .. 800 400 280 200 
4.5 .. .. 600 380 220 
5.0 .. 900 460 280 
5.5 .. .. 650 380 
6.0 .. 1000 500 
6.5 .. .. 800 
7.0 .. .. 
7.5 .. 
8.0 .. 
8.5 .. 
9.0 
9. 

• Sample size more than 1,000. 

TABLE4 
EFFECT OF RISK, TOLERABLE OCCURRENCE RATE, AND 

EXPECTED OCCURRENCE RATE ON INITIAL SAMPLE SIZE ON 

10 

70 
70 
70 

·9o 
90 

100 
100 
140 
160 
200 
200 
280 
300 
400 
600 
800 

.. 

.. 

.. 

.. 

Risk of Concluding the 
Occurrence Rate Is Lower 

Than It Actually Is 
Tolerable 

Occurrence Rate 
Expected Population 

Occurrence Rate 
Initial Sample 

Size 

5% 
5 
5 

10 

6% 
6 
5 
5 

mate of the occurrence rate for the popu-
lation. A statistical table similar to the 
ones in tables 6, 7, or 8 may be used to 
estimate the population's upper occur-
rence rate at the level of risk specified 
earlier. The initial sample size was deter-
mined to be 120. When examining the 
sample, one occurrence was found. The 
librarian would estimate that approxi-
mately 1 percent (computed by dividing 
1 by 120) of English literature books are 
missing. To estimate the population's 

1.0% 
2.0 
2.0 
2.0 

78 
129 
181 
132 

TABLES 
RELATIONSHIP BETWEEN 

OCCURRENCE RATE 
AND SAMPLE SIZE 

Change In 

Expected population 
occurrence rate 

Tolerable occurrence rate 

Risk of concluding the 
occurrence rate is lower 
than it actually is 

Impact on 
Sample Size 

Direct 

Inverse 

Inverse 



Attribute Sampling 545 

TABLE6 
TABLE FOR EVALUATING SAMPLE RESULTS--10% RISK OF CONCLUDING 

OCCURRENCE RATE IS LOWER THAN IT ACTUALLY IS 

Number of Observed Occurrences 
Achieved Upper Precision Limit: % Rate of Occurrence 

Sample------------------------------
Size 2 3 4 5 6 7 8 9 10 12 14 16 18 20 25 30 35 40 45 

