The influence of sample size on informetric characteristics is examined to determine whether theoretical mathematical models can adequately fit large data sets. Two large data sets of queries submitted to the Excite search service were sampled for search characteristics (term frequencies, terms used per query, pages viewed per query, queries submitted per session) producing data sets of various sizes that were fitted to theoretical models to determine how the sample may influence a model’s goodness-of-fit. Although theoretical models could adequately fit smaller data sets of up to 5000 observations in some cases, larger data sets could not be satisfactorily fitted using several goodness-of-fit techniques. Investigators must take into account that sample size does influence goodness-of-fit outcomes. The nature of the data and not the limitations of given goodness-of-fit tests results in significant outcomes. Such goodness-of-fit tests should be used for comparative purposes, rather than significance testing.
R. H. Baayen , Word Frequency Distributions ( Kluwer, Boston , 2001).
2.
M. J. Nelson , Stochastic models for the distribution of index terms , Journal of Documentation45(3) (1989) 227-237 .
3.
M. Nelson and J. S. Downie , Informetric analysis of a music database , Scientometrics54(2) (2002) 243-255 .
4.
I. Ajiferuke and D. Wolfram , Informetric modelling of Internet search and browsing characteristics , Canadian Journal of Information and Library Science28(1) (2004) 1-16 .
5.
M. J. A. Berry , Data Mining Techniques ( Wiley, Indianapolis , 2004).
6.
C. R. Cunha , A. Bestavros and M. E. Crovella , Characteristics of WWW client-based traces (1995). Available at: http://cs-pub.bu.edu/faculty/crovella/paper-archive/TR-95-010/paper.html (accessed 19 October 2005).
7.
C. Silverstein , M. Henzinger , H. Marais and M. Moricz , Analysis of a very large web search engine query log , SIGIR Forum33(3) (1999). Available at: www.acm.org/sigir/forum/F99/Silverstein.pdf (accessed 19 October 2005).
8.
A. Broder , R. Kumar , F. Maghoul , P. Raghavan , S. Rajagopalan , R. Staa , A. Tomlins and J. Wiener , Graph structure in the Web , Computer Networks and ISDN Systems30 (2000) 209-320 .
9.
B. A. Huberman , The laws of the Web: Patterns in the ecology of information ( The MIT Press, Cambridge, MA , 2001).
10.
B. J. Jansen , A. Spink and T. Saracevic , Real life, real users, and real needs: a study of user queries on the Web , Information Processing & Management36(2) (2000) 207-227 .
11.
J. Nielsen , Do Websites have Increasing Returns? (1997). Available at: www.useit.com/alertbox/9704b.html (accessed 19 October 2005).
12.
J. Nielsen , Zipf curves and Website popularity (1997). Available at: http://www.useit.com/alertbox/zipf.html (accessed 19 October 2005).
13.
A. Spink , D. Wolfram , B. J. Jansen and T. Saracevic , Searching the web: the public and their queries . Journal of the American Society for Information Science and Technology52(3) (2001) 226-234 .
14.
M. E. Crovella , M. S. Taqqu and A. Bestavros , Heavy-tailed probability distributions in the World Wide Web. In: R. J. Adler , R. E. Feldman and M. S. Taqqu (eds), A Practical Guide to Heavy Tails: Statistical Techniques and Applications ( Birkhäuser, Boston , 1998).
15.
I. Ajiferuke , D. Wolfram and H. Xie , Modelling website visitation and resource usage characteristics by IP address data . In: H. Julien and S. Thompson (eds) Proceedings of the 32nd Annual Conference of the Canadian Association for Information Science (2004). Available at: www.cais-acsi.ca/proceedings/2004/ajiferuke_2004.pdf (accessed 19 October 2005).
16.
B. Zhu , S. Lemeshow , D. W. Hosmer , J. Klar , J. Avrunin and D. Teres . Factors affecting the performance of the models in the Mortality Probability Model II system and strategies of customization: a simulation study , Critical Care Medicine24(1) (1996) 57-63 .
