Business research methods textbook part 4
>appendix 15a Previous research on the topic A pilot test or pretest of the data instrument among a sample drawn from the population A rule of thumb (one-sixth of the range based on six standard deviations within 99.73 percent confidence) r If the range is from to 30 meals, the rule-of-thumb method produces a standard deviation of meals The researchers want more precision than the rule-of-thumb method provides, so they take a pilot sample of 25 and find the standard deviation to be 4.1 meals Population Size F A final factor affecting the size of a random sample is the size of the population When the size of the sample exceeds percent of the population, the finite limits of the population constrain the sample size needed A correction factor is available in that event The sample size is computed for the first construct, meal frequency, as follows: Determining Sample Size the arithmetic mean, with proportions, it is p (the proportion of the population that has a given attribute)'-in this case, interest in joining the dining club And instead of the standard deviation, dispersion is measured in terms of p X q (in which q is the proportion of the population not having the attribute, and q = (1 - p) The measure of dispersion of the sample statistic also changes from the standard error of the mean to the standard error of the proportion We calculate a sample size I?ased on these data by making the same two subjective decisionsdeciding on an acceptable interval estimate and the degree of confidence Assume that from a pilot test, 30 percent of the students and employees say they will join the dining club We decide to estimate the true proportion in the population within 10 percentage points of this figure ( p = 0.30 0.10) Assume further that we want to be 95 percent confident that the population parameter is within ? 0.10 of the sample proportion The calculation of the sample size proceeds as before: + -t- 0.10 = desired interval range within which the popu- lation proportion is expected (subjective decision) 1.96 up= 95 percent confidence level for estimating the interval within which to expect the population proportion (subjective decision) up= 0.05 = standard error of the proportion (0.1011.96) pq = measure of sample dispersion (used here as an estimate of the population dispersion) n = sample size where ,= 0.255 (0.5111.96) If the researchers are willing to accept a larger interval range (+ meal), and thus a larger amount of risk, then they can reduce the sample size to n = 65 Calculating the Sample Size for Questions Involving Proportions The second key question concerning the dining club study was "What percentage of the population says it would join the dining club, based on the projected rates and services?' In business, we often deal with proportion data An example is a CNN poll that projects the percentage of people who expect to vote for or against a proposition or a candidate This is usually reported with a margin of error of percent In the Metro U study, a pretest answers this question using the same general procedure as before But instead of + The sample size of 81 persons is based on an infinite population assumption If the sample size is less than percent of the-population, there is little to be gained by using a finite population adjustment The students interpreted the data found with a sample of 81 chosen randomly from the population as: "We can be 95 percent confident that 30 percent of the respondents would say they would join the dining club with a margin of error of ? 10 percent." Previously, the researchers used pilot testing to generate the variance estimate for the calculation Suppose this is not an option Proportions data have a feiture concerning >part Ill The Sources and Collect~on Data of the variance that is not found with interval or ratio data The pq ratio can never exceed 0.25 For example, if p = 0.5, then q = 0.5, and their product is 0.25 If either p or q is greater than 0.5, then their product is smaller than 0.25 (0.4 X 0.6 = 0.24, and so on) When we have no information regarding the probable p value, we can assume that p = 0.5 and solve for the sample size where pg = measure of dispersion n = sample size a = standard error of the proportion , If we use this maximum variance estimate in the dining club example, we find the sample size needs to be 96 persons in order to have an adequate sample for the question about joining the club When there are several investigativ; questions of strong interest, researchers calculate the sample size for each such variable-as we did in the Metro U study for "meal frequency" and "joining." The researcher then chooses the calculation that generates the largest sample This ensures that all data will be collected with the necessary level of precision -ssa3old y3leas -a1 aqi JO aseyd s!yi u sdals aqi suaUa1 1-9 I i!q!qx~ 'papauo3 pue pa1ea~3.1 dam s.10.11a y aq hriua eiep 1eyi d a ~ s ~ y l u u n p 11 cap papallo3 ay1 JO Buypue~slapunue 01 Buypea1 dals s! huym!lald layloue s Llewurns 1e3gspels ahpdp3sap e Bupedald s!sd1eue l o j a1epdoldde y alom ale ~ e sqw~o pagyswp pue pa3npa~ mloj M ~ Imolj uoys1a~uo3lyay1 pue elep aql ~ 01 JO L3em33e ay1 salnsua 1eq1 dl!