1. 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. 20 - 24

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

3. 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 1970 3.Surveys measuring attitudes toward statistics (more details on Ramirez et al. 2012) a)Statistics Attitude Survey (SAS) by Roberts and Bilderback, 1980. 34 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and attitudes toward Field of statistics (20 items) d)Statistics Attitude Scale by McCall, Belli and Madjidi, 1990, unpublished report e)Multifactorial Scale of Attitudes Toward Statistics (MSAS) by Auzmendi, 1991, 25 items for 5 dimensions of motivation, enjoyment, anxiety, confidence,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

4. Theory and Development for Survey of Attitudes Toward Statistics (SATS) by Schau, 1995 1.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

5. 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 Responses299389 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

6. 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 293193486 43. Degree you are currently seeking Count Country Total USAChina 43. Degree you are currently seeking: 1 Associate 7613 2. Bachelors 259173432 3. Masters 270 5. Certification 011 6. Post - bachelor's Licensure 022 8. Other 066 Total293188481 44. 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 6999168 A- 80, 51%39, 73%119 B+ 761793 B 552580 B- 11, 49%6, 25%17 C+ 224 C 011 Total293189482 42. Your ethnicity Count Country Total USAChina 42. Your ethnicity: 1. White American 227, 78%192419 2. Native American 011 3. African American 110 4. Hispanic American 22, 7.5%022 5. Asian American 24, 8%024 6. Other American 202 12.Foreign student from other countries 707 Total293193486

7. Major and Age 47. Your age (in years) Average Age: 19 20 Country Total USAChina 47. Your age (in years): 17 404 18 55, 19%1469 19 183, 63%78, 41%261 20 38, 13%50, 26%88 21 1233, 17%45 22 11011 23 055 24 011 Total 293191484 45. 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%048 2. Computer Information Systems/Business Analytics 30, 10%131 3. Economics 1175, 40%86 4. Finance 54, 18%8, 4%62 6. International Business 28, 10%230 7. Management 44, 15%48,25%92 8. Marketing 71172 9. Others 45054 10. Not decided 358 Total 293190483

8. 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: 28 73 Country Total USAChina 48. Number of credit hours earned toward the degree you are currently seeking (don’t count this s... 0 - 15 1221944 16 - 30 8023103 31 - 45 58765 46 - 60 164359 61 - 75 63036 76 - 90 257 91 - 120 6915 121 - 150 11617  150 021 Total 293173466 49. Current grade point average (please estimate if you don’t know; give only one single numeric estimate) Average GPA: 2.92 3.00 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+ 371047 B 661682 B- 61, 72%57, 46%118 C+ 325284 C 151732 C- 4, 22%19, 49%23 D+ 145 Missing 641377 Total293 229 193 180 473

9. # 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 1 19 25% Chance 2 66 50% Chance 3 89 75% Chance 4 93 100% Sure 5 26 Total 293 51. Number of college mathematics and/or statistics courses completed (don’t count this semester) Average # of Courses: 1.47 3.73/Md 2.64 Country Total USAChina 51. Number of college mathematics and/or statistics courses completed (don’t count this semester):.00 503585 1.00 1308138 2.00 8833121 3.00 175774 4.00 61723 5 - 10 21315 10 - 14 066 ≥ 15.00 077 missing 011 Total293177470 50. Number of years of high school mathematics or statistics courses taken Average Number of Years: 4.11 3.06 Country Total USAChina 50. Number of years of high school mathematics or statistics courses taken: 1.00 101 2.00 101 3.00 8179187 4.00 2503253 5.00 260 6.00 505 7.00 101 ≥ 10.00 134 Total293185478

10. 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) Affect0.7450.7610.81 – 0.85 Cognitive Competence0.8400.7200.77 – 0.83 Value0.8720.8710.80 – 0.85 Difficulty0.7450.638 0.64 – 0.77 Interest0.8640.767 Effort0.7840.763 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

11. 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 4.96610.97474.2895.88929 0.67660.13562470.0000.810 Cognitive Competence 5.24290.99255.0877.84857 0.15520.143185.9630.2810.037 Values 5.89640.77975.6462.75119 0.25020.11302470.0280.796 Difficulty 3.24700.69223.4504.66930 -0.20340.10062470.0440.503 Interest 5.30931.06915.0868.91487 0.22250.14212470.1190.059 Effort 6.1864.791386.6829.39227 -0.49650.106967.0680.000 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. Affect4.90050.92114.0275.840520.87300.11622350.0000.256 Cognitive Competence 5.14800.80144.9239.82966 0.22410.10662350.0370.778 Values5.70320.93635.6408.745060.06240.1092234.7020.5690.039 Difficulty3.13010.71863.4383.60750-0.30820.08812350.0010.183 Interest4.92911.15925.0801.86688-0.15100.1316234.8420.2520.001 Effort6.4011.680026.7573.35779-0.35620.0685210.4550.000 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

12. 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. Affect4.92010.9333.933332934.1974.879980.72270.08354850.0000.560 Cognitive Competence 5.17530.8609.860902935.0301.84419 0.14510.07884850.0660.292 Values5.76120.8916.891572935.6443.747770.11690.0748362.70.1320.040 Difficulty3.16860.7101.710112933.4461.64722-0.27750.06234850.0000.130 Interest5.04511.14021.140222935.0845.89681-0.03940.0972345.20.6860.000 Effort 6.33380.7192.719192936.7090.38155 -0.37530.0562265.50.000 The mean differences for Affect, Difficulty and Effort are significant among China and American Students

13. 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 Value0.3030.418 Difficulty0.7330.6550.11 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.

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

15. 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 1981 3. 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 2 + 6 = 24, or 45 – 24 = 21 RMSEA <.05 CountryModelΧ2Χ2 p-valuedfΧ 2 /dfRMSEAp-valueNFICFI USA4 latent factors20.890.47210.9950.0000.9550.9891.000 China4 latent factors22.400.38211.0670.0190.8350.9800.999 China 4 latent factors negative effect13.370.34121.1140.0200.8350.9930.999 China3 latent factors34.080.08241.4200.0470.5300.9690.990 Construct validity of the SATS

17. Other possible tests as suggested by Bechrakis, et al., Sorge and Schau 2002, and Hilton et al. 2004 1.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