Chinese Students Attitudes Toward Statistics Ping Wang , Ph.D. wangpx at jmu.eduComputer Information Systems/Business Analyt icsCol lege of Business, James Madison Universi tyHarr isonburg, VADSI 2015, Seatt le, WA, Nov. 20 - 24

Outline1. Introduction

2. Review of Previous Researcha) Theory b) Survey Instruments

3. Data Collection and Preliminary Analysis

4. Conclusions

5. Discussions

Previous Research1. Expectancy – Value Theory of Achievement Motivation, Wigfield and Eccles 2000

a) Constructs: Ability beliefs, Expectancies for success, and Subjective valuesb) 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 gradesb) Statistical Anxiety Rating Scale by Cruise, Cash and Bolton, 1985, only citationc) 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attitudes toward Field of statistics (20 items)d) Statistics Attitude Scale by McCall, Belli and Madjidi, 1990, unpublished reporte) Multifactorial Scale of Attitudes Toward Statistics (MSAS) by Auzmendi, 1991, 25 items for 5 dimensions of motivation,

enjoyment, anxiety, confidence, and usefulnessf) 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, 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

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 versionsb) Pilot among 21 Chinese students in Introduction Statistics class in Dalian University of Technologyc) Refinement of instrument

3. Data collection: China USAThe number of Responses 299 389Missing at least one item 39 3Univariate outliers by 3 z scores 48 27Univariate outliers by q1 or q3 ±2.2 IQR 25 18Multivariate outliers by Mahalandis - D 9 24

Gender, Ethnicity, Degree, and Expected Grade

41. Your sexCount

Country

TotalUSA China41. Your sex:

Male 1 190, 65% 59, 30% 249Female 2 103, 35% 134, 70% 237

Total 293 193 486

43. Degree you are currently seekingCount

Country

TotalUSA China43. Degree you

are currently

seeking:

1 Associate 7 6 132. Bachelors 259 173 4323. Masters 27 0 275. Certification 0 1 16. Post - bachelor's Licensure 0 2 28. Other 0 6 6

Total 293 188 481

44. What grade do you expect to receive in this course? Count

Country

TotalUSA China44. What grade do you expect to receive in this course?

A 69 99 168A- 80, 51% 39, 73% 119B+ 76 17 93B 55 25 80B- 11, 49% 6, 25% 17C+ 2 2 4C 0 1 1

Total 293 189 482

42. Your ethnicityCount

Country

TotalUSA China42. Your

ethnicity:

1. White American 227, 78% 192 4192. Native American 0 1 13. African American 11 0 114. Hispanic American 22, 7.5% 0 225. Asian American 24, 8% 0 246. Other American 2 0 212 .Foreign student from other countries 7 0 7

Total 293 193 486

Major and Age47. Your age (in years)

Average Age: 19 20

Country

TotalUSA China47. Your age (in

years):

17 4 0 418 55, 19% 14 6919 183, 63% 78, 41% 26120 38, 13% 50, 26% 8821 12 33, 17% 4522 1 10 1123 0 5 524 0 1 1

Total 293 191 484

45. What is your major? If you have a double major, pick the one that bests represents your interest

Count

Country

TotalUSA China45. What is your major? If you have a double major, pick the one that bests represents your interest

1. Accounting 48, 16% 0 482. Computer Information Systems/Business Analytics

30, 10% 1 31

3. Economics 11 75, 40% 864. Finance 54, 18% 8, 4% 626. International Business 28, 10% 2 307. Management 44, 15% 48,25% 928. Marketing 71 1 729. Others 4 50 5410. Not decided 3 5 8

Total 293 190 483

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

TotalUSA China48. Number of credit hours earned toward the degree you are currently seeking (don’t count this s...

0 - 15 122 19 4416 - 30 80 23 10331 - 45 58 7 6546 - 60 16 43 5961 - 75 6 30 3676 - 90 2 5 791 - 120 6 9 15121 - 150 1 16 17 150 0 21 21

Total 293 173 466

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

TotalUSA China49. Current grade point average (please estimate if you don’t know; give only one single numeric estimate)

A- to A 12, 5% 0 12B+ 37 10 47B 66 16 82B- 61, 72% 57, 46% 118C+ 32 52 84C 15 17 32C- 4, 22% 19, 49% 23D+ 1 4 5Missing 64 13 77

Total 293229

193180 473

# 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

TotalUSA53. If the choice had been yours, how likely is it that you would have chosen to take any course...

