2013 PLR for New Zealand Authors Survey.pdf

2013 Public Lending Right
for New Zealand Authors Survey
2013 Public Lending Right
for New Zealand Authors Survey
ACT 1982
Prepared by Statistics New Zealand
for the National Library of New Zeanald
INFORMATION
Charlie Dohrman & Asheel Ramanlal
Statistical Methods
28 September 2012
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2013 Public Lending Right
for New Zealand Authors Survey

1 Objective
The purpose of this document is to outline the method used to redesign the Public Lending Right
Survey. The National Library will be selecting the sample and collecting the information from the survey
with the guidance of the details below, allowing them to be self-sufficient if the population of libraries
do not dramatically change.

2 Background to the survey
The Public Lending Right for New Zealand Authors scheme compensates New Zealand authors for the
ACT 1982
use of their books in New Zealand libraries. The scheme provides annual payments to New Zealand
authors. This is to compensate the loss of royalty income incurred as a result of their books being made
available through New Zealand libraries.
The Public Lending Right survey is run by the National Library of New Zealand and is designed to
distribute this compensation amongst authors who have entered their books on the register. The
amount each author receives depends on the total number of copies of registered titles. Authors who
have an estimated total of 50 copies or more of their titles in New Zealand libraries receive a percentage
of the fund. Authors need to register each year so that their titles become active for that year. If they do
not register, their titles will not be included in any survey or payment that year. If they register and then
INFORMATION
die before payment is made, their estate would receive payment in that year and would not be eligible
to register in future years (as they are deceased).

3 Changes from previous survey
The Public Lending Right for New Zealand Authors Regulations 2009 limited the design of the survey in
2010.
Regulation 9 ‘How New Zealand libraries are to be surveyed or sampled’, comprehensively states that:
“The chief executive must do a triennial survey of the National Library and 39 other New Zealand
libraries to find out how many copies they hold of books by New Zealand authors who entered their
names in the register in the year of the triennial survey. In the first year after the triennial survey, the
chief executive must do an updating survey of the National Library and the 39 other New Zealand
libraries. In the second year after the triennial survey, the chief executive must do an updating survey of
the National Library and the 39 other New Zealand libraries.”
Section 8 states that:
“the 39 New Zealand libraries surveyed must be those named by the Government Statistician and must
be the same 39 libraries for the 3 surveys.”
In 2012, an Amendment to the regulations was put through changing how New Zealand libraries are to
RELEASED UNDER THE OFFICIAL
be surveyed or sampled. Regulation 9 now reads:
“The surveys may be of (a) samples of New Zealand libraries; or (b) all New Zealand libraries. The chief
executive must do the surveys in accordance with the advice of the Statistician on (a) how often to do
the surveys; and (b) the design of the surveys.”
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2013 Public Lending Right

for New Zealand Authors Survey

This amendment gives Statistics New Zealand (the statistician) a lot more freedom in the design of the
survey. This also shifts the responsibility of the survey design entirely up to Statistics New Zealand. To
limit Statistics New Zealand’s involvement, the design of the survey has two fundamental principles:
1.  Robust: To cater for the dynamic population;
2.  Unbiased: To satisfy the needs of a key stakeholder, The New Zealand Society of Authors (PEN NZ
Inc.).
1982

4 Technical objectives
ACT
4.1  Type of surveys
There are two options on the type of survey used each time it’s run:
1.  The complete survey, which is a list of all New Zealand titles in the register.
2.  The update survey, which is a list of New Zealand titles submitted to the register between 1 January
and 30 April in that year. This includes new titles, or titles where an author adequately justifies
including a title in a survey again.

4.2   Accuracy requirements
The accuracy has not been stated by the National Library, who is responsible for running the survey. The
INFORMATION
survey design will be based on previous sample errors, as they were considered acceptable. Sample
errors for this survey are not generally released to the public.

The New Zealand Society of Authors (PEN NZ Inc.) approved the changes to the Public Lending Right for
New Zealand Authors Regulation 2008 only if the Department could guarantee the reliability of the
survey (a guarantee of 90% accuracy). The survey design assumes that this condition implies that
OFFICIAL
relative sampling errors (RSE) of 10% are acceptable.

5 The frame to be used  THE
5.1  Target and survey population
The target population for this survey is all New Zealand libraries with the following exclusions:
1.  School libraries, these are for practical reasons.
2.  Private libraries that are not open to the general public as a full list of libraries are unavailable.

UNDER
5.2  Stratification variables
Information on current public libraries will be known by the National Library, including the total
holdings. In 2010 the decision to use ‘holdings’ (where holdings is the total number of books for each
district) as a stratification variable was made. This was considered to correlate the most with the
number of New Zealand titles in New Zealand libraries (the variable of interest).

