Chinese Students Attitudes Toward Statistics Ping Wang, Ph.D. wangpx at jmu.edu Computer Information Systems/Business Analytics College of Business, James Madison University Harrisonburg, VA DSI 2015, Seattle, WA, Nov

Outline 1.Introduction 2.Review of Previous Research a)Theory b)Survey Instruments 3.Data Collection and Preliminary Analysis 4.Conclusions 5.Discussions

Previous Research 1.Expectancy – Value Theory of Achievement Motivation, Wigfield and Eccles 2000 a)Constructs: Ability beliefs, Expectancies for success, and Subjective values b)Children and adolescents: changes in these 3 aspects, and relationship of the 3 aspects to performance and choices of activities 2.Extended research on attitudes toward mathematics, Aiken and Dreger 1961, Aiken Surveys measuring attitudes toward statistics (more details on Ramirez et al. 2012) a)Statistics Attitude Survey (SAS) by Roberts and Bilderback, items on 5-point Likert scale, moderately related to course grades b)Statistical Anxiety Rating Scale by Cruise, Cash and Bolton, 1985, only citation c)Attitudes Toward Statistics (ATS) by Wise, 1985, 29 items with subscales of attitudes toward statistics Course (9 items) and attitudes toward Field of statistics (20 items) d)Statistics Attitude Scale by McCall, Belli and Madjidi, 1990, unpublished report e)Multifactorial Scale of Attitudes Toward Statistics (MSAS) by Auzmendi, 1991, 25 items for 5 dimensions of motivation, enjoyment, anxiety, confidence, and usefulness f)Statistics Anxiety Inventory by Zeidner, 1991, parallels between mathematics anxiety and statistics test and content anxiety g)Survey of Attitudes Toward Statistics (SATS) by Schau, 1995, 28 – items on 4 components and 36 – items on 6 components for pretest and posttest

Theory and Development for Survey of Attitudes Toward Statistics (SATS) by Schau, Statistics anxiety relates to: negative experience, less appreciative of values and usefulness, less of confidence or competent, with negative feeling 2.Unfavorable attitudes often relate to poor achievements 3.Attitudes Components: a)Affect: (6 items): positive and negative feelings about statistics. Such as, I enjoy taking statistics courses. b)Cognitive Competence (6 items): intellectual knowledge and skills when applied to statistics. Such as I understand statistics equations. c)Value (9 items): usefulness, relevance, and worth of statistics in personal and professional life. Such as Statistics is irrelevant to my life. d)Difficulty (7 items): the difficulty of statistics as a domain. Such as, Statistics is a complicated subject. e)Interest (4 items): individual level of interest. Such as, I am interested in using statistics. f)Effort (4 items): amount of work to learn statistics. Such as, I plan to work hard in my statistics course. Atkinson 1957, Eccles and Wigfield 1995, Weiner 1979, Bandura 1977, Maehr 1984, Kamirez et al. 2012

Instrument Translations, Pilot Tests, Missing Data and Outliers 1.IRB approvals for China, USA and Taiwan 2.Followed Zhao et al 2005: a)Two Chinese authors and one professional translator for English to Chinese versions b)Pilot among 21 Chinese students in Introduction Statistics class in Dalian University of Technology c)Refinement of instrument 3.Data collection: ChinaUSA The number of Responses Missing at least one item393 Univariate outliers by 3 z scores4827 Univariate outliers by q1 or q3 ±2.2 IQR2518 Multivariate outliers by Mahalandis - D924

Gender, Ethnicity, Degree, and Expected Grade 41. Your sex Count Country Total USAChina 41. Your sex: Male 1 190, 65%59, 30%249 Female 2 103, 35%134, 70%237 Total Degree you are currently seeking Count Country Total USAChina 43. Degree you are currently seeking: 1 Associate Bachelors Masters Certification Post - bachelor's Licensure Other 066 Total What grade do you expect to receive in this course? Count Country Total USAChina 44. What grade do you expect to receive in this course? A A- 80, 51%39, 73%119 B B B- 11, 49%6, 25%17 C+ 224 C 011 Total Your ethnicity Count Country Total USAChina 42. Your ethnicity: 1. White American 227, 78% Native American African American Hispanic American 22, 7.5% Asian American 24, 8% Other American Foreign student from other countries 707 Total

Major and Age 47. Your age (in years) Average Age: Country Total USAChina 47. Your age (in years): , 19% , 63%78, 41% , 13%50, 26% , 17% Total What is your major? If you have a double major, pick the one that bests represents your interest Count Country Total USAChina 45. What is your major? If you have a double major, pick the one that bests represents your interest 1. Accounting 48, 16% Computer Information Systems/Business Analytics 30, 10% Economics 1175, 40%86 4. Finance 54, 18%8, 4%62 6. International Business 28, 10% Management 44, 15%48,25%92 8. Marketing Others Not decided 358 Total

