Approaches to extending or customizing (free) statistical software</= title> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"PostalCode"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"country-region"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"State"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"City"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"place"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"PlaceName"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"PlaceType"/>  <style>  </style>  </head> <body lang=3DEN-US link=3Dblue vlink=3Dpurple style=3D'tab-interval:.5in'> <div class=3DSection1> A Survey = on Ways Engineers Learn Sta= tistics After Leaving College <![if !supportLineBreakNewLine]> <![endif]><o:p></o:p> <o:p> </o:p> Jorge Luis Romeu Research Professor, Dept. M= AE, <st1:place w:st=3D"on"><st1:City w:st=3D"on">Syracuse University</st1:City>, <st1:Stat= e w:st=3D"on">NY</st1:State> <st1:PostalCode w:st=3D"on">13224</st1:PostalCode></st1:place>. <a href=3D"mailto:jlromeu@syr.edu">jlromeu@syr.edu</a> <o:p> </o:p> </div> <span lang=3DEN-CA style=3D'font-s= ize:10.0pt; mso-bidi-font-size:12.0pt;font-family:"Times New Roman";mso-fareast-font-fa= mily: "MS Mincho";mso-bidi-font-family:"Courier New";color:#003300;mso-ansi-langu= age: EN-CA;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'> <div class=3DSection2> Abstract <o:p> <= /o:p> This is the first of a three-part work on how engine= ers learn statistics after leaving college. Here we present a survey of practic= ing engineers, undertaken to support the tenants of the main paper, presented at ICOTS-7 in <st1:country-region w:st=3D"on"><st1:place w:st=3D"on">Brazil</s= t1:place></st1:country-region>. We discuss the sample taken, its composition and the questions and answers elicited in the survey. Finally, we present the main survey results <o:p> </o:p> Keywords: Statistics education, surveys, data analysis <o:p></o:p> <o:p> </o:p> 1. Introduction <o:p> </o:p> Two years ago this author was invited to write a pap= er on statistical education for the ICOTS-7 (International Conference on Teaching Statistics), <st1:City w:st=3D"on"><st1:place w:st=3D"on">Salvador</st1:pla= ce></st1:City>, <st1:country-region w:st=3D"on"><st1:place w:st=3D"on">Brazil</st1:place></= st1:country-region>. We chose the topic of how engineers learn statistics after leaving college,= an area where we have worked for over twenty five years (Romeu, 1986). <o:p> </o:p> However, we soon discovered in our literature search= that statisticians had studied how all cohorts studied statistics, from pre-scho= ol children to college graduate students. But there was no research on how pra= cticing engineers approached this problem. <o:p> </o:p> In our ICOTS-7 peer-reviewed paper (Romeu, 2006a), w= e proposed two main hypotheses that we needed to support. Given the lack of previous research on the topic, we decided to investigate this empirically, via a su= rvey of practicing engineers. Such survey would assess whether engineers (1) acquired enough statistics in their college studies and (2) whether they st= udied it, after college, on their own, as best they could (and what means they actually used to learn it). <o:p> </o:p> This survey was taken among American engineers and i= ts results supported our research hypotheses. In a third paper, presented at t= he 2006 ASA/JSM in <st1:City w:st=3D"on"><st1:place w:st=3D"on">Seattle</st1:place>= </st1:City>, we presented the survey results analyses (Romeu, 2006b) <o:p> </o:p> We knew, from our many years teaching statistics in = engineering departments as well as in short courses for industry, that college training fell short, and that many engineers needed substantially more statistics to= be able to do their work. We wanted to assess how they were able to bridge the= gap between their scant initial statistical training, and their professional ne= eds. <o:p> = ;</o:p> This impor= tant problem has two serious components: one is educational and the other is soc= ial. Educational because there is no more room for additional statistics in the engineering curriculum. Hence, the solution has to be to move things up and down stream. Teach more statistics in grade and high school; then teach thinking in college so that the engineer may be able to learn as needed, la= ter, on their own. Finally, to develop better tutorials and support materials for engineer use, during their lifelong learning process. The social component stems from an institutional paralysis (Romeu, 2006c).<o:p></o:p> <o:p> = ;</o:p> In the res= t of this paper, we will discuss how our survey was taken, describe its componen= ts, and how they were filled, and overview its main results <o:p></o:p><= /p> <o:p> </o:p>= 2. The Survey Input<o:p></o:p> <o:p> </o:p>= In order to support our two working hypothesis, that the statistical education of engin= eers is deficient and inadequate, requiring engineers to learn statistics on the= ir own at a later date (and further investigate the specific efforts they made= to solve this need, we implemented a pilot survey. In our questionnaire (see <= span style=3D'mso-bidi-font-weight:bold;mso-bidi-font-style:italic'><a href=3D"http://web.syr.edu/~jlromeu/SurveyICOTS.html">http://web.syr.