Chinese Students Attitudes
Toward Statistics
Ping Wang , P h . D. wa n g px at j m u . e d u
C o m p u te r I nfo r m at i o n Syste m s / B u s i n e s s A n a l y t i c s
C o l l e ge o f B u s i n e s s , J a m e s M a d i s o n U n i ve rs i t y
H a r r i s o n b u rg , VA
D S I 2 0 1 5 , S e att l e , WA , N ov. 2 0 - 2 4
Outline
1.
Introduction
2.
Review of Previous Research
a)
b)
Theory
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)
b)
Constructs: Ability beliefs, Expectancies for success, and Subjective values
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)
b)
c)
d)
e)
f)
g)
Statistics Attitude Survey (SAS) by Roberts and Bilderback, 1980. 34 items on 5-point Likert scale,
moderately related to course grades
Statistical Anxiety Rating Scale by Cruise, Cash and Bolton, 1985, only citation
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)
Statistics Attitude Scale by McCall, Belli and Madjidi, 1990, unpublished report
Multifactorial Scale of Attitudes Toward Statistics (MSAS) by Auzmendi, 1991, 25 items for 5 dimensions of
motivation, enjoyment, anxiety, confidence, and usefulness
Statistics Anxiety Inventory by Zeidner, 1991, parallels between mathematics anxiety and statistics test
and content anxiety
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)
b)
c)
d)
e)
f)
Affect: (6 items): positive and negative feelings about statistics. Such as, I enjoy taking statistics courses.
Cognitive Competence (6 items): intellectual knowledge and skills when applied to statistics. Such as I
understand statistics equations.
Value (9 items): usefulness, relevance, and worth of statistics in personal and professional life. Such as Statistics
is irrelevant to my life.
Difficulty (7 items): the difficulty of statistics as a domain. Such as, Statistics is a complicated subject.
Interest (4 items): individual level of interest. Such as, I am interested in using statistics.
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)
b)
c)
3.
Two Chinese authors and one professional translator for English to Chinese versions
Pilot among 21 Chinese students in Introduction Statistics class in Dalian University of Technology
Refinement of instrument
Data collection:
The number of Responses
Missing at least one item
Univariate outliers by 3 z scores
Univariate outliers by q1 or q3 ±2.2 IQR
Multivariate outliers by Mahalandis - D
China
299
39
48
25
9
USA
389
3
27
18
24
Gender, Ethnicity, Degree, and Expected Grade
41. Your sex
43. Degree you are currently seeking
Count
41. Your Male 1
sex:
Female 2
Total
Country
USA
China
190, 65% 59, 30%
103, 35% 134, 70%
293
193
Count
Total
249
237
486
43. Degree you
are currently
seeking:
42. Your ethnicity
Count
42. Your
ethnicity:
Total
1. White American
2. Native American
3. African American
4. Hispanic American
5. Asian American
6. Other American
12 .Foreign student
from other countries
Country
USA
China
227, 78%
192
0
1
11
0
22, 7.5%
0
24, 8%
0
2
0
Total
419
1
11
22
24
2
7
0
7
293
193
486
Total
1 Associate
2. Bachelors
3. Masters
5. Certification
6. Post - bachelor's
Licensure
8. Other
Country
USA China
7
6
259
173
27
0
0
1
Total
13
432
27
1
0
2
2
0
293
6
188
6
481
44. What grade do you expect to receive in this course?
Count
Country
USA
China
Total
44. What grade do
A
69
99
168
you expect to
A80, 51%
39, 73%
119
B+
76
17
93
receive in this
course?
B
55
25
80
B11, 49%
6, 25%
17
C+
2
2
4
C
0
1
1
Total
293
189
482
Major and Age
45. What is your major? If you have a double major, pick the one
that bests represents your interest
Count
Country
USA
China
Total
45. What is your 1. Accounting
48, 16%
0
48
major? If you
2. Computer
Information
have a double
30, 10%
1
31
major, pick the
Systems/Business
one that bests
Analytics
11
75, 40%
86
represents your 3. Economics
interest
4. Finance
54, 18% 8, 4%
62
6. International
28, 10%
2
30
Business
7. Management
44, 15% 48,25%
92
8. Marketing
71
1
72
9. Others
4
50
54
10. Not decided
3
5
8
Total
293
190
483
47. Your age (in years)
Average Age:
19
20
Country
USA
China
47. Your age (in
17
4
0
years):
18
55, 19%
14
19
183, 63% 78, 41%
20
38, 13% 50, 26%
21
12
33, 17%
22
1
10
23
0
5
24
0
1
Total
293
191
Total
4
69
261
88
45
11
5
1
484
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
USA
China
Total
48. Number of
0 - 15
122
19
44
credit hours earned 16 - 30
80
23
103
58
7
65
toward the degree 31 - 45
you are currently 46 - 60
16
43
59
seeking (don’t
61 - 75
6
30
36
76 - 90
2
5
7
count this s...
91 6
9
15
120
121 1
16
17
150
 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
USA
China
Total
49. Current grade point A- to A 12, 5%
0
12
average (please
B+
37
10
47
B
66
16
82
estimate if you don’t
know; give only one
B61, 72% 57, 46%
118
single numeric
C+
32
52
84
C
15
17
32
estimate)
C4, 22% 19, 49%
23
D+
1
4
5
Missing
64
13
77
Total
293
193
473
229
180
# of Math/Stat Years in HS, College Courses,
and How likely to take stat course?