17.
D. P. Strum , J. H. May and L. G. Vargas . Modeling the uncertainty of surgical procedure times: comparison of log-normal and normal models , Anesthesiology92(4) (2000) 1160-1167 .
18.
F. Yoshikane , Comparative analysis of author productivity of different domains: in consideration of the effect of sample size dependency of the statistical measures . In: M. Davis and C. Wilson (eds.) Proceedings, ISSI-2001(University of N.S.W. Bibliometric and Informetric Research Group, Sydney, 2001) 771-778 .
19.
L. Egghe , Sampling and concentration values of incomplete bibliographies , Journal of the American Society for Information Science and Technology53(4) (2002) 271-281 .
20.
M. R. Henzinger , A. Heydon , M. Mitzenmacher and M. Najork , On near-uniform URL sampling . In Proceedings of the Ninth International World Wide Web Conference, Amsterdam, 2000. Available at: www9.org/w9cdrom/88/88.html (accessed 19 October 2005).
21.
H. C. Ozmutlu , A. Spink and S. Ozmutlu , Analysis of large data logs: an application of Poisson sampling on Excite Web queries , Information Processing & Management38(4) (2002) 473-490 .
22.
D. Wolfram , A. Spink , B. J. Jansen and T. Saracevic , Vox populi: the public searching of the web , Journal of the American Society for Information Science and Technology52(12) (2001) 1073-1074 .
23.
A. Spink , B. J. Jansen , D. Wolfram and T. Saracevic , From e-sex to e-commerce: Web search changes , Computer Magazine35(3) (2002) 107-109 .
24.
R. L. Schaeffer , W. Mendenhall III , and M. A. Stephens , Elementary Survey Sampling ( Thomson Brooks/Cole Publishers, Belmont , 2005).
25.
H. S. Sichel , Anatomy of the generalized inverse Gaussian-Poisson distribution with special applications to bibliometric studies , Information Processing & Management28(1) (1992) 5-17 .
26.
Q. L. Burrell and M. R. Fenton , Yes, the GIGP really does work - and is workable ! Journal of the American Society for Information Science44 (1993) 61-69 .
27.
A. J. Lotka , The frequency distribution of scientific productivity , Journal of the Washington Academy of Science16(12) (1926) 317-323 .
28.
R. B. D’Agostino and M. A. Stephens , Goodness-of-fit Techniques ( Marcel Dekker, New York , 1986).
29.
V. Choulakian and M. A. Stephens , Goodness-of-fit tests for the generalized Pareto distribution , Technometrics43(3) (2001) 478-484 .
30.
V. Choulakian , R. A. Lockhart and M. A. Stephens , Cramér-von Mises statistics for discrete distributions , Canadian Journal of Statistics22(1) (1994) 125-137 .
31.
N. Henze , Empirical-distribution-function goodness-of-fit tests for discrete models , Canadian Journal of Statistics24(1) (1996) 81-93 .
32.
F. Famoye , EDF tests for the generalized Poisson distribution , Journal of Statistical Computation and Simulation63(2) (1999) 159-168 .
33.
NIST/SEMATECH e-Handbook of Statistical Methods. Available at: www.itl.nist.gov/div898/handbook (accessed 19 October 2005).
34.
C. E. McLaren , J. M. Legler and G. M. Brittenham , The generalized χ2 goodness-of-fit test , The Statistician43(2) (1994) 247-258 .
35.
F. C. Drost , W. C. M. Kallenberg , D. S. Moore and J. Oosterhoff , Power approximations to multinomial tests of fit , Journal of the American Statistical Association84 (1989) 130-141 .
36.
W. Wang and F. Famoye , Modeling household fertility decisions with generalized Poisson regression , Journal of Population Economics10(3) (1997) 273-283 .