= edu/~jlromeu/SurveyICOTS.html</a>) we asked, to characterize survey takers, several questions about the practicing engineer’s personal background. We requested their educati= on level (associate bachelor, masters or doctorate), area (academe, industry or government), specialization (mechanical, electrical, industrial, etc.), tot= al number of statistics courses they had taken in college, years practicing engineering, country where they practiced (an overwhelming majority were fr= om the USA) and gender. <o:p> </o:p> Then, we a= sked how they had acquired their post-college statistical knowledge on their own: (1) reading books, journals, manuals or other hard copy materials, (2) reading = Web and Internet materials and tutorials, (3) following on-line courses or lear= ning software, (4) attending symposiums, conferences chapter meetings, talks, et= c., (5) pursuing preparation for professional certifications such as American Society for Quality, (6) taking internal company or commercial short traini= ng courses, (7) receiving mentor= ing from other, more experienced work colleagues and (8) any other sources, suc= h as hands-on (or practical) working experiences (here many survey takers specif= ied having received Six Sigma training courses).<o:p></o:p> <o:p> = ;</o:p> The survey= was submitted to the members of several quality, reliability, manufacturing, et= c., engineering chapters in Central New York (CNY) and to many mid-career consultants, via our teaching of reliability courses to the annual engineer= ing TACNY conference Through the ISOSTAT group, we were able to tap engineers from a pharmaceutical company in Florida. Finally, the survey was also taken by a handful of European engineers, thanks to newsletter promotions graciouly provided by the ASQ, the RSS and ENBIS international professional societies= .<o:p></o:p> <o:p> = ;</o:p> Our sample characterization is the following:<o:p></o:p> <o:p> = ;</o:p> <![if !supportLists]><= span style=3D'mso-list:Ignore'>• <![endif]>So far 64 responses:<o:p></o:p> <![if !supportLists]><= span style=3D'mso-list:Ignore'>• <![endif]> 61 f= rom the <st1:country-region w:st=3D"on"><st1:place w:st=3D"on">US</st1:place></= st1:country-region><o:p></o:p> <![if !supportLists]><= span style=3D'mso-list:Ignore'>• <![endif]> 3 fr= om abroad. <o:p></o:p> <![if !supportLists]><= span style=3D'mso-list:Ignore'>• <![endif]> 8% f= emales<o:p></o:p> <![if !supportLists]><= span style=3D'mso-list:Ignore'>• <![endif]> 56% graduate degrees<o:p></o:p> <![if !supportLists]><= span style=3D'mso-list:Ignore'>• <![endif]> 60% = 16+ years experience <o:p></o:p> <![if !supportLists]>• = <![endif]> 90% = from industry.<o:p></o:p></= span> <o:p> = ;</o:p> According = to engineering technical specialization:<o:p></o:p> <![if !vml]><img width= =3D332 height=3D231 src=3D"KnoxIcotsPaper_files/image002.gif" v:shapes=3D"_x0000_s= 1911"><![endif]><o:p> </o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> And accord= ing to engineering educational level:<o:p></o:p> <![if !vml]><img width=3D328 height=3D218 src=3D"KnoxIcotsPaper_files/image004.gif" v:shapes= =3D"_x0000_s1912"><![endif]><o:p> </o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> Our sample= was not randomly, nor scientifically drawn from a sampling frame (such frame does n= ot exist), nor we claim it was. But, for a pilot effort and given that a sample size of sixty plus individuals responded, at the time we presented the pape= r, we believe it will provide interesting, valid, initial information for furt= her study.<o:p></o:p> <o:p> </o:p>= 3. The Survey Results<o:p></o:p> <o:p> </o:p>= To each su= rvey taker we asked to provide, in rounded percentages, their assessment of the amount of post college statistical knowledge they had acquired, by each of = the eight categories. For example, say an engineer thought they had acquired half of their statistics knowledge by reading books and other hard copy materials, = and the other half, by equal parts, via short courses and mentoring. Then, this engineer would fill the entry “hard copy” with 50, and the entr= ies “short courses” and “mentoring” with 25 each. In ev= ery case, the percentages had to add to 100.<o:p></o:p> <o:p> = ;</o:p> The survey= data collected so far (we are still receiving information) yielded the following results regarding our working hypotheses:<o:p></o:p></sp= an> <o:p> </o:p> <![if !supportLists]>A) </sp= an><![endif]>College Training<o:p></o:p><= /p> <o:p>&nb= sp;</o:p> I) Among all surveyed, 16% have not taken any statis= tics courses in college (33% among BS), 38% took only one (38%) and 26% have tak= en 2 courses (24%). II) 1/3 of those with a BS degree only, have never t= aken a single statistics course in college; another 1/3 of them have taken only one course. Hence, 2/3 engineers = of all surveyed had either none, or very little statistical training (i.e. taken a single course). III) Engineers that pursue graduate school have a la= rger opportunity of taking statistics. Only 7%, in our sample, have never taken a statistics course. <o:p> </o:p> <![if !supportLists]>B) </spa= n><![endif]>Methods