50. Number of years of high school mathematics or
statistics courses taken
Average Number of Years:
4.11
3.06
Country
USA
China
Total
50. Number of years 1.00
1
0
1
of high school
2.00
1
0
1
3.00
8
179
187
mathematics or
statistics courses
4.00
250
3
253
taken:
5.00
26
0
26
6.00
5
0
5
7.00
1
0
1
≥ 10.00
1
3
4
Total
293
185
478
53. If the choice had been yours, how likely is it that you
would have chosen to take any course
Count
Country
USA
Total
53. If the choice had Absolutely
19
19
been yours, how
not 1
25% Chance 2
66
66
likely is it that you
would have chosen 50% Chance 3
89
89
to take any course... 75% Chance 4
93
93
100% 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
USA
China
Total
51. Number of
.00
50
35
85
college mathematics 1.00
130
8
138
2.00
88
33
121
and/or statistics
courses completed 3.00
17
57
74
(don’t count this
4.00
6
17
23
5 - 10
2
13
15
semester):
10 - 14
0
6
6
≥ 15.00
0
7
7
missing
0
1
1
Total
293
177
470
Table 1. Cronbach’s coefficient alpha values for pretest scores
by attitude component (US and China data) are compatible with published results
Affect
Cognitive Competence
Value
Difficulty
Interest
Effort
American
(n = 293)
0.745
0.840
0.872
0.745
0.864
0.784
Chinese
(n = 194)
0.761
0.720
0.871
0.638
0.767
0.763
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
Schau et al 1995
0.81 – 0.85
0.77 – 0.83
0.80 – 0.85
0.64 – 0.77
The mean differences for Affect, Value and Effort are significant among China and American Males students
Male Students
Affect
Cognitive
Competence
Values
Difficulty
Interest
Effort
China (n = 59)
Std.
Mean Deviation
4.9661
0.9747
USA (n = 190)
Std.
Mean
Deviation
4.2895
.88929
5.2429
0.9925
5.0877
.84857
5.8964
3.2470
5.3093
6.1864
0.7797
0.6922
1.0691
.79138
5.6462
3.4504
5.0868
6.6829
.75119
.66930
.91487
.39227
Mean Difference (α = 0.05)
Sig (2 - Levene's Test for Equality
Mean Std Error
df
tailed) of Variances, Sig.
0.6766 0.1356
247
0.000
0.810
0.1552
0.2502
-0.2034
0.2225
-0.4965
0.1431
0.1130
0.1006
0.1421
0.1069
85.963
247
247
247
67.068
0.281
0.028
0.044
0.119
0.000
0.037
0.796
0.503
0.059
0.000
The mean differences for Affect, Difficulty and Effort are significant among China and American Female students
Females
Affect
Cognitive
Competence
Values
Difficulty
Interest
Effort
China (n = 134)
Std.
Mean Deviation
4.9005
0.9211
USA (n = 103)
Std.
Mean
Deviation
4.0275
.84052
5.1480
0.8014
4.9239
.82966
5.7032
3.1301
4.9291
6.4011
0.9363
0.7186
1.1592
.68002
5.6408
3.4383
5.0801
6.7573
.74506
.60750
.86688
.35779
Mean Difference (α = 0.05)
Sig (2 - Levene's Test for Equality
Mean
Std Error
df
tailed) of Variances, Sig.
0.8730
0.1162
235
0.000
0.256
0.2241
0.0624
-0.3082
-0.1510
-0.3562
0.1066
235
0.1092 234.702
0.0881
235
0.1316 234.842
0.0685 210.455
0.037
0.569
0.001
0.252
0.000
0.778
0.039
0.183
0.001
0.000
Affect
Cognitive
Competence
Values
Difficulty
Interest
Effort
China (n = 194)
USA (n = 293)
Mean Difference (α = 0.05)
Std.
Std.
Std.
Std
Sig (2 - Levene's Test for Equality
Mean Deviation Deviation N
Mean Deviation Mean Error
df tailed) of Variances, Sig.
0.560
4.9201 0.9333
.93333
293 4.1974
.87998 0.7227 0.0835 485 0.000
5.1753
0.8609
.86090
293
5.0301
.84419
5.7612
3.1686
5.0451
6.3338
0.8916
0.7101
1.1402
0.7192
.89157
.71011
1.14022
.71919
293
293
293
293
5.6443
3.4461
5.0845
6.7090
.74777
.64722
.89681
.38155
0.1451
0.1169
-0.2775
-0.0394
-0.3753
0.0788
0.0748
0.0623
0.0972
0.0562
485
362.7
485
345.2
265.5
0.066
0.132
0.000
0.686
0.000
0.292
0.040
0.130
0.000
0.000
The mean differences for Affect, Difficulty and Effort are significant among China and American Students
Figure 7 Standardized Estimates China Fall 2014
with 194 Responses
Figure 2 Standardized Estimates for US Pre - Stat Fall 2015
with 293 Responses
Cognitive
Competence
Value
Difficulty
Affect
Cognitive
Competence
Value
0.95
0.303
0.733
0.418
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
Figure 8 T - values China Jan 2014 w/ 194 Responses
Figure 3 T - values US Pre - Stat Fall 2015 with 293 Responses
Construct validity of the SATS
Country
Model
Χ2
p-value
df
Χ2/df
RMSEA <.05
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
China
4 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
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
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