10 

20 

30 

40 

50 

60 

70 

80 

90 

100 

120 

140 

160 

180 

200 0 

220 

240 ' 0 

260 0 

280 0 

300 0 

320 0 

340 0 

360 0 

380 0 

0 

0 

0 

0 

0 

0 

0 

0 1 

0 

0 1 

1 

1 2 

1 2 

1 2 

2 

2 3 

3 4 

4 5 

0 

1 

1 2 

0 1 2 

0 1 2 3 4 5 

2 4 5 6 8 9 

1 2 3 4 6 7 9 11 13 

2 3 4 5 8 10 12 15 17 

3 4 5 6 7 10 13 15 18 21 

2 3 4 5 6 8 9 12 15 18 22 25 

2 3 4 5 6 8 9 10 14 18 22 25 29 

3 4 6 7 9 11 12 16 20 25 29 33 

3 4 

4 5 

5 6 

6 8 

5 7 9 10 12 14 19 23 28 33 38 

6 7 9 11 13 15 17 23 29 34 40 46 

7 9 11 13 16 18 ' 21 27 34 41 48 54 

9 10 13 16 19 22 25 32 40 47 55 63 

0 2 3 4 6 7 9 10 12 15 18 22 25 28 37 45 54 63 71 

2 4 5 7 8 10 12 14 17 21 24 28 32 41 51 60 70 80 

1 

1 

2 4 

3 5 

6 8 10 12 13 15 19 23 27 31 35 46 56 67 78 89 

7 9 11 13 15 17 21 26 30 35 39 50 62 74 85 97 

1 3 5 8 10 12 14 17 19 . 24 28 33 38 43 55 68 80 93 106 

2 4 6 8 11 13 16 18 21 26 31 36 41 46 60 73 87 101 114 

2 4 7 9 12 14 17 20 22 28 33 39 45 50 64 79 93 108 123 

2 5 7 10 13 16 18 21 24 30 36 42 48 54 69 85 100 116 132 

3 5 8 11 14 17 20 23 26 32 38 45 51 58 74 90 107 123 140 

3 6 9 12 15 18 21 25 28 34 41 48 55 61 79 96 113 131 149 

3 6 9 13 16 19 23 26 30 37 44 51 58 65 83 102 120 139 158 

400 

420 

1 4 

1 . 4 

7 10 14 17 21 24 28 31 39 46 54 61 69 88 107 127 146 166 

7 11 14 18 22 26 29 33 41 49 57 65 73 93 113 134 154 175 

460 4 8 12 16 20 ' 24 28 33 37 45 54 63 71 80 102 124 147 170 192 

500 1 

550 2 

600 2 

650 2 

5 9 13 18 22 27 31 36 40 50 59 69 78 88 112 136 160 185 210 

6 10 15 20 25 30 35 40 45 55 66 76 87 97 124 150 177 204 232 

7 12 17 22 28 33 39 44 50 61 72 84 95 107 135 165 194 224 253 

8 13 19 24 30 36 42 48 54 66 79 91 104 116 147 179 211 243 275 

700 3 . 8 14 20 27 33 39 46 52 59 72 85 99 112 126 159 194 228 262 297 

800 4 10 17 24 31 38 46 53 61 68 83 99 114 129 145 183 222 262 301 341 

900 4 12 20 28 36 44 52 61 69 78 95 112 129 146 164 207 251 296 340 385 

1000 5 13 22 31 40 49 59 68 77 87 106 125 144 164 183 232 280 330 379 429 



546 College & Research Libraries November 1993 

TABLE 7 
TABLE FOR EVALUATING SAMPLE RESULTS-5% RISK OF CONCLUDING 

OCCURRENCE RATE IS LOWER THAN IT ACTUALLY IS 

Number of Observed Occurrences 
Achieved Upper Precision Limit: % Rate of Occurrence 

~~e-----------------------------------------------------------
Size 2 3 4 5 6 7 8 9 10 12 14 16 18 20 25 30 35 40 45 

10 

20 

30 

40 

50 

60 

70 

80 

90 

100 

120 

140 

160 

180 

200 

0 

0 

0 

0 1 

0 1 

0 1 

0 

0 

1 

0 

0 

1 

1 2 

2 3 

2 3 

3 4 

0 

1 

1 2 

2 

2 3 

3 4. 

