A Hybrid Course for Probability and Statistics for Engineers: A Readiness Study at Shahid Beheshti University

Probability and Statistics for Engineers covers verities of subjects in the set theory, the combinatory analysis, probability, statistics, and (in some universities) the stochastic processes. Since, course receives only 3 credits it has to be thought 3 hours/week. This overloading content along with time limitation make course as a challenging and difficult one for students. Also, many instructors, including the first author, found the course very challenging to teach. Two popular on-site and e-learning training systems do not provide any appropriate solution. This article suggests a hybrid training system, which combines some elements of both training systems to reduce the disadvantages of both systems. Readiness of such hybrid course is measured by preparedness of students for online activities. The readiness study at Shahid Beheshti University shows that Internet skills, self-directed learning, learner attitude toward elearning, e-mail skills, and software ability of students are factors which are significantly affect readiness of students.

INTRODUCTION Probability and Statistics for Engineers is one of the challenging co urses fo r bot h i nstructors and st udents i n engineering. Overloading of the course content, time limitation, an d si multaneous offering t he c ourse wi th several difficult courses (such as fundam ental of physics, multivariate calculus, differential equations) transform an interesting course to a difficult on e. Some instr uctors s uggest dropping some less important materials of the course, and teaching the rest with more care. But, the majority of them believe t hat t he course co ntents have been chosen based upon st udents' needs i n ot her courses and t heir research. Therefore, it is reasona ble to em ploy a tr aining syste m which have n o t ime l imitation and can be a dapted based upon learners' abilities.
An e-learning training syst em can provide an interactive, individualized, and repeatable environment to teach a subject. Un iversities are wit nessing m any benefits o f elearning, su ch as co st sav ing, in creasing fle xibility, p roductivity, rapidly developing, deploy and update a course, providing an effectiv e train ing syste m, availability anytime and any where, providing broadly training opportunities, st aying com petitive, im proving m otivation and m orale, and im plementing st rategic i nitiatives more effectively (Bonk, 2002;So and Swatman, 2007;Minton, 2000 ). O n the oth er han d, there are situations where a n elearning t raining system i s not an appro priate one. M any instructors believe that mathematics and statistics need the traditional face-to-face traini ng system and they cannot teach using an online traini ng syste m (Broadbent, 2001 andChapnick, 2000).
To overcome such bar riers and l imitations, several authors s uggest using a hy brid cou rse; see Garnham and Kaleta (200 2) and Sands (2002), am ong ot hers f or m ore detail. Many universities have sought to develop their own hybrid learning courses as another option for students and instructors who prefer to replace some portion of traditional face-to-face meeting time with online instruction (Olapiriyakul & Scher, 2006). In a hybrid training system, similar to the traditional training system, students participate i n a cl assroom and l earn si gnificant p ortion of t he course on-site. But, some complimentary activities such as advanced topi cs, assignm ents, quizzes, more exam ples, and etc are m oved to a n online part. T he goal of hy brid courses is to join the best features of in-class teaching with the best features of online le arning t o p romote act ive i ndependent l earning an d red uce class seat time (Garnham and Kaleta, 2002). Moreover, Arbaugh (2000) pointed out that hybrid courses m ay be acco mpanied benefits of bot h on-site and e-l earning techniques to reduce disadvantages of both techniques. To have a successful hybrid course an instructor must invest significant time and effort in redesigning a trad itional course. Since, online activities require special abilitie s, equipm ents, and etc. of learners. Garnham and Kaleta (2002) pointed out that readiness of a hybrid course measured by preparedness, mentally or p hysically, of learners in online activities. Sands ( 2002) described how one m ay integrate onl ine activities wi th classro om wo rk to ob tain a su ccessful h ybrid co urse. Based up on Sands' su ggestions, ou r ex perience, and several in-deep interview with some experts and instructors, we decide to design a hybrid course, which (i) the course contents teach in the On-site pa rt; ( ii) Class materials companies with some new exa mples and m ore advanced materials as well as quizzes and assignments are moved to the On-line part.
This article re ports th e read iness o f Sh ahid Beh eshti university (say SB U) st udents, wh o regi stered t he cours e in 2009 winter semester. This article develops as t he following. Section 2 reviews some relevant literature regarding readiness. Research's hypothesizes as well as statistical methods ar e gi ven i n Section 3. R esearch's desi gn i s given i n Sect ion 4 . While Sect ion 5 repres ents resul ts of the research. Finally, Secti on 6 p rovides a concl usion regarding our findings. http://www.i-jet.org A HYBRID COURSE FOR PROBABILITY AND STATISTICS FOR ENGINEERS: A READINESS STUDY AT SHAHID BEHESHTI UNIVERSITY II. LITERATURE REVIEW Webster's New Collegiate Dictionary defines readiness as bei ng prepa red, m entally or phy sically, for som e experience or act ions. B orotis and p oulymenakou (2004) defined e-learning readiness of an or ganization as pre paredness, m entally or phy sically, for s ome e-l earning experience or actions. Kaur and Abas (2004), Anderson (2002), Bean (2003), Chapnick (2000), Clark and Mayer (2003), and Gold et al. (2001) are aut hors, am ong o thers, wh o di scussed t he necessity of a re adiness study in an e-learning training system. Th ey war ned th at with out a careful pl anning m ost likely an e-l earning system will be ended wi th cost overruns, unappealing t raining p roducts, and failure. M oreover, they stated that (similar to any other major innovations) e-l earning st rategies r equire co nsiderable up -front analysis, developm ent tim e, money, technological i nfrastructure, and leadership su pport to be successful . Therefore, managers must assess their companies' readiness for an e-l earning system, before im plementing t his i nnovation. Several authors st udied fact ors w hich m ay affect readiness of learners. Table 1 summarizes some of their results.

