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Operationalization and Data Analysis Methods

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Design of Incentive Systems

Part of the book series: Contributions to Management Science ((MANAGEMENT SC.))

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Abstract

Having introduced the expectations of this research in the previous chapter, this chapter deals with how the expectations are tested. First, it is presented how the individual attributes which are used in the hypotheses are operationalized and measured. This is followed by introducing the analysis methods for analyzing the hypotheses.

Measure what you can measure and make measureable what you cannot measure.

Galileo Galilei (1564 Pisa – 1642 Florence)

Cited in Gaarder (1996), p. 169

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Notes

  1. 1.

    Cf. Wright (2003), p. 133.

  2. 2.

    The term inventory is regularly used in psychology in order to describe a set of questions, which together form a hypothetical construct.

  3. 3.

    It shall be noted that the measures used not inevitably lead to the targeted individual attributes. In literature measurements are often said to lead to hypothetical constructs, which are supposed to approximate the individual attribute, which shall be measured. See e.g. Heckhausen (1980), pp. ff. for a discussion concerning hypothetical constructs.

  4. 4.

    Cf. Mauldin (2003), p. 29; GRE is a standardized test created and administered by the Educational Testing Service. Refer to http://www.ets.org/ for further information.

  5. 5.

    Cf. Dohmen and Falk (2011).

  6. 6.

    Cf. Baiman and Lewis (1989), p. 9.

  7. 7.

    Cf. Waller and Chow (1985), p. 462.

  8. 8.

    Cf. McClelland et al. (1953); Schmalt (1976), p. 18.

  9. 9.

    Cf. Schmalt and Sokolowski (2000), p. 115.

  10. 10.

    Cf. Biernat (1989), p. 69; Brunstein and Heckhausen (2006), p. 154.

  11. 11.

    Cf. Schmalt (1976).

  12. 12.

    Cf. Stein (1990), p. 235.

  13. 13.

    Refer to Brunstein and Heckhausen (2006), pp. 145ff. for a review of measuring the motive to achieve.

  14. 14.

    Cf. Tent (1963); Mikula et al. (1976); Dahme et al. (1993).

  15. 15.

    Cf. Mehrabian (1968); Mehrabian (1969); Brunstein and Heckhausen (2006), pp. 154ff.

  16. 16.

    Cf. Mikula et al. (1976), pp. 90ff.

  17. 17.

    Cf. Matiakse and Stein (1992), pp. 247 f.

  18. 18.

    Cf. Mikula et al. (1976), p. 91; Matiakse and Stein (1992), p. 246; Cronbach’s alpha, calculated for the 134 participants who report a German mother tongue, results in 0.36. Cronbach’s alpha is equivalent to the Kuder-Richardson 20 procedure, because of the binary response format.

  19. 19.

    If Cronbach’s alpha is only calculated with these six items, the value is 0.37. Refer to Sect. 3.2.4.2 for details concerning the items-to-total-score correlation test.

  20. 20.

    Cf. Matiakse and Stein (1992), pp. 246ff.

  21. 21.

    Cf. Cacioppo and Petty (1982); Cacioppo et al. (1984); Bless et al. (1994).

  22. 22.

    Please refer to the appendix for the single items.

  23. 23.

    Cf. Bless et al. (1994), pp. 149f.

  24. 24.

    Cf. Gulgoz (2001), p. 103; Cacioppo et al. (1984) and Bless et al. (1994) do not state mean values.

  25. 25.

    Cf. Cacioppo et al. (1984), p. 306; Bless et al. (1994), p. 149; Gulgoz (2001), p. 102.

  26. 26.

    Cf. Rheinberg et al. (2001), pp. 57ff.; The single factors forming the hypothetical construct also appear independently from each other in literature (Cf. e.g. Scott Jr. (1967); Farh et al. (1991)).

  27. 27.

    Cf. Rheinberg et al. (2001), p. 58.

  28. 28.

    Cf. Rheinberg et al. (2001), pp. supplemental material.