Preferred<o:p></o:p>= <o:p> </o:p> I) “<st1:City w:st=3D"on"><st1:place w:st=3D"o= n">Readings</st1:place></st1:City>” constitute the preferred means of learning: books and journals, as well as = web tutorials, provide 38% of statistics knowledge. The use of web tutorials (1= 0%) is increasing with time: older engineers prefer hard copy, whereas younger = ones read web-based material. II) Short courses, exam preparations for the profess= ional certifications, and Black Belt training, are also important methods of lear= ning statistics (33%). III) mentoring received from more experienced collea= gues and hands-on (learning by doing), also constitute frequent learning activit= ies (22%). <o:p> </o:p> The descriptive statistics for the variables are: Parametric Confidence Intervals<o:p></o:p> <o:p> </o:p> Variable N Mean StDev 95.0 % CI<o:p></o:p> HardRead 64 26.08 24.31 (20.00, 32.15)<o:p></o:p></= p> WebRead 64 9.58 13.22 ( 6.28, 12.88)<o:p></o:p></= p> OnLnTuto 64 2.016 4.682 (0.846, 3.185)<o:p></o:p></= p> ProfMtgs 64 6.43 9.74 ( 4.00, 8.86)<o:p></o:p> Certific 64 12.47 18.44 ( 7.86, 17.08)<o:p></o:p></= p> ShortCou 64 12.15 16.05 ( 8.14, 16.16)<o:p></o:p></= p> Mentorin 64 14.41 14.58 (10.76, 18.05)<o:p></o:p></= p> OtherWay 64 15.47 24.19 ( 9.43, 21.51)<o:p></o:p></= p> StatCour<s= pan style=3D'mso-spacerun:yes'> 51 1.725 1.686 (1.251, 2.200)<o:p></o:p></= p> YrsPract 55 18.93 10.80 (16.01, 21.85)<o:p></o:p></= p> <o:p> </o:p> If we are not willing to make assumptions about the Normality or symmetry of the data and prefer to work with non-parametric estimators, we have: <o:p> </o:p> Wilcoxon = Signed Rank Confidence Interval<o:p></o:p> <o:p> </o:p>= = Estimat. <= o:p></o:p> N Median Confidence Interval<o:= p></o:p> HardRead 64 0 95.0= (15.0, 30.0)<o:p></o:p> WebRead 64 0 95.0 (5.00,10.00)<o:p></o:p> OnLnTuto 64 0 95.0= (0.00, 2.50)<o:p></o:p> ProfMtgs 64 0 95.0= (2.50, 6.50)<o:p></o:p> Certific 64 0 95.0= ( 5.0, 15.0)<o:p></o:p> ShortCou 64 0 95.0= ( 5.0, 15.0)<o:p></o:p> Mentorin 64 0 95.0= (10.0, 15.0)<o:p></o:p> OtherWay 64 0 95.0= ( 5.0, 17.5)<o:p></o:p> StatCour 51 1 95.0= (1.00, 2.00)<o:p></o:p> YearsPra 55 9 95.0= (15.5, 22.5)<o:p></o:p> <o:p> </o:p> We then converted the survey results from percentage= s to ranks. For example, in the previous case of filling an entry, we assumed th= at the engineer had most learned via reading hard copy, then equally via short courses and mentoring, and finally, least via all other means up to the eig= ht that we had included in our survey. Hence, hard copy would get a rank of 8 = (Highest rank being the most preferred</= span>), short courses and mentoring would tie for ranks 6.5 and all other means wou= ld tie for ranks 2.5 each (as they were 1 through 5). The statistical analysis= of such rank data yielded: <o:p> </o:p> Si= gn CI for median of rank data:<o:p></o:p> <o:p> </o:p> N Median Conf. CI. <o:p></o:p> HrdRd 64 6.00 0.939 (5.5, 7.0) <o:p></o:p> WbRd 64 4.00 0.939 (3.5, 4.5) <o:p></o:p> OnLnTut 64 2.50 0.939 (2.5, 3.0) <o:p></o:p> PrfMtgs 64 3.50 0.939 (3.0, 4.5) <o:p></o:p> Certif 64 4.00 0.939 (3.0, 5.5) <o:p></o:p> ShrtCrs 64 4.75 0.939 (3.5, 5.5) <o:p></o:p> Mentor 64 6.00 0.939 (4.5, 6.0) <o:p></o:p> OthrWys 64 3.50 0.939 (3.0, 4.5) <o:p></o:p> <o:p> </o:p> We can observe how in all three cases, the ranking of the variables is consistently maintained and supports the findings reported above.<o:p></o:p> 4. Survey Conclusions<o:p></o:p> <o:p> </o:p>= The present pilot survey was taken mainly from indus= trial, manufacturing, reliability, quality and such. We compare it with the total = <st1:country-region w:st=3D"on"><st1:place w:st=3D"on">US</st1:place></st1:country-region> nati= onal percentages: <o:p> </o:p> <table class=3DMsoNormalTable border=3D0 cellspacing=3D0 cellpadding=3D0 wi= dth=3D210 style=3D'width:157.6pt;margin-left:.5in;border-collapse:collapse;mso-paddi= ng-alt: 0in 5.4pt 0in 5.4pt'> <tr style=3D'mso-yfti-irow:0;mso-yfti-firstrow:yes;height:12.75pt'> <td width=3D90 valign=3Dbottom style=3D'width:67.15pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> <sp= an lang=3DEN-CA style=3D'font-size:10.0pt;color:black'>Specialty<o:p></o:p><= /span> </td> <td width=3D62 valign=3Dbottom style=3D'width:46.25pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> <sp= an lang=3DEN-CA style=3D'font-size:10.0pt;color:black'>Actual<o:p></o:p></sp= an> </td> <td width=3D59 nowrap valign=3Dbottom style=3D'width:44.2pt;padding:0in 5= .4pt 0in 5.4pt; height:12.75pt'> Survey<o:p></o:p> </td> </tr> <tr style=3D'mso-yfti-irow:1;height:25.5pt'> <td width=3D90 valign=3Dbottom style=3D'width:67.15pt;padding:0in 5.4pt 0= in 5.4pt; height:25.5pt'> Total, All Engineers<o:p></o:p></s= pan> </td> <td width=3D62 valign=3Dbottom style=3D'width:46.25pt;padding:0in 5.4pt 0= in 5.4pt; height:25.5pt'> 100<o:p></o:p> </td> <td width=3D59 valign=3Dbottom style=3D'width:44.2pt;padding:0in 5.4pt 0i= n 5.4pt; height:25.5pt'> 100<o:p></o:p> </td> </tr> <tr style=3D'mso-yfti-irow:2;height:25.5pt'> <td width=3D90 valign=3Dbottom style=3D'width:67.15pt;padding:0in 5.4pt 0= in 5.4pt; height:25.5pt'> Electrical & Electronics<o:p><= /o:p> </td> <td width=3D62 valign=3Dbottom