~!i3e ayl SF pue hrlua elep PUT! ' ~ ~'3u!l!pa sspnpu! UO!$ 03 - e ~ e d a ~ d slsd@ue eiep oi sumn~ elea uo!lua11e s,.1aq31easa1 e 'MOU 01 uy3aq e1ep aql a3uo rchapter 16 Data P t q ~ a r a t ~ o n Descr~ption and F Exhibit 16-1 Data Preparation in the Research Process Po4co& Free,r m n r nu- 6:~ > Editing The customary first step in analysis is to edit the raw data Editing detects errors and omissions, corrects them when possible, and certifies that maximum data quality standards are achieved The editor's purpose is to guarantee that data are: Accurate Consistent with the intent of the question and other information in the survey Uniformly entered Complete Arranged to simplify coding and tabulation In the following question asked of adults18 or older, one respondent checked two categories, indicating that he was a retired officer and currently serving on active duty Please indicate your current military status: Active duty National Guard Reserve Retired Separated Never served i n the military The editor's responsibility is to decide which of the responses is both consistent with the intent of the question or other information in the survey and most accurate for this individual participant Field Editing In large projects, field editing review is a responsibility of the field supervisor It, too, should be done soon after the data have been gathered During the stress of data collection in a personal interview and paper-and-pencil recording in an observation, the researcher often uses ad hoc abbreviations and special symbols Soon after the interview, experiment, or observation, the investigator should review the reporting forms It is difficult to complete what was abbreviated or written in shorthand or noted illegibly if the entry is not caught that day When entry gaps are present from interviews, a callback should be made rather than guessing what the respondent "probably would have said." Self-interviewing has no place in quality research A second important control function of the field supervisor is to validate the field results This normally means he or she will reinterview some percentage of the respondents, at least on some questions, verifying that they have participated and that the interviewer performed adequately Many research firms will recontact about 10 percent of the respondents in this process of data validation Central Editing Western Wats, a data collection specialist, reminds us that speed without accuracy won't help a researcher choose the right direction "After all, being quick on the draw doesn't any good if you miss the mark." www.westernwats.com At this point, the data should get a thorough editing For a small study, the use of a single editor produces maximum consistency In large studies, editing tasks should be allocated so that each editor deals with one entire section Although the latter approach will not identify inconsistencies between answers in different sections, the problem can be handled by identifvina cluestions in different sections that I might point to possible inconsistency and having one editor check the data generated by these questions Sometimes it is obvious that an entry is incorrect-for example, when data clearly specify time in days (e.g., 13) when it was requested in weeks (you expect a number of or less)-or is entered in the wrong place When replies are inappropriate or missing, the editor can sometimes detect the proper answer by reviewing the other information in the data set This practice, however, should be limited to the few cases where it is obvious what the correct answer is It may be better to contact the respondent for correct information, if time and budget allow Another alternative is for the editor to strike out the answer if it is inappropriate Here an editing entry of "no answer" or "unknown" is called for Another problem that editing can detect concerns faking an interview that never took place This "armchair interviewing" is difficult to spot, but the editor is in the best posi- >chapter 16 Data Preparat~orl and Descript~on tion to so One approach is to check responses to open-ended questions These are most difficult to fake Distinctive response patterns in other questions will often emerge if data falsification is occurring To uncover this, the editor must analyze as a set the instruments used by each interviewer Here are some useful rules to guide editors in their work: Be familiar with instructions given to interviewers and coders Do not destroy, erase, or make illegible the original entry by the interviewer; original entries should remain legible Make all editing entries on an instrument in some distinctive color and in a standardized form Initial all answers changed or supplied Place initials and date of editing on each instrument completed > Coding Codhg involves assigning numbers or other symbols to answers so that the responses can be grouped into a limited number of categories In coding, categories are the partitions of a data set of a given variable (for example, if the variable is gender, the paairions are d e and female) Categorization is the process