  29. 29.

    A different approach to measure interest in a task or task attractiveness is used by Scott Jr. (1967) or Farh et al. (1991). They do not use complete questions but use opposite ratings such as attractive versus unattractive as an instrument. Since Rheinberg et al. (2001), p. 58 provide an integration of the factor interest into the motivation concept, their approach is pursued for the factor interest as well as for the other factors in order to measure a current motivation construct.

  30. 30.

    Cf. Rheinberg et al. (2001), pp. 58f.

  31. 31.

    Cf. Rheinberg et al. (2001), pp. supplemental material.

  32. 32.

    Cf. Rheinberg et al. (2001), pp. supplemental material.

  33. 33.

    In the underlying research probability of success is also captured by (L.1/ SKILL) ∙ L.2, which is denoted L.PROBABILITYOFSUCCESS.

  34. 34.

    Cf. Rheinberg et al. (2001), p. 58.

  35. 35.

    Cf. Rheinberg et al. (2001), p. 59.

  36. 36.

    Since the factor probability of success merely consists of one question, Cronbach’s alpha cannot be calculated.

  37. 37.

    Cf. Krampen (1979), p. 579; Refer to Krampen (1982), p. 115 for an extensive survey of German and English locus of control inventories.

  38. 38.

    Cf. Levenson (1974).

  39. 39.

    Cf. Rotter (1966), p. 1; Levenson (1974); Logsdon et al. (1978), p. 538; Krampen (1982), p. 108.

  40. 40.

    Cf. Logsdon et al. (1978), p. 538.

  41. 41.

    Cf. Krampen (1979), p. 579.

  42. 42.

    Cf. Krampen (1979), p. 581.

  43. 43.

    Cf. Krampen (1979), p. 581.

  44. 44.

    Cf. Krampen (1979), p. 579.

  45. 45.

    Cf. MacCrimmon and Wehrung (1985b), p. 10.

  46. 46.

    Cf. Botella et al. (2008), pp. 530 f.; The different categories are not mutually exclusive. Refer to Skeel et al. (2007) for a study investigating predictions of risky behavior with a multiple-factor personality inventory (NEO-inventory).

  47. 47.

    Cf. Botella et al. (2008), pp. 530 f.; Participants’ honest contribution is not only key to the success of questionnaire-based risk measures, but also to the success of the whole study. For further comments refer to Sect. 3.2.4.3.

  48. 48.

    MacCrimmon and Wehrung (1985b), p. 22.

  49. 49.

    Cf. MacCrimmon and Wehrung (1985b), p. 24.

  50. 50.

    Refer to Harrison et al. (2005), pp. 1394ff. for a review on risk measurements.

  51. 51.

    Cf. Hyatt and Taylor (2008), pp. supplemental material.

  52. 52.

    Cf. Botella et al. (2008), p. 531.

  53. 53.

    Cf. Shields and Waller (1988), pp. 585–586; Cadsby et al. (2007).

  54. 54.

    Cf. Shields and Waller (1988), p. 590.

  55. 55.

    Cf. Shields and Waller (1988), p. 585.

  56. 56.

    Cf. Holt and Laury (2002).

  57. 57.

    Cf. Holt and Laury (2002); Dohmen and Falk (2006), p. 10; Cadsby et al. (2007), p. 390.

  58. 58.

    Cf. Holt and Laury (2002), p. 1645.

  59. 59.

    Cf. Holt and Laury (2002), p. 1646.

  60. 60.

    Cf. Weber et al. (2002).

  61. 61.

    Cf. Weber et al. (2002); Johnson et al. (2004); Harrison et al. (2005), p. 1394; Blais and Weber (2006).

  62. 62.

    Cf. Sitkin and Weingart (1995), p. 1592; Williams et al. (2008), p. 66.

  63. 63.

    Cf. Betsch (2004), p. 183.

  64. 64.

    Cf. Schunk and Betsch (2006), p. 399.

  65. 65.