5.3  Details of updating
RELEASED
Information on the holdings for the tertiary libraries, consisting of universities and polytechnics, were
found on the following links:
Universities: http://www.universitiesnz.ac.nz/aboutus/sc/CONZUL/Statistics
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2013 Public Lending Right
for New Zealand Authors Survey
Polytechnics: http://wikieducator.org/File:Polystats_2005-2011.pdf
This information will enable the design variable ‘holdings’ to be updated for the population each year.
This is important if libraries form new consortiums, join existing consortiums or amalgamate. It will help
to establish if a consortium or amalgamation is large enough to move into the full-coverage stratum. If
the full-coverage stratum becomes too large, the constraint for the cut-off between full-coverage and
smaller strata will have to be revised. Statistics New Zealand should be involved in the revision to
ensure that sample errors do not become too high with the change.
The tertiary libraries appear more static and are thus divided into two strata: Universities and
ACT 1982
Polytechnics. If the tertiary population becomes more dynamic, then the boundaries for the cut-off on
stratum should also be revised. Statistics New Zealand should be involved in the revision to eliminate
the possibility of high sample errors.

6 The sample design details
6.1  Option 1: rotating panel design
Initially the population needs to have the design variable ‘holdings’ updated.
INFORMATION
Divide this population into 4 strata:
1. Public libraries with holdings >200,000;
2. Remaining public libraries;
3. University libraries;
4. Polytechnic libraries.
Both large public libraries and university libraries will be made full coverage.
The remaining two strata will have a rotating panel that is kept in for two years. In the panels' first year,
the complete survey is used, and in the second year the updated survey is used. In the third year, when
the panel is rotated out of the sample, it is also removed from the survey population for that year only,
allowing other libraries to be chosen. Each year a new panel is chosen which will have a size that is half
the sample size. See Appendix A for a graphical representation of this process.
The justification for only sending the updated survey to the panel in the second year is based on the life-
cycle of a book. Smaller stratum libraries are less likely to remove a large number of books from their
shelves each year, leaving the results from the prior year a good representation of the number of NZ
titles held in the current year. This rotation will also decrease large shifts seen in the change of the
yearly count of the number of books per NZ title, which is a large concern of the one of the key
shareholders involved, PEN NZ Inc.
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2013 Public Lending Right
for New Zealand Authors Survey
Stratum (h)
Population size
Sample size
Weight  Overall sample
(Nh)
(nh)
(wh)
error
Public libraries >200,000
11
11
1
Small public libraries
36
10
3.6
University libraries
8
8
1
Polytechnic libraries
20
6
3.3
TOTAL
75
35
3.3%
ACT 1982
The sample size is based on the total sample error of 3.3%. In 2010 the design had a total sample error
of 3.55%.
6.2  Option 2: alternating two-year cycle design
Initially the population needs to have the design variable ‘holdings’ updated.
Divide this population into 4 strata:
1. Public libraries with holdings >200,000;
2. Remaining public libraries;
INFORMATION
3. University libraries;
4. Polytechnic libraries.
Both large public libraries and university libraries will be made full coverage.
The remaining two strata will be a sample. The type of survey will alternative each year between
complete and updating surveys. The year the sample is chosen, will be the year the complete survey is
used, keeping the same sample in for two years. The second year will be only the updating survey. See
Appendix B for a graphical representation of this process.
The assumption as to why the sample is only sent the updated survey in the second year is based on the
life-cycle of a book. Libraries are less likely to remove a large number of books from their shelves each
year, leaving the results from the prior year a good representation of the number of New Zealand titles
held in the current year.
Stratum (h)
Population size
Sample size
Weight  Overall sample
(Nh)
(nh)
(wh)
error
Public libraries >200,000
11
11
1
Small public libraries
36
9
4
University libraries
8
8
1
Polytechnic libraries
20
5
4
TOTAL
75
33
3.51%
RELEASED UNDER THE OFFICIAL
The sample size is based on the total sample error of 3.51%. In 2010 the design had a total sample error
of 3.55%.
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2013 Public Lending Right
for New Zealand Authors Survey
6.3  Option 3: one-year cycle design
Initially the population needs to have the design variable ‘holdings’ updated.
Divide this population into 4 strata:
1. Public libraries with holdings >200,000;
2. Remaining public libraries;
3. University libraries;
4. Polytechnic libraries.
ACT 1982
Both large public libraries and university libraries will be made full coverage.
The remaining two strata will be a sample. The type of survey each year will be the complete survey
only. See Appendix C for a graphical representation of this process.
Stratum (h)
Population size
Sample size
Weight  Overall sample
(Nh)
(nh)
(wh)
error
Public libraries >200,000
11
11
1
Small public libraries
36
5
7.2
University libraries
8
8
1
INFORMATION
Polytechnic libraries
20
3
6.67
TOTAL
75
27
5.03%
The sample size is based on the total sample error of 5.03%. In 2010 the design had a total sample error
of 3.55%.
6.4  Allocation to strata
6.4.1  For public libraries:
A program called ‘Strat’ was used to find the cut-off boundary between large and small public libraries.
Strat was run with a range of sample errors, continually giving a size of 11 for large public libraries. The
Strat results, as well as the ‘cumulative of the square root of the frequency method’ results were used
to confirm boundaries (this method was used in 2010 to establish the stratum boundaries). Both
methods gave the same results indicating that the boundary set a reasonable cut-off for public libraries.
Previously, the sample selection method for public libraries was ordered by geographical location and
then a systematic sample was taken. Since then, libraries have amalgamated or formed consortiums
decreasing the remaining libraries in the small stratum (the consortiums are a group of libraries from a
similar region, disrupting the spread of libraries throughout New Zealand). The proportion of south
island libraries to north island libraries has also decreased, and to create a sample design that is
independent of these shifts, a randomised sample based on the proportion of remaining south island
libraries is used.
RELEASED UNDER THE OFFICIAL
In 2012, there were 10 south island public libraries in the small strata, a proportion of 10/36
approximate to 3/10. So instead of ordering libraries, they were split into two groups - South Island and
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for New Zealand Authors Survey