of using rules to partition a body of data Both closed and free-response questions must be coded The categorization of data sacrifices some data detail but is necessary for eff~cient analysis Most statistical and banneritable software programs work more efficiently in the numeric mode Instead of entering the word male orfemale in response to a question that mks for the identification of one%gender, we would use numeric codes (for example, O for male m d for female) Nutneric coding simplifies the researcher's task in amvesting a nominal variable, like gender, to a "dummy variable," a topic we discuss in Chapter 20 Statistical software also can use alphanumeric codes, as when we use M and F, other let1 ters, in combination with numbers and symbols for gender Cumulabve Vew Good Qualm + Mlsslng Good Qualm Average Qualm Poor Qualm Total System 80 83 120 24 964 36 1000 20 125 25 loan 1000 CUmUlatlw Vew Good Qralm Good Qualm Average Qualm Total M~ssmng System Total 32 15 36 163 100 83 1000 The researcher here requested a frequency printout of all variables when 83 cases had been entered SPSS presents them sequentially in one document The left frame indicates all the variables included in this particular output file Both variables Qua12 and Qua13 indicate missing cases This would be a cautionary flag to a good researcher During editing the researcher would want to verify that these are true instances where participants did not rate the quality of both objects, rather than data entry errors www.spss.com >part IV Arialys~s and Plesentarlon of Ddta I I CBS: Some Labs Codebook Construction A codebook, or coding scheme, contains each variable in the study and specifies the application of coding rules to the variable It is used by the researcher or research staff to promote more accurate and more efficient data entry It is also the definitive source for locating the positions of variables in the data file during analysis In many statistical programs, the coding scheme is integral to the data file Most codebooks computerized or not contain the question number, variable name, location of the variable's code on the input medium (e.g., spreadsheet or SPSS data file), descriptors for the response options, and whether the variable is alphabetic or numeric An example of a paper-based codebook is shown in Exhibit 16-2 Pilot testing of an instrument provides sufficient information about the variables to prepare a codebook A codebook used with pilot data may reveal coding problems that will need to be corrected before the data for the final study are collected and processed Coding Closed Questions The responses to closed questions include scaled items for which answers can be anticipated Closed questions are favored by researchers over open-ended questions for their efficiency and specificity They are easier to code, record, and analyze When codes are established in the instrument design phase of tho research process, it is possible to precode the questionnaire during the design stage With computerized survey design, and computerassisted, computer-administered,or online collection of data, precoding is necessary as the software tallies data as they are collected Preceding is particularly helpful for manual data entry (for ex&nple, from mail or self-administered surveys) because it makes the intermediate step of completing a data entry coding sheet unnecessary With a precoded instrument, the codes for variable categories are accessible directly from the questionnaire A participant, interviewer, field supervisor, or researcher (depending on the data collection method) is able to assign the appropriate code on the instrument by checking, circling, or printing it in the proper coding location >chapter 20 Multivariate Arlalysi,;: All Overview > Selecting a Multivariate Technique Multivariate techniques may be classified as dependency and interdependency techniques Selecting an appropriate technique starts with an understanding of this distinction If criterion and predictor variables exist in the research question, then we will have an assumption of dependence Multiple regression, multivariate analysis of variance (MANOYA), and discriminant analysis are techniques where criterion or dependent variables and predictor or independent variables are present Alternatively, if the variables are interrelated without designating some as dependent and others independent, then interdependence of the variables is assumed Factor analysis, cluster analysis, and multidimensional scaling are examples of interdependency techniques Exhibit 20-1 provides a diagram to guide in the selection of techniques Let's take an example to show how you might make a decision Every other year since 1978, the Roper organization has tracked public opinion toward business by providing a list of items that are said to be the responsibility of business The respondents are asked whether business fulfills these responsibilities "fully, fairly well, not too well, or not at all well." The following issues make up the list: • Developing new products and services • Producing good-quality products and services • Making products that are safe to use • Hiring