III. VARIABLES AND HYPOTHESIZES OF RESEARCH
A two -section su rvey en titled, "e-Learning Readiness Survey" has been developed to assess e-learning readiness of st udents at SB U, wh o re gistered t he course i n 2009 winter semester. The fi rst section consisted of 5 i tems to gather dat a about dem ographic charact eristics, such as gender, schola stic success (which is measured by Gra d Point Average, GPA), major, computer usage, and Internet usage in the week who takes the survey. The second section included 41 item s to asse ss respon dents' self-report perceptions of their readines s for an e-learning training system. No w observe th at: (i) th e On -line part o f th e h ybrid training system is a new part, which added to the traditional part. Therefore, it is reasonable to measure readiness of l earners for t he hy brid t raining syst em t hrough their readiness for an online training syste m; (ii) R eadiness defi nes b ased upo n m entally and phy sically preparedness of studen ts who will p articipate th e course. Fro m these observations one can conc lude that, readiness of the hybrid training system (dependent variable) can be measured, only, by students' online preparedness, mentally and physically, using q uestions 1 to 9. It is worth to mention that q uestions 1 to 5 assesses th e m ental read iness wh ile questions 6 t o 9 assess t he physical readiness of st udents in the survey.
DeVellis (2003) indicated that th e first step in d eveloping an instrument is, clearly, d etermining what it is th e researcher wants to measure. The variables, or factors, of this research identified afte r d etailed an alyses o f th e available e-le arning readi ness assessm ent instrum ents, and au thors' personal ex perience. As a result, 12 m ajor factors that can be helped organizations to measure how ready they are for an e -learning training system are identified.
Based upon previous researches, partly given in Section 2, a questionnaire devel oped t o m easure readi ness of a learner for the online course . Ap pendix A r epresents t he questionnaire items as well as their sources. Now, the followings present the hypotheses of this research.

Hypothesis 1. Skills of users influence on learners' readiness for an online course.
Learners with h igh sk ills h ave more co nfident to accomplish e-lea rning activ ities an d i mprove t heir satisfaction. Many studies explore influences of self-efficiency on users' recognition effects. Wang and Ne wlin (2002) from a research, on 122 students, concluded that students with higher skills are more inclined to adopt a network-base d learning sy stem and earned, si gnificantly, bet ter fi nal grades. Users' Sk ills wh ich considered in this stu dy are learners' ab ility to ev aluate their ab ility to use th e so ftware, har dware, e-mail and Internet to perform an e-Learning activity.

