Abstract

     After apply web usage mining techniques, we have identified 14,174 sessions
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Table 1. An example of web session with length 4 and from a search engine

IP	Date	Time	Access	Referrer
202.174.136.*	26/06/2006	9:33:49	/top3000.asp.htm	http://www.google.com.hk/search?q=webometrics...
202.174.136.*	26/06/2006	9:50:46	/top3000.asp-offset=50.htm	http://www.webometrics.info/top3000.asp.htm
202.174.136.*	26/06/2006	9:53:54	/university_by_country_select.asp.htm	http://www.webometrics.info/top3000.asp-offset=50.htm
202.174.136.*	26/06/2006	9:55:16	/methodology.html	http://www.webometrics.info/top3000.asp-offset=50.htm

     We defined three main ways to access to a website: 1) through a search engine request: a query launched to a search engine allows to retrieve a link to the website demanded; 2) through a web link: surfing the web we may access to a website through a link from other website; 3) through the website root: typing in our web browser the URL of the website demanded. So, we classified the sessions in accesses through a search engine, through a web link and typing the URL (root). The origin of each session was detected through the referrer field in the log file. So, we observed the referrer of the access that originated the session. For example, this session (Table 1) was created from a search engine query, and then it was classified in the search engine category.
    We also classified each session according to its length. We define the length as the number of access carried out by the same IP in an interval less than 30 min. This timeout has been defined as a standard measure in several studies (Mahoui and Cunningham, 2000; Mat-Hassan and Levene, 2005; Jansen et al. 2007) from the empirical observations of Catledge and Pitkow (1995). This convention is used because it is impossible to observe when a user leaves a web page form the web log data. This lack of data affects to the exact definition of the session length because we can not know how many time one user spends in the last page (Huntington, Nicholas & Jamali, 2008). Due to this, the last view was not computed. We understand that this technical limitation is the same for the three types of access, so the differences in the session length will be the same in root, link and search engine access. The above session (Table 1) was defined as 4 length session, because the fifth access was made after than 30 min. and it includes four accesses in less than 30 min. between them. As we said before, this is the limit to separate different sessions.

     Statistic tools
     To process the data and to answer the above questions we used several statistical tests:

• Kruskall-Wallis H test (1952) detects if n data groups belong or not to the same population. This statistic is a non-parametric test, suitable to no-normal distributions such as the exponential distributions observed in web log analysis.
• Dunn’s post test (1961) compares the difference in the sum of ranks between two columns with the expected average difference (based on the number of groups and their size). It is used after to apply the Kruskall-Wallis or Friedman test. The Dunn’s test shows what samples are different.

     Results

     Session length
     We defined a k-session as the number of k access performed by a unique user in a time interval of >30 seconds, between one access and other.

Figure 1. Distribution of observed and calculated sessions by length

     Figure 1 shows the observed and calculated number of sessions according to the length of each session. Thus, we observed 3586 (25,3%) 2-sessions, 3188 (22,5%) 3-sessions, 2227 (15,7%) 4-sessions and so on. We also appreciated that the length distribution of sessions follows an exponential decay (Bianco et al, 2005) similar to the observed in other longitudinal web phenomena (Ortega et al, 2009). The fit of the distribution is high (R2=.98), so we may estimate the number of sessions by length not identified. We may hence estimate that there are 388 10-sessions and 290 11-sessions.
     We introduce a new indicator, half-length, which allows us to detect the median value in non-parametric distributions. It shows what n-sessions are the most frequent ones and the maximum number of clicks is needed to request the information demanded in the website.
     Mathematically the half length is expressed as:

where the half-length l1/2 is the natural logarithm of 2 divided by the decay constant (lamda) and is found from the exponential regression:

where Wa is the number of Web pages which have the length a and W1 is the number of 1-sessions.

     In our sample the half-length or median is 2.38, so we can argue that more than the half of the sessions has a length 2, if one surfs through the webometrics.info website. This low length is because this website is a ranking of universities and its information is displayed through tables which are accessible with just two clicks. We think that this indicator makes possible to characterize the length of the sessions and detect if the browsing of a website is fast or slow, their contents can be quickly located or otherwise it has a winding architecture with makes contents hardly accessible.