    Cf. Betsch (2004), p. 183; Schunk and Betsch (2006), p. 392.

  66. 66.

    Cf. Jaccard (2005a); Backhaus et al. (2006), p. 8; Field (2007), pp. 309ff.

  67. 67.

    Cf. Backhaus et al. (2006), p. 10; See also Allison (2004), pp. 20ff. for a discussion of the advantages of multiple regression in the context of experiments.

  68. 68.

    Cf. Field (2009), pp. 395ff.

  69. 69.

    Cf. Hardy (2007), p. 1; Cohen (2009), pp. 1f.

  70. 70.

    There is a discussion in literature whether data from rating scales can be treated as continuous data. The general understanding is that rating scales with enough steps approximate the metric quality of true continuous scales. In this text Srinivasan and Basu (1989), p. 226’s opinion is followed that five levels provide good metric quality. Thus, the five level scales are supposed to result in continuous measures in the study.

  71. 71.

    Cf. Wendorf (2004), p. 47; Hardy (2007); Field (2007), pp. 309ff.; Refer to Wendorf (2004), p. 47 for a comparison of contrast procedures between the ANOVA and regression paradigm.

  72. 72.

    Cf. Jaccard et al. (1997), p. 10; Cohen (2009), pp. 4f.; Refer to Jaccard et al. (1997), pp. 10ff. for a discussion of different effect size indices with a focus to interaction effects.

  73. 73.

    Cf. Jaccard et al. (1997), p. 10; Cohen (2009), p. 5.

  74. 74.

    Cf. Anderson (1986), pp. 188f.; Jaccard et al. (1997), pp. 15, 65ff.

  75. 75.

    Cohen (2009), p. 151, comparing regression with correlational analysis, state that regression coefficients often lead to the most informative results and answers. Refer to Baron and Kenny (1986), p. 1175 for details concerning deficiencies, or to Cohen (2009), pp. 151–192 for a detailed methodological comparison of regression and correlational analysis.

  76. 76.

    Refer to Fahrmeir et al. (2007), pp. 55ff. or Jaccard et al. (1997), pp. 50ff. for an overview of different functional relationships.

  77. 77.

    Cf. Henderson (1998); The SPSS package used offers both analysis techniques. It is important to note that regression, if based on the general linear model, and ANOVA, if also based on the general linear model, are conceptually the same. In the SPSS package used, the general linear model is used for both paradigms (Cf. Field (2007), p. 311; Cohen (2009), p. 5).

  78. 78.

    Cf. Rack and Christophersen (2007), p. 19.

  79. 79.

    Cf. Evans and Rooney (2008), pp. 194f.

  80. 80.

    Cf. Irwin and McClelland (2003), p. 366; Ravichandran and Fitzmaurice (2008), p. 610.

  81. 81.

    Cf. Irwin and McClelland (2003), p. 366.

  82. 82.

    Cf. Irwin and McClelland (2003), pp. 366ff.; Ravichandran and Fitzmaurice (2008), p. 610.

  83. 83.

    Cf. Irwin and McClelland (2003), p. 369.

  84. 84.

    Cf. Baron and Kenny (1986), p. 1176; Jaccard et al. (1997), p. 49.

  85. 85.

    Cf. Irwin and McClelland (2003), p. 371.

  86. 86.

    Cf. Jaccard et al. (1997), p. 49.

  87. 87.

    Ordinary least squares is the method used for estimating the linear regression parameters.

  88. 88.

    Cf. Jaccard et al. (1997), pp. 10f.

  89. 89.

    Cf. Jaccard et al. (1997), p. 33; For comparison reason, additionally, standardized coefficients are given in the relevant tables.

  90. 90.

    Cf. Hardy (2007), pp. 19ff.

  91. 91.

    Cf. Jaccard et al. (1997), pp. 25f.

  92. 92.

    Cf. Baron and Kenny (1986), p. 1176.

  93. 93.

    Cf. Baron and Kenny (1986), p. 1174.

  94. 94.