Hypothesis 2. Self-directed ability of learners influences learners' readiness for an online course.
In an online course, a learner goes through instructional material, delivered via the We b, at his/her own pace with no (m ore preci sely, wi th minimal) interaction fr om an instructor. Self-directed of l earners is a factor which can be used to measure whether or not a leaner can stand alone, whe never an instructor is not avai lable (Haney, 2001). Piskurich (2003) believes an ability to work alone, persistence i n learning, and ability to devel op a pl an t o complete a wo rk are su ch sk ills wh ich may affect read iness of e-learners.  attitude, towards e-learning, are an im portant factor in elearning readi ness. Learner' s at titude can be defi ned as learner's im pression t o part icipate in an e-le arning activity. In structors p ost th eir m aterials on the platform and learners part icipate t hrough c omputer net works. A m ore positive atti tude to ward e-l earning, for ex ample, wh en students are not afrai d of t he com plexity of using computers, will result in more satisfaction and effectiveness of learners in a n e-learning environment (Piccoli et al. , 2001). Fu rthermore, p ositive att itudes to ward e-learn ing increase the c hances of succ ess of an e-learning syste m, while negative attitudes reduce it. Therefore, this research considers learners' attitu de to wards co mputers as an important factor in e-learning readiness.

Hypothesis 4. Learners' computer anxiety influences on their readiness for an online course.
Piccoli et al . (20 01) bel ieve com puter anxi ety, si gnificantly, affects an e-learning environment. Com puters are communication t ools i n e-l earning environments. Therefore, any fear in com puter usage would certainly hamper learning (Piccoli et al., 2001) . C omputer anxiety is an emotional fear wh ich co mes u p so me p otential n egative outcomes, such as dam aging t o equi pments or l ooking foolish ( Barbeite and Weiss, 2004). The higher computer anxiety causes the lower level of e-learning readiness. The definition of co mputer anxiety in this research is th e level of learners' anxiety, when they apply computers.

Hypothesis 5. Equipments influence on learners' readiness for an online course.
Other fact ors contributing t o an increase in e-learning readiness are the i nfrastructure of t echnology and t echnical support of an e-l earning sy stem. It is im portant to bring into account the reliability and quality of the system, because they play important ro les in e-learning readiness. To build an acceptable e-learning environment, one has to maintain and up-t o-date t echnology and material represented by the environment (Folorunso et al., 2006;Poon et al., 2004;Selim, 2005). Hypothesis 6. Scholastic success of learners, influence on learners' readiness for an online course. Carmel and Gold (2007) pointed out those learners who reported hi gher readi ness t ended t o be m ore successful , scholastically.

Hypothesis 7. Gender of learners influences on learners' readiness for an online course.
Summer (199 0) an d M cMahon an d Ga rdner ( 1995) found out that male students experience less anxiety about ICT t han fem ale st udents. M oreover, Ol iver (1 993) an d Van B raak (2 001) di scovered t hat fem ale students have lower confidence or knowledge ability than males regarding com puter usage. However, m any ot her aut hors (s uch as K oohang, 1989; K ay, 1 989; H unt an d Bohlin, 19 93; Marshall and Bannon, 1986; Woodrow, 1991 among others) are agree with the claim that "there are no significant different between attitude of male and female students regarding ICT usage". Hypothesis 8. Major of learners influences on their readiness for an online course. Summers and Easdown (1996) mentioned that student's major and spe cialization are such factors which influence on e-learning's readiness.

IV. RESEARCH DESIGN
A series o f in -depth in terviews, with v arious ex perienced e-learning and instructor s of t he course, have been conducted to examine the validity of our res earch model. After that, questionnaire items developed based upon previous literatu re an d co mments g athered fro m the in terviews. Questionnaires were revised with help from experts (including academic s and practitioners ) wi th significant experience in e-learning and Probability an d Statist ics. A 5-point Likert scale ranging from 1, as st rongly disagrees, to 5, as strongly agrees, is used for the measurement.
A pret est, t o measure val idity and rel iability of st udy, was con ducted wi th 3 i nstructors and 2 e-l earning's e xperts. Fol lowed by pret est to veri fy rel iability of questionnaire, a pi lot t est has been con ducted u sing 20 ra ndomly chosen students fr om the t arget pop ulation. Questions reg arding sk ills o f u sers, on line au dio/video, selfdirected leanin g, learner att itude t oward l earning, l eaner computer anxiety, equip ments, and e-learning readiness can be su mmarized into 7 single factors . ,..., 7 1 F F The Cronbach's al pha fr om t hose fact ors are 80.2%, 75.34%, 95.01%, 89 .32%, 73 .02%, 89.54%, an d 78.9 3% r espectively, which indicate an acceptable reliability of the questionnaire.
The research population included all undergraduate students in computer and electronic majors, who registered in the Probability and Statistics course in 2009 winter semester at SB U (wi th pop ulation si ze N= 130) . Aft er a pi lot test, a census st udy was c onducted by distributing t he questionnaire among al l st udents. Thi s sur vey generat ed 109 useable responses from students resulting in a response rate of 83. 8%, which is indicated that the respondents found the topic interesting and relevant.
This research used two sta tistical packages, Minitab 13, SPSS 16, to analyze the data. Data was analyzed using the following two techniques.