4 5 

5 6 

6 7 

0 

1 

2 

2 

0 

1 

3 

1 

2 

3 

4 

0 

1 

2 

2 3 4 

3 4 5 

4 5 7 
5 7 8 

2 

0 

1 2 3 

3 4 5 

4 

7 8 

3 5 6 8 10 12 

5 7 9 11 13 16 

6 9 11 14 17 20 

8 11 14 17 20 24 

9 13 16 20 24 28 

3 4 5 6 8 9 11 15 19 23 27 32 

3 4 6 8 9 11 13 17 22 26 31 36 

4 5 6 8 10 12 14 16 21 27 33 38 44 

5 6 7 10 12 14 17 19 26 32 39 46 52 

6 8 9 12 14 17 20 23 30 38 45 53 61 

8 9 11 14 17 20 23 26 35 43 52 60 69 

9 11 12 16 19 23 26 30 39 48 58 68 77 

220 0 2 3 5 7 8 10 12 14 18 22 25 29 33 44 54 64 75 86 

240 1 2 4 6 8 10 12 14 16 20 24 28 33 37 48 59 71 83 94 

260 1 3 4 7 9 11 13 15 17 22 26 31 36 41 53 65 77 90 103 

280 1 3 5 7 10 12 14 17 19 24 29 34 39 44 57 71 84 98 111 

300 0 

320 0 

340 0 

360 0 

380 0 

400 0 

420 0 

1 3 6 8 11 13 16 18 21 26 31 37 42 48 62 76 91 105 120 

2 4 6 9 11 14 17 20 22 28 34 40 45 51 66 82 97 113 128 

2 4 7 10 12 15 18 21 24 30 36 42 49 55 71 87 104 120 137 

2 5 8 10 13 17 20 23 26 32 39 45 52 59 76 93 110 128 146 

2 5 8 11 14 18 21 24 28 34 41 48 55 62 80 98 117 135 154 

3 6 9 12 15 19 22 26 29 37 44 51 59 66 85 104 123 143 163 

3 6 9 13 16 20 24 27 31 39 46 54 62 70 90 110 130 151 171 

460 0 4 7 11 15 18 22 26 31 35 43 51 60 68 77 99 121 143 166 188 

500 1 4 8 12 16 21 25 29 34 38 47 56 66 75 84 108 132 157 181 197 

550 1 5 9 14 18 23 28 33 38 43 53 63 73 83 94 120 146 173 200 227 

600 1 6 10 15 20 26 31 36 42 47 58 69 80 92 103 ' 132 161 190 219 249 

650 2 6 12 17 23 28 34 40 46 52 64 76 88 100 112 143 175 207 239 271 

700 2 7 13 19 25 31 37 43 50 56 69 82 95 -108 122 155 189 223 258 292 

800 3 9 15 22 29 36 43 51 58 65 80 95 110 125 141 179 218 257 296 336 

900 4 10 18 26 34 42 50 58 66 74 91 108 125 142 159 203 247 291 335 379 

1000 4 12 20 29 38 47 56 65 74 84 102 121 140 159 178 227 275 324 374 423 



Attribute Sampling 547 

TABLES 
TABLE FOR EVALUATING SAMPLE RESULTS-1% RISK OF CONCLUDING 

OCCURRENCE RATE IS LOWER THAN IT ACTUALLY IS 

Number of Observed Occurrences 
Achieved Upper Precision Umit: % Rate of Occurrence 

Sample------------------------------
Size 2 3 4 5 6 7 8 9 10 12 14 16 18 20 25 30 35 40 45 

10 

20 

30 

40 

50 

60 

70 

80 

90 

100 

120 

140 

160 

180 

200 

220 

240 

260 

280 

300 

0 

0 

0 

0 

0 

0 

0 

0 1 

0 1 

0 1 2 

0 1 2 3 

0 

0 1 

0 1 3 4 

0 

2 3 

5 6 

0 1 2 3 5 7 8 10 

1 2 3 5 7 9 11 13 

1 2 3 4 7 9 12 14 17 

1 2 3 4 5 6 9 11 14 18 21 

1 2 4 5 6 7 10 14 17 21 25 

2 3 5 6 7 9 12 16 20 24 29 

2 3 4 6 7 9 10 14 19 23 28 33 

3 4 6 8 9 11 13 18 24 29 35 40 

4 5 7 10 12 14 16 22 29 35 42 48 

0 2 3 5 6 7 9 12 14 17 20 27 34 41 49 56 

0 1 

0 1 

0 2 

2 3 4 

3 4 5 

3 5 6 

6 7 8 11 14 17 20 23 31 39 47 56 65 

7 8 10 13 16 19 23 26 35 44 54 63 73 

8 10 11 15 18 22 26 30 39 50 60 70 81 

1 2 4 

1 3 5 

2 3 4 

2 4 6 

6 7 9 11 13 17 21 25 29 33 44 55 66 78 89 

6 8 10 12 14 19 23 27 32 36 48 60 72 85 97 

7 9 12 14 16 21 25 30 35 40 53 65 79 . 92 106 

8 10 13 15 18 23 28 33 38 43 57 71 85 99 114 

320 0 2 4 7 9 11 14 17 19 24 30 35 41 47 61 76 91 107 122 

340 1 3 s 7 10 13 1s 18 21 26 32 38 44 ·so 66 82 98 114 131 

360 1 3 6 8 11 14 16 19 22 28 35 41 47 54 70 87 104 122 139 

380 1 3 6 9 12 15 18 21 24 30 37 44 50 57 75 93 111 129 148 

400 1 

420 2 

460 0 2 

500 0 3 

550 0 3 

4 7 10 13 16 19 22 26 32 39 46 54 61 79 98 117 136 156 

4 7 10 14 17 20 24 27 35 42 49 57 64 84 103 124 144 164 

5 8 12 15 19 23 27 31 39 47 55 63 72 93 114 136 159 181 

6 10 13 17 21 26 30 34 43 52 60 70 79 102 125 149 174 198 

7 11 15 20 24 29 34 38 48 58 68 78 88 113 139 166 192 219 

600 0 4 8 13 17 22 27 32 37 43 53 64 78 86 97 125 153 182 211 241 

650 0 4 9 14 19 25 30 36 41 47 58 70 82 94 106 136 167 198 230 262 

700 1 5 10 16 21 27 33 39 45 51 64 76 89 102 115 148 181 215 249 283 

800 1 7 13 19 25 32 39 46 53 60 74 89 103 118 133 171 209 248 287 326 

900 2 8 15 22 29 37 45 53 61 69 85 .101 118 135 152 194 237 281 325 369 

1000 2 9 17 25 34 42 51 60 69 78 96 114 133 151 170 218 266 314 363 412 



548 College & Research Libraries November 1993 

TABLE9 
EXAMPLES SHOWING EFFECT ON COMPUTED UPPER OCCURRENCE RATE 
OF CHANGING RISK, SAMPLE SIZE, AND NUMBER OF DEVIATIONS FOUND 

Risk of Concluding 
the Occurrence 

Rate Is Lower Than Computed Upper 
Case It Actually Is Sample Size No. of Deviations Occurrence Rate 

1 5% 
2 5 
3 5 
4 5 
5 10 
6 10 

upper occurrence rate (called the com-
puted upper occurrence rate), these steps 
should be followed: 

1. Locate the table that corresponds to 
the risk of concluding that the oc-
currence rate is lower than it actu-
ally is that was specified earlier. 