    Cf. Chatterjee and Hadi (2006), p. 86; Fahrmeir et al. (2007), pp. 19 ff., 25; Fahrmeir et al. (2007), pp. 25 ff. show exemplarily that by other transformations of predictor variables, also non-linear relationships can be implemented into the GLM.

  95. 95.

    Cf. Baron and Kenny (1986), p. 1174.

  96. 96.

    Cf. Janssen and Laatz (2007), pp. 426f.

  97. 97.

    Cf. Backhaus et al. (2006), pp. 74,116; Janssen and Laatz (2007), pp. 421f.; Field (2007), pp. 151ff.

  98. 98.

    SPSS generally states two-tailed significance values. However, as directed hypotheses are formulated, significance values based on one-tailed tests are also appropriate as suggested for example in Allison (2004), p. 42, Backhaus et al. (2006), pp. 76f. or Janssen and Laatz (2007), p. 426. Still, as it is standard practice in linear regression to report two-tailed tests, significance levels based on two-tailed tests are reported in the underlying experiment. Thus, the significance levels can be regarded as being rather conservative.

  99. 99.

    Cf. Jaccard et al. (1997), p. 16; Hardy (2007), pp. 48f.

  100. 100.

    For instance, Cadsby et al. (2007), p. 397 or Mauldin (2003), p. 35 only analyze product term coefficients for investigating interaction effects.

  101. 101.

    Cf. Jaccard et al. (1997), p. 24; Menard (2000), p. 54.

  102. 102.

    Cf. Anderson (1986), p. 191; Jaccard et al. (1997), pp. 18, 21.

  103. 103.

    Cf. Baron and Kenny (1986), p. 1177.

  104. 104.

    Cf. Baron and Kenny (1986), p. 1177.

  105. 105.

    Cf. Sitkin and Weingart (1995), pp. 1582f.

  106. 106.

    Cf. Field (2007), pp. 111f. Albeit this guideline actually refers to effect sizes of correlation coefficients, it can be taken as guideline in various effect size measures as e.g. in Field (2007), pp. 172, 357.

  107. 107.

    Cf. Jaccard et al. (1997), pp. 24f.

  108. 108.

    Cf. Jaccard et al. (1997), pp. 17f.

  109. 109.

    In linear regression analysis SPSS merely shows differences between unadjusted \( {{\mathrm{ R}}^2} \) s as well.

  110. 110.

    Cf. Field (2007), pp. 171f.

  111. 111.

    As the number of cases and the number of predictor variables are also reported, any adjustments to \( {{\mathrm{ R}}^2} \) can be still performed without needing further information. It shall be also noted that adjustments to \( {{\mathrm{ R}}^2} \) based on Wherry’s equation within the underlying analyses are quantitatively small and do not change the analysis qualitatively.

  112. 112.

    Cf. Schroeder et al. (2005), pp. 73ff.; Berry (2006), pp. 1ff.; Chatterjee and Hadi (2006), pp. 85ff., 233ff.; Field (2007), pp. 169ff.

  113. 113.

    Backhaus et al. (2006), p. 94 note that regression analysis is relatively robust against small violations of its assumptions.

  114. 114.

    Cf. Schroeder et al. (2005), pp. 24ff.; Field (2007), p. 186.

  115. 115.

    Cf. Jaccard et al. (1997), pp. 30ff.

  116. 116.

    Cf. Field (2007), p. 175.

  117. 117.

    Cf. Chatterjee and Hadi (2006), p. 238; Field (2007), p. 196.

  118. 118.

    Cf. Durbin and Watson (1951), pp. 159ff.; Chatterjee and Hadi (2006), p. 201; Backhaus et al. (2006), p. 89.

  119. 119.

    Cf. Schroeder et al. (2005), p. 67; Backhaus et al. (2006), p. 102.

  120. 120.

    Cf. Goldfeld and Quandt (1965); Backhaus et al. (2006), p. 89; Hackl (2008), pp. 178f.; Refer to Eckey et al. (2005) for an applied introduction to the application of the Goldfeld-Quandt, White and Breusch-Pagan test within SPSS.