A. Ordinal Logistic Regression
The bi nary l ogistic regression i s a wel l-known t echnique t o set up a general ized l inear model for t he bi nary dependent vari able. B ut for multiple ordi nal depende nt variables, t he binary l ogistic regressi on d oes not work properly. St atisticians devel oped an or dinal l ogistic regression t o ha ndle m ultiple ordinal de pendent vari ables. Minitab 13 is a statistical software package that can fit an ordinal logistic regression to data. The out put of t he software i ncludes: ( 1) Response and Factor Information, which di splays t he nu mber of obse rvations and t he response and factor categories; (2) Logistic Regression Table, which shows the estimated coefficients, p-values (related to a tes t that th e corresponding coeffi cient is zero), and odds ratio (which shows effect of each variables on the m odel); (3) Goodness-of-Fit Tests, w hich di splays both Pearson goodness-of-fit test of the model to data. The steps i n m odel b uilding f or a n ordinal l ogistic model are similar to t hose for t he bi nary l ogistic regressi on model. Unfortunately, th e fu ll array o f m odeling to ols is no t available in the softwa re packages. So, one has to c hoose a final and appropriate m odel by en tering variables with significant coefficients (p-value<0.05) and ordering effect of vari ables fr om t heir Odds ratio (negative coefficient along smallest odds ratio indicate more impact of the variable on t he de pendent vari able, M cCullagh and Nel der, 1992). Finally, appropriative of model is evaluated by (i) a A HYBRID COURSE FOR PROBABILITY AND STATISTICS FOR ENGINEERS: A READINESS STUDY AT SHAHID BEHESHTI UNIVERSITY

B. Contingency table
A co ntingency t able (or cr oss t abulation) describes the di stribution o f t wo or more vari ables sim ultaneously. Each cell shows the number of respondents, who gave a specific combination of responses. Since contingency table is easy to understand, can be used with any kind of data, (the contingency tables treat nominal, ordinal, interval, and ratio scales as a nom inal scale), provides g reater i nsight t han si ngle st atistics, and ca n be used as a tool to measure association among variables is one of most popular techniques in statistics. I n a twoways contingency Which t he chi -square t est is t he most pop ular one. The sm all enoug h p -value o f t he t est (l ess than 0. 05) indicates that there is no evidence for association between these variables.
V. RESULTS AND DISCUSSION Demographic profile and descri ptive statistics of t arget population are summarized in Table 2. Table 3 summarizes personal facilities and attitude of students about university facilities.

A. Ordinal Logistic Regression
As mentioned the above, sev eral 5-point Likert scale variables have been used to measure readiness of a learner (see Appendix A). To summarize such variables into a single one, say the dependent variable, one has to use t he m edian, w hich i s an appropriate central tendency for Like rt scale variables, see Agresti, 2003 a nd Johnson at al, 1999, among others. Therefore, readiness of each learner has 9 levels, b ecause median of those 5point Li kert scal e vari ables generat es 1, 1. 5, 2, 2. 5, 3, 3.5, 4, 4.5, and 5.
To di scover a ffect of i ndependent vari ables t he dependent vari able an ordi nal l ogistic regressi on can be employed. The fol lowing t able represents coefficients, p-values and odds ratios of such ordinal logistic regression.
Results of Table 4 (bel ow) can be summarized as the following: 1. There is significant evidence to conclude that skills of u sers (e-m ail sk ills), sk ills o f u sers (software ability), sk ills o f u sers (In ternet sk ills), selfdirected learn ing, and learn er attitu de to ward elearning are s uch variables whose a ffect learning readiness, the dependent variable (their p-values is smaller than 0.05). 2. Small odds ratio i ndicates t hat im pact of si gnificant fact ors can be or dered a s ( 1) sk ills o f u sers (Internet sk ills), ( 2) self-di rected learning, ( 3) learner attitude toward e-learning, (4) skills of users (e-mail skills), and ( 5) skills of users (software ability). 3. P-value= 0.00 fo r test th at "all coefficie nts are zero" al ong with t he p-va lue= 0.89 9 fo r "t he   Table 5.
A HYBRID COURSE FOR PROBABILITY AND STATISTICS FOR ENGINEERS: A READINESS STUDY AT SHAHID BEHESHTI UNIVERSITY