Figure 2. Marginal distribution of sessions by length

     We intend to see if the length of a session is related to the referrer of each session or the length is independent of the place from the user comes. As we see before, the sessions have been classified in three classes: sessions from a search engine, from a link in other website and from the root URL typed in the web browser. The Figure 2 and Table 2 show slight differences between the three classes of sessions, being the sessions from search engines referrer those with the largest mean (4.163) and the sessions from the root the ones with the smallest mean (4.069). The half-length or median shows that the first half of the link sessions has a length lesser than 2.42 clicks, while the root half has a length lesser than 2.33 clicks. To detect if these differences between the marginal distributions are or not statistically significant, we have used the Kruskall-Wallis test.

K (Observed value)	6.314
K (Critical value)	5.991
DF	2
p-value (Two-tail)	0.043
Alpha)	0.05

Sample	Frequency	Mean	Median (half-length)	Standard deviation	Groups
Root	1620	4.069	2.33	2.018	A
Link	3487	4.155	2.42	2.016	A/B
Search engine	9066	4.163	2.38	1.977	B

Table 2. Kruskal-Wallis test with the Dunn’s post test

     Table 2 shows that there are significant differences between the three access methods in the web navigation (p-value=.043; a= .05). So we can assume that the referrer may be an important factor in determining the number of clicks that a user does in a navigation session. The bilateral tests between the three types of session show that those differences are significant between the session from search engines and the session from the root. However, there is no difference between sessions from links and the other two ones.

     Session length

     The duration of the web sessions was defined as the total time performed by a unique user during the website navigation in which a time interval of = 30 seconds was carried out between one access and other.

Figure 3. Sessions frequency distribution by duration (sec.), (log-log).

     Figure 3 shows the distribution of sessions by their duration in seconds. It follows an exponential model with a high fit (R2= .94).The equation that better describe the session duration is:

     Where Si is the number of sessions that last i seconds, S1 the number of sessions that last 1 second and lamda is the decay constant (lamda=.99). This good fit allows us to estimate how many sessions last i seconds. For example, this model estimates 2074 sessions with duration of 30 sec., 3609 ones with 60 sec., and 5584 ones with 120 sec. If we interprete it from a cumulative point of view, 14.66% of the sessions have a duration of less or equal than 30 sec., 25.51% ones are less or equal than 60 sec., and 39.47% ones are less or equal than 120 sec. In our sample, we found that the most frequent session duration is 10 sec., while the 50% of the sessions have a duration higher than 2.2 min.

Figure 4. Marginal distribution of sessions by duration, grouped by type of access

Duration	Frequency	R2	S1	lamda
Search engine	9066	.916	44.06	.995
Links	3487	.87	22.86	.993
Root	1620	.8	18.07	.984

Table 3. Fit and coefficients of the three types of distribution

     Figure 3 shows the frequency distribution of the three classes of sessions according to their access point (search engine, links and root), which also follow an exponential decay. We observe that the sessions from search engines are those with the largest duration distribution, followed by Links and Root. Table 4 shows the principal parameters of the three distributions. The fit in the three distributions is high, although it decreases due to the sample size. It is interesting to notice that the decay constant (lamda) remain roughly the same in the three samples (˜.99). We may estimate that the 13.41% of the sessions from a search engines have duration of less or equal than 30 sec., while the percentage of sessions less or equal than 30 sec. is 17.66% for session from links and 26.33% for sessions from the root.

K (Observed value)	234.728
K (Critical value)	5.991
DF	2
p-value (Two-tail)	<0.0001
Alpha)	0.05

Sample	Frequency	Mean	Median (half-length)	Standard deviation	Groups
Root	1620	273.156	92	481.909	A
Link	3487	234.281	108	439.560	B
Search engine	9066	328.570	148	530.502	C

Table 4. Kruskal-Wallis test with the Dunn’s post test

     Table 4 shows the Kruskal-Wallis test for differences in non-parametric sample distributions. Dunn’s post test confirms the significant bilateral differences between the three samples. So we can state that the duration of the sessions is different according to the referrer of each session. Being the users from the search engines who most time pass in the website (median=148 sec.), followed by link’s users (median= 108 sec.) and root’s users (median= 92 sec.).