minorities • Providing jobs for people • Being good citizens of the communities in which they operate • Paying good salaries and benefits to employees • Charging reasonable prices for goods and services • Keeping profits at reasonable levels • Advertising honestly • Paying their fair share • Cleaning up their own air and water pollution You have access to data on these items and wish to know if they could be reduced to a smaller set of variables that would account for most of the variation among respondents In response to the first question in Exhibit 20-1, you correctly determine there are no dependent variables in the data set You then check to see if the variables are metric or nonmetric measures In the exhibit, metric refers to ratio and interval measurements, and nonmetric refers to data that are nominal and ordinal Based on the measure!Dent scale, which appears to have equal intervals, and preliminary findings that show a linear relationship between several variables, you decide the data are metric This decision leads you to three options: multidimensional scaling, cluster analysis, or factor analysis Multidimensional scaling develops a perceptual map of the locations of some objects relative to others This map specifies how the objects differ Cluster analysis identifies homogeneous subgroups or clusters Factor analysis looks for patterns among the variables to discover if an underlying combination of the original variables (a factor) can summarize the original set Based on your research objective, you select factor analysis Suppose you are interested in predicting f~mily food expenditures from family income, family size, and whether the family's location is rural or urban Returning to Exhibit 20-1, you conclude there is a single dependent variable, family food expenditures You decide this variable is metric since dollars are measured on a ratio scale The independent variables, income and family size, also meet the criteria for metric data However, you are not sure about the location variable since it appears to be a dichotomous nominal variable According to the exhibit, your choices are automatic interaction detection (AID), multiple classification 573 574 >part IV 1\l1alysis alKJ Pres811tation 01 Data > Exhibit 20-1 Selecting from the Most Common Multivariate Techniques No Cluster analysis Factor analysis Multidimensional scaling 'The independent variable is metric only in the sense that a transformed proportion is used 2"fhe independent variable is metric only when we consider that the number of cases in the cross-tabulation cell is used to calculate the logs 3Factors may be considered nonmetric independent variables in that they organize the data into groups We not classify MANOVA and other multivariate analysis of variance models 4SEM refers to structural equation modeling for latent variables It is a family of models appropriate for confirmatory factor analysis, path analysis, time series analysis, recursive and nonrecursive models, and covariance structure models Because it may handle dependence and interdependence, metric and nonmetric, it is arbitrarily placed in this diagram Source: Partially adapted from T C Kinnear and J R Taylor, "Multivariate Methods in Marketing: A Further Attempt at Classification," Journal of Marketing, October 1971, p 57; and J F Hair Jr., Rolph E Anderson, Ronald L Tatham, and Bernie J Grablowsky, Multivariate Data Analysis (Tulsa, OK: Petroleum Publishing Co., 1979), pp 10-14 analysis (MCA), and multiple regression You recall from Chapter 17 that AID was designed to locate the most important predictors in a set of numerous independent variables and create a treelike answer MCA handles weak predictors (including nominal variables), correlated predictors, and nonlinear relationships.,Multiple regression is the extension of bivariate regression You believe that your data exceed the assumptions for the first two techniques and that by treating the nominal variable's values as Oor I, you could use it as an independent variable in a multiple regression model You prefer this to losing information from the other two variables-a certainty if you reduce them to nonmetric data In the next two sections, we will extend this discussion as we illustrate dependency and interdependency techniques > Dependency Tec'hniques Multiple Regression Multiple regression is used as a descriptive tool in three types of situations First, it is often used to develop a self-weighting estimating equation by which to predict values for a criterion variable (DV) from the values for several predictor variables (IVs) Thus, we "if f.ll t 11 , 'f , 'f , , '1 TTT1 '1'Ti ! l' r r >chapter 20 'I!rlll 575 Multivariate Allalysis: An Overview v 10 predict company sales on the basis of new housing starts, new marriage rates, dl'posable income, and a time factor Another prediction study might be one in \\T \'slimate a student's academic performance in college from the variables of rank I' hil'h ,,'liool class, SAT verbal scores, SAT quantitative scores, and a rating scale ret1ect'f' 1IIIi'II'ssions from an interview '.,', Ollt! a descriptive application of multiple regression calls for controlling