2. Locate the actual sample size at the 
left of the table. 

3. Look across the row (identified in 
step 2) to find the actual number of 
occurrences found when examin-
ing the sample 

4. Look to the top of that column 
(identified in step 3) to read the 
computed upper occurrence rate. 

Librarians, too, may find attribute 
sampling useful to make inferences 
about characteristics such as the 
portion of books misclassified, .the 
error rate in the catalog record, or the 
portion of books missing. 

Using table 7, the librarian would con-
clude that the maximum percent of 
books missing (computed upper occur-
rence rate) is 4 percent. Comparing the 
computed upper occurrence rate to the 
maximum tolerable rate indicates that 
the records meet the librarian's criteria. 
If the computed upper occurrence rate is 
less than or equal to the tolerable occur-
rence rate, the librarian may statistically 
conclude that the records are satis-
factory. Earlier, the librarian specified a 

50 
100 
150 
200 
100 
100 

1 9.1% 
2 6.2 
3 5.1 
4 4.5 
2 5.2 
3 6.6 

tolerable occurrence rate of 4 percent. 
Hence, the librarian may conclude that 
the records are okay unless the qualita-
tive aspects of the occurrence should be 
considered. In contrast, had the librarian 
found two occurrences, the librarian 
should have concluded that the maxi-
mum occurrence rate was 6 percent, 
which exceeds the tolerable rate. Two 
occurrences yield a significantly higher 
ocCl:J.rrence rate than the librarian origi-
nally expected. Hence, because the ac-
tual occurrence rate is much greater than 
anticipated, a librarian may choose to 
expand the sample. We will discuss 
qualitative aspects of occurrences later. 

Table 9 presents a series of cases which 
show the effect on the computed upper 
deviation rate of changing the number of 
occurrences found and risk. 

Consider the Qualitative 
Aspects of Deviations 

Before drawing a conclusion about the 
results of the sample, one should con-
sider the qualitative characteristics of 
any occurrence found. Sometimes devia-
tions in the sample may signal that un-
examined population items include 
many occurrences or deviations. For ex-
ample, deviations may occur because an 
employee was untrained or an em-
ployee's personal problems have re-
sulted in less than quality performance. 

CONCLUSION 

Attribute sampling is a technique 
widely used by CPAs when auditing to 
make inferences about a population they 



want to know about but cannot afford 
the time or cost to examine all items in 
the population. Librarians, too, may find 
attribute sampling useful to make infer-
ences about characteristics such as the 
portion of books misclassified, the error 
rate in the catalog record, or the portion 
of books missing. Attribute sampling 
techniques provide a basis for making 
defensible statements about an attribute 
of a population. This article describes 

Attribute Sampling 549 

techniques auditors utilize that librari-
ans may apply when sampling to esti-
mate occurrence rates. These tech-
niques also enable librarians to eval-
uate the risk of making an incorrect esti-
mate. While that risk always exists, the 
tables used for determining initial sample 
size and evaluating results enable the · 
sampler to control the risk of concluding 
that the occurrence rate is lower than it 
actually is. 

REFERENCES 

1. D. M. Guy and D. R. Carmichael. Audit Sampling: An Introduction to Statistical Sampling 
in Auditing. New York: Wiley, 1986. 

2. Carl M. Drott. "Random Sampling: A Tool for Library Research." College & Research 
Libraries 30 (March 1969) 119-25. 

3. Richard M. Dougherty and Fred J. Heinritz with the assistance of Neal K. Kaske. 
Scientific Management of Library Operations. Metuchen, N.J. and London: Scarecrow, 
1982. 

4. Ronald R. Powell. Basic Research Methods for Librarians, 2d ed. Norwood, N.J.: Ablex, 
1991. . 

5. D. M. Roberts. Statistical Auditing. New York: American Institute of Certified Public 
Accountants, 1978. 

6. I. S. Simpson. Basic Statistics for Librarians, 3d ed. London: Library Association, 1988. 

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