style=3D'width:46.25pt;padding:0in 5.4pt 0= in 5.4pt; height:25.5pt'> 24<o:p></o:p> </td> <td width=3D59 nowrap valign=3Dbottom style=3D'width:44.2pt;padding:0in 5= .4pt 0in 5.4pt; height:25.5pt'> 9.4<o:p></o:p> </td> </tr> <tr style=3D'mso-yfti-irow:3;height:12.75pt'> <td width=3D90 valign=3Dbottom style=3D'width:67.15pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> Mech&Aero<o:p></o:p> </td> <td width=3D62 valign=3Dbottom style=3D'width:46.25pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> 19<o:p></o:p> </td> <td width=3D59 nowrap valign=3Dbottom style=3D'width:44.2pt;padding:0in 5= .4pt 0in 5.4pt; height:12.75pt'> 17.2<o:p></o:p> </td> </tr> <tr style=3D'mso-yfti-irow:4;height:12.75pt'> <td width=3D90 valign=3Dbottom style=3D'width:67.15pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> Civil<o:p></o:p> </td> <td width=3D62 valign=3Dbottom style=3D'width:46.25pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> 13<o:p></o:p> </td> <td width=3D59 nowrap valign=3Dbottom style=3D'width:44.2pt;padding:0in 5= .4pt 0in 5.4pt; height:12.75pt'> 4.7<o:p></o:p> </td> </tr> <tr style=3D'mso-yfti-irow:5;height:12.75pt'> <td width=3D90 valign=3Dbottom style=3D'width:67.15pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> Industrial<o:p></o:p> </td> <td width=3D62 valign=3Dbottom style=3D'width:46.25pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> 9<o:p></o:p> </td> <td width=3D59 nowrap valign=3Dbottom style=3D'width:44.2pt;padding:0in 5= .4pt 0in 5.4pt; height:12.75pt'> 15.6<o:p></o:p> </td> </tr> <tr style=3D'mso-yfti-irow:6;height:12.75pt'> <td width=3D90 valign=3Dbottom style=3D'width:67.15pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> Chemical<o:p></o:p> </td> <td width=3D62 valign=3Dbottom style=3D'width:46.25pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> 3<o:p></o:p> </td> <td width=3D59 nowrap valign=3Dbottom style=3D'width:44.2pt;padding:0in 5= .4pt 0in 5.4pt; height:12.75pt'> 17.2<o:p></o:p> </td> </tr> <tr style=3D'mso-yfti-irow:7;height:12.75pt'> <td width=3D90 valign=3Dbottom style=3D'width:67.15pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> Materials<o:p></o:p> </td> <td width=3D62 valign=3Dbottom style=3D'width:46.25pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> 1<o:p></o:p> </td> <td width=3D59 nowrap valign=3Dbottom style=3D'width:44.2pt;padding:0in 5= .4pt 0in 5.4pt; height:12.75pt'> 6.2<o:p></o:p> </td> </tr> <tr style=3D'mso-yfti-irow:8;mso-yfti-lastrow:yes;height:12.75pt'> <td width=3D90 valign=3Dbottom style=3D'width:67.15pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> All Other<o:p></o:p> </td> <td width=3D62 nowrap valign=3Dbottom style=3D'width:46.25pt;padding:0in = 5.4pt 0in 5.4pt; height:12.75pt'> 31<o:p></o:p> </td> <td width=3D59 nowrap valign=3Dbottom style=3D'width:44.2pt;padding:0in 5= .4pt 0in 5.4pt; height:12.75pt'> 29.7<o:p></o:p> </td> </tr> </table> <o:p>&nbs= p;</o:p> The sample is still large enough that its results pr= ovide general trends for further study. They also support both of our working hypotheses: that engineers take very little statistics in college and that = they have to learn on their own. Finally, the survey shows the actual means that engineers use in their learning process. <o:p> </o:p> Acknowledgements<o:p></o:p> <o:p> = </o:p> We thank our colleagues in the various professional = organizations: of CNY, ENBIS, RSS, ASA and ASQ, and the newsletter editors that helped us advertise this survey, and all the engineers who volunteered to fill it.<sp= an style=3D'color:#003300'><o:p></o:p> <o:p> </o:p> <a name=3D"_Toc24434173"></a><a name=3D"_Toc218= 48811">References</a> <o:p>&nb= sp;</o:p> Romeu, J. L. (1986). Teaching Engineering Statistics = with Simulation. Journal of the <st1:pla= ce w:st=3D"on"><st1:PlaceType w:st=3D"on">Institute</st1:PlaceType> of <st1:Pl= aceName w:st=3D"on">Statistician</st1:PlaceName></st1:place> (RSS Series D). V= ol. 35, No. 4. Also, visit: <a href=3D"http://myprofile.cos.com/romeu">http://m= yprofile.cos.com/romeu</a>. Romeu, J. L. and M. Land (2004). Group Learning, Cont= extual Projects, Simulation Models and Student Presentations in Enticing Engineeri= ng Statistics Students. CD Proceedings of the Edu= cation Section. ASA Meeting.= <st1:place w:st=3D"on"><st1:City w:st=3D"on">Toronto</st1:City>, <st1:State w:st=3D"on= ">CA</st1:State></st1:place>. Romeu, J. L. (2006a). Teaching Engineering Statistics= to Practicing Engineers. Proceedings of ICOTS-7. <st1:City w:st=3D"on">= <st1:place w:st=3D"on">Salvador</st1:place></st1:City> (<st1:place w:st=3D"on">Bahia<= /st1:place>), Brasil. Romeu, J. L. (2006b). Analyzing a Pilot Survey on Ways Engineers Learn Statistics. CD Proceedings of the Education Section.= ASA Meeting, Seattle. Romeu, J. L. (2006c). <st1:place w:st=3D"on"><st1:Pla= ceName w:st=3D"on">Engineering</st1:PlaceName> <st1:PlaceName w:st=3D"on">Post</s= t1:PlaceName> <st1:PlaceType w:st=3D"on">College</st1:PlaceType></st1:place> Education in Statistics. ASQ Education Division Newsletter. 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MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C9E07D.140B79C0" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C9E07D.140B79C0 Content-Location: file:///C:/EB324D12/KnoxIcotsPaper.