for con.llll,hll!' variables to better evaluate the contribution of other variables For example, one , Ildll wish 10 control the brand of a product and the store in whioh it is bought to study the III \ t ' 011 price as an indicator of product quality.3 A third use of multiple regression is to " ,1'101 n.plain causal theories In this approach, often referred to as path analysis, reI ~itll1 is IIsed to describe an entire structure of linkages that have been advanced from a IltollIII1l:ory:1In addition to being a descriptive tool, multiple regression is also used as an HI!'II'lh'I' 1(0) to test hypotheses and to estimate population values II "'lI"d Ii, " thod t Iltlpk regression is an extension of the bivariate linear regression presented in Chapter lilt' lerms defined in that chapter will not be repeated here Although dummy vari"'.\~ ( l1,lI11 i nal variables coded 0, I) may be used, all other variables must be interval or raI" lhl' generalized equation is 'I 111'11 ' II" a constant, the value of Y when all X values are zero 1\, (he slope of the regression surface (The 13 represents the regression coefficient associated with each X;,) all error term, normally distributed about a mean of (For purposes of computation, the f is assumed to be 0.) IIi!' regression coefficients are stated either in raw score units (the actual X values) or as IIl1lClllrdizcd coefficients (X values restated in terms of their standard scores) In either • I~I', 1he value of the regression coefficient states the amount that Y varies with each unit 11I1IIFL' Ill' Ihe associated X variable when the effects of all other X variables are being held 1111',1:1111 When the regression coefficients are standardized, they are called beta weights t II I, ,lilt I Iheir values indicate the relative importance of the associated X values, particularly '1"'i1 Ihe predictors are unrelated For example, in an equation where 131 = ,60 and 132 = 'II, i III" concludes that XI has three times the influence on Yas does X xample III II SI1,tpshot later in this chapter, we describe an e-business that uses multivariate ap1'1\ tlh 'hcs (0 understand its target market in the global "hybrid-mail" business SuperLetter's 1, 1" ,service enables users to create a document on any PC and send it in a secure, enI I\ pled Illode over the Internet to a distant international terminal near the addressee, where II 1\ III he printed, processed, and delivered via a local postal service Spread like a "fishnet" 11"'1 the world's major commercial markets, the network connects corresponding parties, Ill1k IlIg Ihe world's "wired" with its "nonwiroo." The British Armed Forces and some U.S, IlIdli;lry organizations have used it to speed correspondence between families and service 1lI,'llIl'ers in Afghanistan and Iraq W" lise multiple regression in this example to evaluate the key drivers of customer usage I' 'I Iryhrid mail Among the available independent or predictor variables, we expect some to 111'1 explain or predict the dependent or criterion variable than others (thus they are key to 11111 1I11lIerstanding) The independent variables are customer perceptions of (1) cost/speed \ ,oIl1:rlioll, (2) security (limits on changing, editing, or forwarding a document and document : ~ , 576 part IV IIrlCllysis ailU PrOSOlltation oi D}£' Jlfj ' ;-/ ;~; I~~lctors:~constam) ,'COst/~ \~~mY,'relj¢>ility ~/:'r ,"c;!;", :,;; ~.~ ;":- l~cientS:'; i:( ;; " ';0 / C"" •.: ' ; ~J 0' l' Standardized Coefficients Std Error B 151 857 035 9.501E-02 130 537 042 551 428 9.326E-02 042 127 437 Cost/speed Security (Constant) t Sig 3.834 879 ~~~t·~··i:·i,~: ' Collinearity Statistics 000 464 12.842 10.182 000 :i~/~~ ~ ::~ t~ t< r< .' :'~ :~>.; 000 24.753 733 '::''; ;c: VIF 579 (Constant) I ;, '; ::c Beta (Constant) Cost/speed r.·,;',·.;:,: ,;, : ;:.' ':~ ~~t:: ::;-!-,-,.- :.', : ') " Unstandardized Coefficients Model ,',: ' : , ~".; ~,'; "i.; 1.000 I ;~ -,-,- / :- 3.~~:: .734 000 464 2.289 ')('.~ 2.289 "c'.;;:: or i' G :r, 2.7 Co"",,,"d 448.043.460 10.428 000 Security 315 045 321 6.948 000 3.025 Reliability 254 050 236 5.059 000 - 3.067 ,;: ~~e:dJstomenisage";·chapter 20 583 Multivariate Analysis: An Overview > Exhibit 20-6 MANOVA Homogeneity-of-Variance Tests in the CalAudio Study VARIABLE RESULTS TEST FAILURE Cochran's Bartlett-~ox (14,2) = F (1,2352) 58954, P = 506 (approx.) 44347, P = 506 SPECIFICATIONS = 862 Cochran's C (14,2) Bartlett-Box F (1,2352) 52366, P 03029, P Cochran's C (14,2) = Bartlett-Box F (1,2352) 55526, P = 684 (approx.) 16608, P = 684 = 862 (approx.) SPEED nultivariate Test for Homogeneity of Dispersion Matrices Box's M = Fwith (6,5680) DF = Chi-Square with DF = 6.07877 89446, P = 498 (approx.) 