Number of Credit Hours Earned and GPA 48. Number of credit hours earned toward the degree you are currently seeking (don’t count this semester) Average # of Credit Hours: Country Total USAChina 48. Number of credit hours earned toward the degree you are currently seeking (don’t count this s  Total Current grade point average (please estimate if you don’t know; give only one single numeric estimate) Average GPA: Country Total USAChina 49. Current grade point average (please estimate if you don’t know; give only one single numeric estimate) A- to A 12, 5%012 B B B- 61, 72%57, 46%118 C C C- 4, 22%19, 49%23 D+ 145 Missing Total

# of Math/Stat Years in HS, College Courses, and How likely to take stat course? 53. If the choice had been yours, how likely is it that you would have chosen to take any course Count Country Total USA 53. If the choice had been yours, how likely is it that you would have chosen to take any course... Absolutely not % Chance % Chance % Chance % Sure 5 26 Total Number of college mathematics and/or statistics courses completed (don’t count this semester) Average # of Courses: /Md 2.64 Country Total USAChina 51. Number of college mathematics and/or statistics courses completed (don’t count this semester): ≥ missing 011 Total Number of years of high school mathematics or statistics courses taken Average Number of Years: Country Total USAChina 50. Number of years of high school mathematics or statistics courses taken: ≥ Total

Table 1. Cronbach’s coefficient alpha values for pretest scores by attitude component (US and China data) are compatible with published results American Chinese Schau et al 1995 (n = 293)(n = 194) Affect – 0.85 Cognitive Competence – 0.83 Value – 0.85 Difficulty – 0.77 Interest Effort Cronbach’s α= 0.7 as acceptable for compatible internal reliability Dunn, Baguley and Drunsden 399 – 412 Predhazur and Schwelkin 1991 Schau et al 2012

Male StudentsChina (n = 59)USA (n = 190) Mean Difference (α = 0.05) Mean Std. DeviationMean Std. DeviationMeanStd Errordf Sig (2 - tailed) Levene's Test for Equality of Variances, Sig. Affect Cognitive Competence Values Difficulty Interest Effort FemalesChina (n = 134)USA (n = 103)Mean Difference (α = 0.05) Mean Std. DeviationMean Std. DeviationMeanStd Errordf Sig (2 - tailed) Levene's Test for Equality of Variances, Sig. Affect Cognitive Competence Values Difficulty Interest Effort The mean differences for Affect, Value and Effort are significant among China and American Males students The mean differences for Affect, Difficulty and Effort are significant among China and American Female students Mean differences more than ½ point or more are as important. Schau & Emmioglu 2012, pg 88

China (n = 194)USA (n = 293) Mean Difference (α = 0.05) Mean Std. Deviation NMean Std. DeviationMean Std Errordf Sig (2 - tailed) Levene's Test for Equality of Variances, Sig. Affect Cognitive Competence Values Difficulty Interest Effort The mean differences for Affect, Difficulty and Effort are significant among China and American Students

Figure 2 Standardized Estimates for US Pre - Stat Fall 2015 with 293 Responses Figure 7 Standardized Estimates China Fall 2014 with 194 Responses Affect Cognitive CompetenceValue Cognitive Competence0.95 Value Difficulty Parcels are used for CFA based on Dauphiness, Schau and Stevens 1997, and Byrne 1988, Schau et al. 1995, and Holt 2004, Bandalos and Finney, pgs 269 – 295, and loaded significantly strongly on hypothesized latent factor.

Figure 3 T - values US Pre - Stat Fall 2015 with 293 ResponsesFigure 8 T - values China Jan 2014 w/ 194 Responses

1. Chi – square goodness of fit statistics were not significant for all of the models with p – value > 0.05, indicated the good fit 2. Ratio of Chi – square to degree of freedom as adjunct discrepancy – based fit index, lower than 2 or 3 are acceptable, Carmines and McIver Incremental fit indices: Normed Fit Index (NFI,), Comparative Fit Index (CFI), as compared to the independent model 4. Root Mean Squared Error Approximation (RMSEA) <.05 indicates better fit of the model with the degree of freedom 5. df = # of observed variables: 9 x (9+1) / 2 = 45, minus # of parameters to be estimated: 9 x = 24, or 45 – 24 = 21 RMSEA <.05 CountryModelΧ2Χ2 p-valuedfΧ 2 /dfRMSEAp-valueNFICFI USA4 latent factors China4 latent factors China 4 latent factors negative effect China3 latent factors Construct validity of the SATS

Other possible tests as suggested by Bechrakis, et al., Sorge and Schau 2002, and Hilton et al Pearson product – moment correlation coefficients among the attitudes components and the supplementary variables, include What grade do you expect to receive in this course? As good indicator of course performance 2.Gender Invariance tests among Chinese and American students 3.Course performance, the expected grade and attitudes toward statistics 4.Relationships between attitudes and statistics achievements or performance as suggested by Sorge and Schau 2002