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Approaches to extending or customizing (free) statistical software</= title> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"PostalCode"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"country-region"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"State"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"City"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"place"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"PlaceName"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"PlaceType"/>  <style>  </style>  </head> <body lang=3DEN-US link=3Dblue vlink=3Dpurple style=3D'tab-interval:.5in'> <div class=3DSection1> A Survey = on Ways Engineers Learn Sta= tistics After Leaving College <![if !supportLineBreakNewLine]> <![endif]><o:p></o:p> <o:p> </o:p> Jorge Luis Romeu Research Professor, Dept. M= AE, <st1:place w:st=3D"on"><st1:City w:st=3D"on">Syracuse University</st1:City>, <st1:Stat= e w:st=3D"on">NY</st1:State> <st1:PostalCode w:st=3D"on">13224</st1:PostalCode></st1:place>. <a href=3D"mailto:jlromeu@syr.edu">jlromeu@syr.edu</a> <o:p> </o:p> </div> <span lang=3DEN-CA style=3D'font-s= ize:10.0pt; mso-bidi-font-size:12.0pt;font-family:"Times New Roman";mso-fareast-font-fa= mily: "MS Mincho";mso-bidi-font-family:"Courier New";color:#003300;mso-ansi-langu= age: EN-CA;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'> <div class=3DSection2> Abstract <o:p> <= /o:p> This is the first of a three-part work on how engine= ers learn statistics after leaving college. Here we present a survey of practic= ing engineers, undertaken to support the tenants of the main paper, presented at ICOTS-7 in <st1:country-region w:st=3D"on"><st1:place w:st=3D"on">Brazil</s= t1:place></st1:country-region>. We discuss the sample taken, its composition and the questions and answers elicited in the survey. Finally, we present the main survey results <o:p> </o:p> Keywords: Statistics education, surveys, data analysis <o:p></o:p> <o:p> </o:p> 1. Introduction <o:p> </o:p> Two years ago this author was invited to write a pap= er on statistical education for the ICOTS-7 (International Conference on Teaching Statistics), <st1:City w:st=3D"on"><st1:place w:st=3D"on">Salvador</st1:pla= ce></st1:City>, <st1:country-region w:st=3D"on"><st1:place w:st=3D"on">Brazil</st1:place></= st1:country-region>. We chose the topic of how engineers learn statistics after leaving college,= an area where we have worked for over twenty five years (Romeu, 1986). <o:p> </o:p> However, we soon discovered in our literature search= that statisticians had studied how all cohorts studied statistics, from pre-scho= ol children to college graduate students. But there was no research on how pra= cticing engineers approached this problem. <o:p> </o:p> In our ICOTS-7 peer-reviewed paper (Romeu, 2006a), w= e proposed two main hypotheses that we needed to support. Given the lack of previous research on the topic, we decided to investigate this empirically, via a su= rvey of practicing engineers. Such survey would assess whether engineers (1) acquired enough statistics in their college studies and (2) whether they st= udied it, after college, on their own, as best they could (and what means they actually used to learn it). <o:p> </o:p> This survey was taken among American engineers and i= ts results supported our research hypotheses. In a third paper, presented at t= he 2006 ASA/JSM in <st1:City w:st=3D"on"><st1:place w:st=3D"on">Seattle</st1:place>= </st1:City>, we presented the survey results analyses (Romeu, 2006b) <o:p> </o:p> We knew, from our many years teaching statistics in = engineering departments as well as in short courses for industry, that college training fell short, and that many engineers needed substantially more statistics to= be able to do their work. We wanted to assess how they were able to bridge the= gap between their scant initial statistical training, and their professional ne= eds. <o:p> = ;</o:p> This impor= tant problem has two serious components: one is educational and the other is soc= ial. Educational because there is no more room for additional statistics in the engineering curriculum. Hence, the solution has to be to move things up and down stream. Teach more statistics in grade and high school; then teach thinking in college so that the engineer may be able to learn as needed, la= ter, on their own. Finally, to develop better tutorials and support materials for engineer use, during their lifelong learning process. The social component stems from an institutional paralysis (Romeu, 2006c).<o:p></o:p> <o:p> = ;</o:p> In the res= t of this paper, we will discuss how our survey was taken, describe its componen= ts, and how they were filled, and overview its main results <o:p></o:p><= /p> <o:p> </o:p>= 2. The Survey Input<o:p></o:p> <o:p> </o:p>= In order to support our two working hypothesis, that the statistical education of engin= eers is deficient and inadequate, requiring engineers to learn statistics on the= ir own at a later date (and further investigate the specific efforts they made= to solve this need, we implemented a pilot survey. In our questionnaire (see <= span style=3D'mso-bidi-font-weight:bold;mso-bidi-font-style:italic'><a href=3D"http://web.syr.edu/~jlromeu/SurveyICOTS.html">http://web.syr.