  121. 121.

    Cf. Chatterjee and Hadi (2006), pp. 90ff.; Field (2007), pp. 202ff.

  122. 122.

    Cf. Backhaus et al. (2006), pp. 92f.

  123. 123.

    Cf. Cook (1977); Chatterjee and Hadi (2006), pp. 88, 103ff.; Field (2007), pp. 165ff., 199ff.

  124. 124.

    Cf. Chatterjee and Hadi (2006), pp. 88, 103f.

  125. 125.

    Cf. Field (2007), p. 165; In the findings section Cook’s distance values higher than 1.25 are further investigated.

  126. 126.

    Cf. Menard (2000), pp. 1–16.

  127. 127.

    Cf. Norušis (2010), p. 69.

  128. 128.

    Cf. Bühl (2006), p. 111.

  129. 129.

    Cf. Bühl (2006), pp. 353f., 372ff.; Multinomial regression (regression with dependent variables having more than two categories) has also been called polytomous or polychotomous (Cf. Menard (2000), p. 80).

  130. 130.

    When the magnitude of incentive variable is used as predictor, the linear ordinary least squares regression analysis can be used independently from the variable’s classification being ordinal or nominal.

  131. 131.

    Cf. Janssen and Laatz (2007), p. 459.

  132. 132.

    For a discussion about how to treat ordinal dependent variables refer to Menard (2000), pp. 86ff.

  133. 133.

    Refer to Backhaus et al. (2006), pp. 425ff. or Menard (2000) for a detailed introduction to logistic regression and Jaccard (2005b) for an introduction to logistic regression with a focus on interactions.

  134. 134.

    Cf. Backhaus et al. (2006), p. 428.

  135. 135.

    Cf. Backhaus et al. (2006), pp. 471f.

  136. 136.

    Cf. Liao (2006), p. 7.

  137. 137.

    Cf. Menard (2000), pp. 38ff.; Backhaus et al. (2006), pp. 460f.

  138. 138.

    Cf. Field (2007), p. 224; see Hosmer and Lemeshow (2000), p. 35 for details concerning the derivation of logistic regression coefficients’ standard errors.

  139. 139.

    Differences of Nagelkerke’s pseudo R2 values are evaluated qualitatively, as no test is introduced in the underlying literature.

  140. 140.

    Cf. Field (2007), p. 223.

  141. 141.

    Cf. Backhaus et al. (2006), pp. 449, 456.

  142. 142.

    Cf. Menard (2000), p. 32; In this context, classification relates to a model’s prediction for an element belonging to one or the other category. For instance, by means of classification tables, the number of correctly predicted categories can be compared to the falsely predicted categories. For further methods to gauge the classification accuracy of logistic regression models refer to Menard (2000), pp. 28ff. In general goodness-of-fit and accuracy of classification measures produce consistent results (Menard (2000), p. 32).

  143. 143.

    Cf. Backhaus et al. (2006), p. 440; Liao (2006), p. 18.

  144. 144.

    Refer to Dohmen and Falk (2011) for an example for the use of marginal effect sizes in probit models.

  145. 145.

    Refer to Liao (2006), pp. 6ff., 13ff. for an in-depth discussion of parameter estimates’ interpretation possibilities.

  146. 146.

    Cf. Backhaus et al. (2006), p. 480.

  147. 147.

    Refer to Sect. 3.2.3 for a more general discussion on sample size.

  148. 148.

    Refer to Hardy (2007), pp. 9ff. or Fahrmeir et al. (2007), pp. 80ff. for further information about dummy coding.

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  1. Institute of Business Administration, Universität Stuttgart, Stuttgart, Germany

    Dennis D. Fehrenbacher

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Fehrenbacher, D.D. (2013). Operationalization and Data Analysis Methods. In: Design of Incentive Systems. Contributions to Management Science. Physica, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33599-0_5

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