North Island, assigned a random number, and 7 North Island public libraries with the lowest random
number were selected as well as 3 south island public libraries with the lowest random number.
6.4.2  For tertiary libraries:
All university libraries were bigger (by number of holdings) than all polytechnic libraries, so it was
decided to make university libraries full-coverage and sample the polytechnic libraries.

The sampling method for the polytechnic libraries has not changed. Polytechnic libraries will be
assigned a random number and 6 will be chosen that have the lowest random number.

ACT 1982
A census was not considered for this survey because the cost of enumeration is too high at the present.

6.5  Collection and selection procedures used
The National Library will be operating the collection process. The selection of sample will be clearly
outlined, so the National Library will be able to follow and be self-sufficient in the selection process.

Libraries amalgamating or forming consortiums reduces the costs involved in the collection. A search for
titles can be completed in one location and obtaining all information from the libraries within the
amalgamation or consortium.
INFORMATION

6.6  Estimation procedure
The sampling weight for a stratum h, (  ) is calculated as follows:



Where
         opulation si e of stratum
      Sample si e of stratum
The total number of each specified title in New Zealand libraries (  ) is calculated as follows:

       (∑         )


Where
      the specified title
         the total number of a specified title in stratum

Each library is assigned to a stratum and given the stratum weight. The aggregated total will be
considered the count of the current year, and the Authors’ Fund will split accordingly to the number of
qualifying books.

RELEASED UNDER THE OFFICIAL
In New Zealand payments to authors are determined by the book rate, which is calculated by dividing
the available funds among the number of qualifying books:
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for New Zealand Authors Survey






6.7  Editing & imputation
Given the method of collection, there is no non-response for this survey. Each library surveyed will
complete the survey. There is no need for any editing & imputation processes applied to the data.
Hence there is, if any, very little non-sampling error.

6.8  Sources of error
The estimates in this report are based on a sample of libraries. Because the estimates are based on a
ACT 1982
sample of libraries, all estimates have a sampling error associated with them. The variability of a survey
estimate, due to the random nature of the sample selection process, is measured by its sampling error.
Sampling errors vary from estimate to estimate, and with population breakdown and population size.

The sampling errors have been calculated based on previous data supplied on the 2010 triennial survey.

Additional notation:
               where     is the number of libraries in stratum h
              where   is the total number of stratums in the sample
INFORMATION




which is the stratum weight

( ̅


)



which is the stratum variance


∑
[ ̅

]

which is the stratum mean

The relative sampling error (RSE) of a stratum is calculated by
  [ ̅
√ [ ̅
[ ̅
]
]
]

[ ̅ ]
[ ̅ ]
To find the overall RSE the calculation used follows;

  [ ̅
√∑


    (
̅ )
[ ̅
  ]
  ]

[ ̅

  ]
∑


   (
̅ )

6.9  Dissemination of outputs
Decisions have to be made by the surveying agency (the National Library) on the commercial sensitivity
of the data collected. As the survey outputs monetary amounts, unit record data should be adequately
confidentialised in order to protect authors.

RELEASED UNDER THE OFFICIAL
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for New Zealand Authors Survey

7 Appendices
7.1  Appendix A: rotating panel design
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ACT 1982
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RELEASED UNDER THE OFFICIAL
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Page 10
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* R

2013 Public Lending Right

for New Zealand Authors Survey

7.2  Appendix B: alternating two-year cycle design

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ACT 1982
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INFORMATION
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RELEASED UNDER THE OFFICIAL
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7.3  Appendix C: one-year cycle design

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ACT 1982
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C INFORMATION
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n
n
RELEASED UNDER THE OFFICIAL '
w
o
latio
ar 1
ar 2
u
akd
e
e
ar 'n
p
Y
Y
e
Y
o
P
re
B
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