= edu/~jlromeu/SurveyICOTS.html</a>) we asked, to characterize survey takers, several questions about the practicing engineer’s personal background. We requested their educati= on level (associate bachelor, masters or doctorate), area (academe, industry or government), specialization (mechanical, electrical, industrial, etc.), tot= al number of statistics courses they had taken in college, years practicing engineering, country where they practiced (an overwhelming majority were fr= om the USA) and gender. <o:p> </o:p> Then, we a= sked how they had acquired their post-college statistical knowledge on their own: (1) reading books, journals, manuals or other hard copy materials, (2) reading = Web and Internet materials and tutorials, (3) following on-line courses or lear= ning software, (4) attending symposiums, conferences chapter meetings, talks, et= c., (5) pursuing preparation for professional certifications such as American Society for Quality, (6) taking internal company or commercial short traini= ng courses, (7) receiving mentor= ing from other, more experienced work colleagues and (8) any other sources, suc= h as hands-on (or practical) working experiences (here many survey takers specif= ied having received Six Sigma training courses).<o:p></o:p> <o:p> = ;</o:p> The survey= was submitted to the members of several quality, reliability, manufacturing, et= c., engineering chapters in Central New York (CNY) and to many mid-career consultants, via our teaching of reliability courses to the annual engineer= ing TACNY conference Through the ISOSTAT group, we were able to tap engineers from a pharmaceutical company in Florida. Finally, the survey was also taken by a handful of European engineers, thanks to newsletter promotions graciouly provided by the ASQ, the RSS and ENBIS international professional societies= .<o:p></o:p> <o:p> = ;</o:p> Our sample characterization is the following:<o:p></o:p> <o:p> = ;</o:p> <![if !supportLists]><= span style=3D'mso-list:Ignore'>• <![endif]>So far 64 responses:<o:p></o:p> <![if !supportLists]><= span style=3D'mso-list:Ignore'>• <![endif]> 61 f= rom the <st1:country-region w:st=3D"on"><st1:place w:st=3D"on">US</st1:place></= st1:country-region><o:p></o:p> <![if !supportLists]><= span style=3D'mso-list:Ignore'>• <![endif]> 3 fr= om abroad. <o:p></o:p> <![if !supportLists]><= span style=3D'mso-list:Ignore'>• <![endif]> 8% f= emales<o:p></o:p> <![if !supportLists]><= span style=3D'mso-list:Ignore'>• <![endif]> 56% graduate degrees<o:p></o:p> <![if !supportLists]><= span style=3D'mso-list:Ignore'>• <![endif]> 60% = 16+ years experience <o:p></o:p> <![if !supportLists]>• = <![endif]> 90% = from industry.<o:p></o:p></= span> <o:p> = ;</o:p> According = to engineering technical specialization:<o:p></o:p> <![if !vml]><img width= =3D332 height=3D231 src=3D"KnoxIcotsPaper_files/image002.gif" v:shapes=3D"_x0000_s= 1911"><![endif]><o:p> </o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> And accord= ing to engineering educational level:<o:p></o:p> <![if !vml]><img width=3D328 height=3D218 src=3D"KnoxIcotsPaper_files/image004.gif" v:shapes= =3D"_x0000_s1912"><![endif]><o:p> </o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> <o:p> = ;</o:p> Our sample= was not randomly, nor scientifically drawn from a sampling frame (such frame does n= ot exist), nor we claim it was. But, for a pilot effort and given that a sample size of sixty plus individuals responded, at the time we presented the pape= r, we believe it will provide interesting, valid, initial information for furt= her study.<o:p></o:p> <o:p> </o:p>= 3. The Survey Results<o:p></o:p> <o:p> </o:p>= To each su= rvey taker we asked to provide, in rounded percentages, their assessment of the amount of post college statistical knowledge they had acquired, by each of = the eight categories. For example, say an engineer thought they had acquired half of their statistics knowledge by reading books and other hard copy materials, = and the other half, by equal parts, via short courses and mentoring. Then, this engineer would fill the entry “hard copy” with 50, and the entr= ies “short courses” and “mentoring” with 25 each. In ev= ery case, the percentages had to add to 100.<o:p></o:p> <o:p> = ;</o:p> The survey= data collected so far (we are still receiving information) yielded the following results regarding our working hypotheses:<o:p></o:p></sp= an> <o:p> </o:p> <![if !supportLists]>A) </sp= an><![endif]>College Training<o:p></o:p><= /p> <o:p>&nb= sp;</o:p> I) Among all surveyed, 16% have not taken any statis= tics courses in college (33% among BS), 38% took only one (38%) and 26% have tak= en 2 courses (24%). II) 1/3 of those with a BS degree only, have never t= aken a single statistics course in college; another 1/3 of them have taken only one course. Hence, 2/3 engineers = of all surveyed had either none, or very little statistical training (i.e. taken a single course). III) Engineers that pursue graduate school have a la= rger opportunity of