5.37320, P = 497 (approx.) > Exhibit 20-7 Bartlett's Test of Sphericity in the CalAudio Study Statistics for WITHIN CELLS correlations lug (Determinant) = Bartlett's test pf sphericity Signi ficance = = -3.92663 102.74687 with D.F • •000 7354.80161 with (3,28) D.F Exhibit 20-8 shows three tests, including the Hotelling T • All the tests provided are compared to the F distribution for interpretation Since the observed significance level is less than ex = 05 for the T2 test, we reject the null hypothesis that said methods and provide equal results with respect to failure, specifications, and speed Similar results are obtained from the Pillai trace and Wilks's statistic Finally, to detect where the differences lie, we can examine the results of univariate F tests in Exhibit 20-9 Since there are only two methods, the F is equivalent to t2 for a twosample t-test The significance levels for these tests not reflect that several comparisons are being made, and we should use them principally for diagnostic plirposes This is similar to problems that require the use of multiple comparison tests in univariate analysis of variance Note, however, that there are statistically significant differences in all three dependent variables resulting from the new manufacturing method Techniques for further analysis of MANOVA results were listed at the beginning of this section Structural Equation Modeling Since the late 1980s, researchers have relied increasingly on structural equation modeling to test hypotheses about the dimensionality of, and relationships among, latent and observed variables Structural equation modeling (SEM) implies a structure for the covariances between observed variables, and accordingly it is sometimes called covariance structure modeling More commonly, researchers refer to structural equation models as LISREL (linear structural relations) models-the name of the first and most widely cited SEM computer program < See Chapter 18's discussion of multiple comparison procedures 584 >part IV Analysis and Presentation of Data > Exhibit 20-8 Multivariate Tests of Significance in the CalAudio Study Multivariate Tests of Significance (S = 1, ~ = 1/2, N = 12) , Test Name Value Exact F Hypoth DF Error DF Si:g of F Hotelling Pillai Wilks 51.33492 98089 01911 444.90268 444.90268 444.90268 3.00 3.00 3.00 26.00 26.00 26.00 000 000 000 F Sig of Note: F statistics are exact > Exhibit 20-9 Univariate Tests of Significance in the CalAudio Study Univariate F Tests with (1,28) D.F Error 55 652.bb667 126.&0000 11593 Hypoth ~5 36chapter 20 Multlvariato Allaly~;is: 1\/1 OVl;lvicw After selecting the factors and their levels, a computer program determines the number to estimate the utilities SPSS procedures build a file structure for all possible combinations, generate the subset required for testing, produce the card descriptions, and analyze results The command structure within these procedures provides for holdout sampling, simulations, and other requirements frequently used in commercial applications or product descriptions necessary Example Watersports enthusiasts know the dangers of ultraviolet (UV) light It fades paint and clothing; yellows surfboards, skis, and sailboards; and destroys sails More important, UV damages the eye's retina and cornea In the 1990s, Americans were spending $1.3 billion on 189 million pairs of sunglasses, most of which failed to provide adequate UV protection Manufacturers of sunglasses for specialty markets have improved their products to such a degree that all of the companies in our example advertised 100 percent UV protection Many other features influence trends in this market For this example, we chose four factors from information contained in a review of sun protection products 10 Brand Bolle Hobbies Oakley Ski Optiks Style· A A A A B B B B C C C C $100 $100 $100 $100 $72 $72 $72 $72 $60 $60 $60 $60 $40 $40 $40 $40 Price *A = multiple color choices for frames, lenses, and temples B = multiple color choices for frames, lenses, and straps (no hard temples) C = limited colors for frames, lenses, and temples This is a (brand) X (style) X (flotation) X (price) design, or a 96-option fullconcept study The algorithm selected 16 cards to estimate the utilities for the full concept Combinations of interest that were not selected can be estimated later from the utilities In addition, four holdout cards were administered to subjects but evaluated separately The cards shown in Exhibit 20-11 were administered to a small sample (n = 10) Subjects were asked to order their cards from most to least desirable The data produced the results presented in Exhibits 20-12 and 20-13 Exhibit 20-12 contains the results of the eighth participant's preferences This individual was an avid windsurfer, and flotation wa~ the most important attribute for her, followed by style and price and then brand From her preferences, we can compute her maximum utility score: (Style B) 3.46 + (Oakley brand) 1.31 + (flotation) 20.75 + (price @ $40) 5.90 + (constant) - 8.21 = 23.21 587 ... (OMR) 45 7 codebook 44 4 database 45 6 optical scanning 45 7 coding 44 3 "don''t know" (DK) response 45 2 precoding 44 4 content analysis 44 8 editing 44 1 record 45 6 '' > data entry 45 5 missing data 45 3... billboard 10 100 - TV-A TV-B TV-C TV-D RAD-A RAD-B RAD-C M GA MAG-B OutD AMEDIA Histograms The histogram is a conventional solution for the display of interval-ratio data Histograms are used... houu:holds 3 34. t.55 145 112 186.529 Number of households DlGIW C.\I4W > 143 lSolmCAMW._· 18 {DIWl CAMERA E'' I 2 1 -4 5 4Ir41 6 8-1 00 ,0 1-1 15 FAIRFAX COUNTY VA Number of households 3&1.056 158 1 14 ORANGE