B. Hypothesis tests:
As pointed out the above, readiness of each learners is a 9 l evel variable to test the given hypothesizes, one has to categori ze the second variable in each hypothesizes i nto so me l evels. Popu lation can be categorized into some groups regarding skills (low and high), selfdirected abi lity (l ow and hi gh), l earners' attitude t o-ward the online course (negative, neutral, and positive), learners' computer anxiety (negative, neutral, and positive), IC T's equi pments (en ough and l ack), gen der (male and fem ale), major (computer sciences and Electronic), and sc holastic succes s, according to their GPA (week, GPA< 12, average, 12  GPA<17, and str ong, GPA  17). The contingency analysis has been con http://www.i-jet.org   Table 4.
From Table 4, one can observe that: 1. Computer anxi ety, equi pment, and gen der o f st udents do not affect their readiness reading the online training system. 2. Skills, self-d irected ab ility, attitude to ward th e online t raining sy stem, schol astic, and m ajor of students affect their readin ess reading the training system. In order to h elp m anagers o f u niversities, we in troduce a d iscriminative in dex to id entify lev el o f read iness of each individual. Figure 2 duplicates such index.
The bar chart above d uplicates l evel of readi ness of the t arget pop ulation, regar ding t he ab ove discriminative index.
Using the discriminative index, provided by Figure 2, one can observe that, more than 80% of the target population i s ready for t he onl ine course and co nsequently for t he hy brid course. B ut, they need so me im provements, which vary from an individual to another one.

VI. CONCLUSION AND SUGGESTION
This st udy made t heoretical and p ractical cont ributions to the literature of the hybrid course readiness and more specifically on students' perceptions of the hybrid course im plementation at SBU. The em pirical results showed that the most of factors that were extracted from the d ata were g enuinely sig nificant in p redicting th e criterion vari able. Our fi ndings co uld hav e pract ical importance for any uni versity as whose p lanning t o implement su ch h ybrid cou rse. Un iversities, in th eir rush to im plement the hybr id courses often place too much e mphasis o n th e equ ipment an d to o litt le o n th e human part. So, this research comes up with authorizes must take a h ard look at sk ills of users (Internet skills), self-directed learn ing, learner attitu de t oward elearning, skills of users (e-mail skills), and skills of users (soft ware abi lity) even t hought other n onsignificant, sta tistically, fact ors sh ould b e tak en in to account to have efficient a nd successful hybrid training system.
This st udy wa s t he fi rst part of a l ong t erm project , which desi gnation and im plementation of t he hy brid course a nd st udy sat isfaction and follow-up st udy are the last part of such project. Already, the second part of the project has been started. Th e On-lin e p art o f th e hybrid course available at: http://faculties.sbu.ac.ir/ ~payandeh/efront/www/index.php?logout=true, w here students i n su mmer sem ester, i n 20 09, used i t to wri te quizzes, download and upload assignments, and review the course materials.
To desi gn t he website, we us e an ope n so urce W eb designer nam ed Efront. Efron t p rovides abili ty to th e Web administrator to orient e-learners' activities by (i) defining some rules for e-learners; (ii) providing a complete database about activities of e-learners on the webpage; ( iii) ability to ass ign, randomly, a quizzes to learners. Oth er Efro nt's ab ilities may b e fo und in Zaharia (20 07) and i ts offi cial websi te avai lable at http://www.epignosis.com.gr/.