Absolutely not 1 19 1925% Chance 2 66 6650% Chance 3 89 8975% Chance 4 93 93100% Sure 5 26 26

Total 293 293

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

TotalUSA China51. Number of college mathematics and/or statistics courses completed (don’t count this semester):

.00 50 35 851.00 130 8 1382.00 88 33 1213.00 17 57 744.00 6 17 235 - 10 2 13 1510 - 14 0 6 6≥ 15.00 0 7 7missing 0 1 1

Total 293 177 470

50. Number of years of high school mathematics or statistics courses taken

Average Number of Years: 4.11 3.06

Country

TotalUSA China50. Number of years of high school mathematics or statistics courses taken:

1.00 1 0 12.00 1 0 13.00 8 179 1874.00 250 3 2535.00 26 0 266.00 5 0 57.00 1 0 1≥ 10.00 1 3 4

Total 293 185 478

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 0.745 0.761

0.81 – 0.85Cognitive Competence 0.840 0.720 0.77 – 0.83Value 0.872 0.871

0.80 – 0.85Difficulty 0.745 0.638

0.64 – 0.77Interest 0.8640.767Effort 0.784 0.763

Cronbach’s α= 0.7 as acceptable for compatible internal reliability Dunn, Baguley and Drunsden 399 – 412Predhazur and Schwelkin 1991Schau et al 2012

Male Students China (n = 59) USA (n = 190) Mean Difference (α = 0.05)

MeanStd.

Deviation MeanStd.

Deviation Mean Std Error dfSig (2 - tailed)

Levene's Test for Equality of Variances, Sig.

Affect 4.9661 0.9747 4.2895 .88929 0.6766 0.1356 247 0.000 0.810Cognitive Competence 5.2429 0.9925 5.0877 .84857 0.1552 0.1431 85.963 0.281 0.037Values 5.8964 0.7797 5.6462 .75119 0.2502 0.1130 247 0.028 0.796Difficulty 3.2470 0.6922 3.4504 .66930 -0.2034 0.1006 247 0.044 0.503Interest 5.3093 1.0691 5.0868 .91487 0.2225 0.1421 247 0.119 0.059Effort 6.1864 .79138 6.6829 .39227 -0.4965 0.1069 67.068 0.000 0.000

Females China (n = 134) USA (n = 103) Mean Difference (α = 0.05)

MeanStd.

Deviation MeanStd.

Deviation Mean Std Error dfSig (2 - tailed)

Levene's Test for Equality of Variances, Sig.

Affect 4.9005 0.9211 4.0275 .84052 0.8730 0.1162 235 0.000 0.256Cognitive Competence 5.1480 0.8014 4.9239 .82966 0.2241 0.1066 235 0.037 0.778Values 5.7032 0.9363 5.6408 .74506 0.0624 0.1092 234.702 0.569 0.039Difficulty 3.1301 0.7186 3.4383 .60750 -0.3082 0.0881 235 0.001 0.183Interest 4.9291 1.1592 5.0801 .86688 -0.1510 0.1316 234.842 0.252 0.001Effort 6.4011 .68002 6.7573 .35779 -0.3562 0.0685 210.455 0.000 0.000

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

China (n = 194) USA (n = 293) Mean Difference (α = 0.05)

MeanStd.

DeviationStd.

Deviation N MeanStd.

Deviation MeanStd

Error dfSig (2 - tailed)

Levene's Test for Equality of Variances, Sig.

Affect 4.9201 0.9333 .93333 293 4.1974 .87998 0.7227 0.0835 485 0.000 0.560Cognitive Competence 5.1753 0.8609 .86090 293 5.0301 .84419 0.1451 0.0788 485 0.066 0.292Values 5.7612 0.8916 .89157 293 5.6443 .74777 0.1169 0.0748 362.7 0.132 0.040Difficulty 3.1686 0.7101 .71011 293 3.4461 .64722 -0.2775 0.0623 485 0.000 0.130Interest 5.0451 1.1402 1.14022 293 5.0845 .89681 -0.0394 0.0972 345.2 0.686 0.000Effort 6.3338 0.7192 .71919 293 6.7090 .38155 -0.3753 0.0562 265.5 0.000 0.000

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

AffectCognitive

Competence ValueCognitive

Competence 0.95 Value 0.303 0.418

Difficulty 0.733 0.655 0.11

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.

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 1981 3. Incremental fit indices: Normed Fit Index (NFI,), Comparative Fit Index (CFI), as compared to the independent model4. Root Mean Squared Error Approximation (RMSEA) < .05 indicates better fit of the model with the degree of freedom5. 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 Country Model Χ2 p-value df Χ2/df RMSEA p-value NFI CFI

USA 4 latent factors 20.89 0.47 21 0.995 0.000 0.955 0.989 1.000

China 4 latent factors 22.40 0.38 21 1.067 0.019 0.835 0.980 0.999

China4 latent factors negative effect 13.37 0.34 12 1.114 0.020 0.835 0.993 0.999

China 3 latent factors 34.08 0.08 24 1.420 0.047 0.530 0.969 0.990

Construct validity of the SATS

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, includeWhat 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