taking statistics. Only 7%, in our sample, have never taken a statistics course. <o:p> </o:p> <![if !supportLists]>B) </spa= n><![endif]>Methods Preferred<o:p></o:p>= <o:p> </o:p> I) “<st1:City w:st=3D"on"><st1:place w:st=3D"o= n">Readings</st1:place></st1:City>” constitute the preferred means of learning: books and journals, as well as = web tutorials, provide 38% of statistics knowledge. The use of web tutorials (1= 0%) is increasing with time: older engineers prefer hard copy, whereas younger = ones read web-based material. II) Short courses, exam preparations for the profess= ional certifications, and Black Belt training, are also important methods of lear= ning statistics (33%). III) mentoring received from more experienced collea= gues and hands-on (learning by doing), also constitute frequent learning activit= ies (22%). <o:p> </o:p> The descriptive statistics for the variables are: Parametric Confidence Intervals<o:p></o:p> <o:p> </o:p> Variable N Mean StDev 95.0 % CI<o:p></o:p> HardRead 64 26.08 24.31 (20.00, 32.15)<o:p></o:p></= p> WebRead 64 9.58 13.22 ( 6.28, 12.88)<o:p></o:p></= p> OnLnTuto 64 2.016 4.682 (0.846, 3.185)<o:p></o:p></= p> ProfMtgs 64 6.43 9.74 ( 4.00, 8.86)<o:p></o:p> Certific 64 12.47 18.44 ( 7.86, 17.08)<o:p></o:p></= p> ShortCou 64 12.15 16.05 ( 8.14, 16.16)<o:p></o:p></= p> Mentorin 64 14.41 14.58 (10.76, 18.05)<o:p></o:p></= p> OtherWay 64 15.47 24.19 ( 9.43, 21.51)<o:p></o:p></= p> StatCour<s= pan style=3D'mso-spacerun:yes'> 51 1.725 1.686 (1.251, 2.200)<o:p></o:p></= p> YrsPract 55 18.93 10.80 (16.01, 21.85)<o:p></o:p></= p> <o:p> </o:p> If we are not willing to make assumptions about the Normality or symmetry of the data and prefer to work with non-parametric estimators, we have: <o:p> </o:p> Wilcoxon = Signed Rank Confidence Interval<o:p></o:p> <o:p> </o:p>= = Estimat. <= o:p></o:p> N Median Confidence Interval<o:= p></o:p> HardRead 64 0 95.0= (15.0, 30.0)<o:p></o:p> WebRead 64 0 95.0 (5.00,10.00)<o:p></o:p> OnLnTuto 64 0 95.0= (0.00, 2.50)<o:p></o:p> ProfMtgs 64 0 95.0= (2.50, 6.50)<o:p></o:p> Certific 64 0 95.0= ( 5.0, 15.0)<o:p></o:p> ShortCou 64 0 95.0= ( 5.0, 15.0)<o:p></o:p> Mentorin 64 0 95.0= (10.0, 15.0)<o:p></o:p> OtherWay 64 0 95.0= ( 5.0, 17.5)<o:p></o:p> StatCour 51 1 95.0= (1.00, 2.00)<o:p></o:p> YearsPra 55 9 95.0= (15.5, 22.5)<o:p></o:p> <o:p> </o:p> We then converted the survey results from percentage= s to ranks. For example, in the previous case of filling an entry, we assumed th= at the engineer had most learned via reading hard copy, then equally via short courses and mentoring, and finally, least via all other means up to the eig= ht that we had included in our survey. Hence, hard copy would get a rank of 8 = (Highest rank being the most preferred</= span>), short courses and mentoring would tie for ranks 6.5 and all other means wou= ld tie for ranks 2.5 each (as they were 1 through 5). The statistical analysis= of such rank data yielded: <o:p> </o:p> Si= gn CI for median of rank data:<o:p></o:p> <o:p> </o:p> N Median Conf. CI. <o:p></o:p> HrdRd 64 6.00 0.939 (5.5, 7.0) <o:p></o:p> WbRd 64 4.00 0.939 (3.5, 4.5) <o:p></o:p> OnLnTut 64 2.50 0.939 (2.5, 3.0) <o:p></o:p> PrfMtgs 64 3.50 0.939 (3.0, 4.5) <o:p></o:p> Certif 64 4.00 0.939 (3.0, 5.5) <o:p></o:p> ShrtCrs 64 4.75 0.939 (3.5, 5.5) <o:p></o:p> Mentor 64 6.00 0.939 (4.5, 6.0) <o:p></o:p> OthrWys 64 3.50 0.939 (3.0, 4.5) <o:p></o:p> <o:p> </o:p> We can observe how in all three cases, the ranking of the variables is consistently maintained and supports the findings reported above.<o:p></o:p> 4. Survey Conclusions<o:p></o:p> <o:p> </o:p>= The present pilot survey was taken mainly from indus= trial, manufacturing, reliability, quality and such. We compare it with the total = <st1:country-region w:st=3D"on"><st1:place w:st=3D"on">US</st1:place></st1:country-region> nati= onal percentages: <o:p> </o:p> <table class=3DMsoNormalTable border=3D0 cellspacing=3D0 cellpadding=3D0 wi= dth=3D210 style=3D'width:157.6pt;margin-left:.5in;border-collapse:collapse;mso-paddi= ng-alt: 0in 5.4pt 0in 5.4pt'> <tr style=3D'mso-yfti-irow:0;mso-yfti-firstrow:yes;height:12.75pt'> <td width=3D90 valign=3Dbottom style=3D'width:67.15pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> <sp= an lang=3DEN-CA style=3D'font-size:10.0pt;color:black'>Specialty<o:p></o:p><= /span> </td> <td width=3D62 valign=3Dbottom style=3D'width:46.25pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> <sp= an lang=3DEN-CA style=3D'font-size:10.0pt;color:black'>Actual<o:p></o:p></sp= an> </td> <td width=3D59 nowrap valign=3Dbottom style=3D'width:44.2pt;padding:0in 5= .4pt 0in 5.4pt; height:12.75pt'> Survey<o:p></o:p> </td> </tr> <tr style=3D'mso-yfti-irow:1;height:25.5pt'> <td width=3D90 valign=3Dbottom style=3D'width:67.15pt;padding:0in 5.4pt 0= in 5.4pt; height:25.5pt'> Total, All Engineers<o:p></o:p></s= pan> </td> <td width=3D62 valign=3Dbottom style=3D'width:46.25pt;padding:0in 5.4pt 0= in 5.4pt; height:25.5pt'> 100<o:p></o:p> </td> <td width=3D59 valign=3Dbottom style=3D'width:44.2pt;padding:0in 5.4pt 0i= n 5.4pt; height:25.5pt'> 100<o:p></o:p> </td> </tr> <tr style=3D'mso-yfti-irow:2;height:25.5pt'> <td width=3D90 valign=3Dbottom style=3D'width:67.15pt;padding:0in 5.4pt 0= in 5.4pt; height:25.5pt'> Electrical & Electronics<o:p><= /o:p> </td> <td width=3D62 valign=3Dbottom style=3D'width:46.25pt;padding:0in 5.4pt 0= in 5.4pt; height:25.5pt'> 24<o:p></o:p> </td> <td width=3D59 nowrap valign=3Dbottom style=3D'width:44.2pt;padding:0in 5= .4pt 0in 5.4pt; height:25.5pt'> 9.4<o:p></o:p> </td> </tr> <tr style=3D'mso-yfti-irow:3;height:12.75pt'> <td width=3D90 valign=3Dbottom style=3D'width:67.15pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> Mech&Aero<o:p></o:p> </td> <td width=3D62 valign=3Dbottom style=3D'width:46.25pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> 19<o:p></o:p> </td> <td width=3D59 nowrap valign=3Dbottom style=3D'width:44.2pt;padding:0in 5= .4pt 0in 5.4pt; height:12.75pt'> 17.2<o:p></o:p> </td> </tr> <tr style=3D'mso-yfti-irow:4;height:12.75pt'> <td width=3D90 valign=3Dbottom style=3D'width:67.15pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> Civil<o:p></o:p> </td> <td width=3D62 valign=3Dbottom style=3D'width:46.25pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> 13<o:p></o:p> </td> <td width=3D59 nowrap valign=3Dbottom style=3D'width:44.2pt;padding:0in 5= .4pt 0in 5.4pt; height:12.75pt'> 4.7<o:p></o:p> </td> </tr> <tr style=3D'mso-yfti-irow:5;height:12.75pt'> <td width=3D90 valign=3Dbottom style=3D'width:67.15pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> Industrial<o:p></o:p> </td> <td width=3D62 valign=3Dbottom style=3D'width:46.25pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> 9<o:p></o:p> </td> <td width=3D59 nowrap valign=3Dbottom style=3D'width:44.2pt;padding:0in 5= .4pt 0in 5.4pt; height:12.75pt'> 15.6<o:p></o:p> </td> </tr> <tr style=3D'mso-yfti-irow:6;height:12.75pt'> <td width=3D90 valign=3Dbottom style=3D'width:67.15pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> Chemical<o:p></o:p> </td> <td width=3D62 valign=3Dbottom style=3D'width:46.25pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> 3<o:p></o:p> </td> <td width=3D59 nowrap valign=3Dbottom style=3D'width:44.2pt;padding:0in 5= .4pt 0in 5.4pt; height:12.75pt'> 17.2<o:p></o:p> </td> </tr> <tr style=3D'mso-yfti-irow:7;height:12.75pt'> <td width=3D90 valign=3Dbottom style=3D'width:67.15pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> Materials<o:p></o:p> </td> <td width=3D62 valign=3Dbottom style=3D'width:46.25pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> 1<o:p></o:p> </td> <td width=3D59 nowrap valign=3Dbottom style=3D'width:44.2pt;padding:0in 5= .4pt 0in 5.4pt; height:12.75pt'> 6.2<o:p></o:p> </td> </tr> <tr style=3D'mso-yfti-irow:8;mso-yfti-lastrow:yes;height:12.75pt'> <td width=3D90 valign=3Dbottom style=3D'width:67.15pt;padding:0in 5.4pt 0= in 5.4pt; height:12.75pt'> All Other<o:p></o:p> </td> <td width=3D62 nowrap valign=3Dbottom style=3D'width:46.25pt;padding:0in = 5.4pt 0in 5.4pt; height:12.75pt'> 31<o:p></o:p> </td> <td width=3D59 nowrap valign=3Dbottom style=3D'width:44.2pt;padding:0in 5= .4pt 0in 5.4pt; height:12.75pt'> 29.7<o:p></o:p> </td> </tr> </table> <o:p>&nbs= p;</o:p> The sample is still large enough that its results pr= ovide general trends for further study. They also support both of our working hypotheses: that engineers take very little statistics in college and that = they have to learn on their own. Finally, the survey shows the actual means that engineers use in their learning process. <o:p> </o:p> Acknowledgements<o:p></o:p> <o:p> = </o:p> We thank our colleagues in the various professional = organizations: of CNY, ENBIS, RSS, ASA and ASQ, and the newsletter editors that helped us advertise this survey, and all the engineers who volunteered to fill it.<sp= an style=3D'color:#003300'><o:p></o:p> <o:p> </o:p> <a name=3D"_Toc24434173"></a><a name=3D"_Toc218= 48811">References</a> <o:p>&nb= sp;</o:p> Romeu, J. L. (1986). Teaching Engineering Statistics = with Simulation. Journal of the <st1:pla= ce w:st=3D"on"><st1:PlaceType w:st=3D"on">Institute</st1:PlaceType> of <st1:Pl= aceName w:st=3D"on">Statistician</st1:PlaceName></st1:place> (RSS Series D). V= ol. 35, No. 4. Also, visit: <a href=3D"http://myprofile.cos.com/romeu">http://m= yprofile.cos.com/romeu</a>. Romeu, J. L. and M. Land (2004). Group Learning, Cont= extual Projects, Simulation Models and Student Presentations in Enticing Engineeri= ng Statistics Students. CD Proceedings of the Edu= cation Section. ASA Meeting.= <st1:place w:st=3D"on"><st1:City w:st=3D"on">Toronto</st1:City>, <st1:State w:st=3D"on= ">CA</st1:State></st1:place>. Romeu, J. L. (2006a). Teaching Engineering Statistics= to Practicing Engineers. Proceedings of ICOTS-7. <st1:City w:st=3D"on">= <st1:place w:st=3D"on">Salvador</st1:place></st1:City> (<st1:place w:st=3D"on">Bahia<= /st1:place>), Brasil. Romeu, J. L. (2006b). Analyzing a Pilot Survey on Ways Engineers Learn Statistics. CD Proceedings of the Education Section.= ASA Meeting, Seattle. Romeu, J. L. (2006c). <st1:place w:st=3D"on"><st1:Pla= ceName w:st=3D"on">Engineering</st1:PlaceName> <st1:PlaceName w:st=3D"on">Post</s= t1:PlaceName> <st1:PlaceType w:st=3D"on">College</st1:PlaceType></st1:place> Education in Statistics. ASQ Education Division Newsletter. 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