what can we learn from quantitative data in statistics education research?

University of MinnesotaEducational Psychology

What Can We Learn from Quantitative Data in Statistics

Education Research?

Sterling Hilton Brigham Young University

Andy Zieffler University of Minnesota

John Holcomb Cleveland State University

Marsha Lovett Carnegie Mellon University

Introduction

Components of a research program Generate ideas (pre-clinical)

Develop a conceptual framework Frame question (pre-clinical, Phase I)

Constructs and Measurement Design and Methods Pilot study

Examine question (Phase I, Phase II) Establish efficacy (small)

Generalize findings (Phase III) Larger studies in varied settings

Extend findings (Phase IV) Longitudinal studies Different populations

Introduction

Quantitative methods in research program Framing: measurement development

Validity and reliability Framing: pilot study Examine Generalize Extend

Statistics education research is primarily in the “generate” and “frame” phases

Introduction

Purpose: Introduce two instruments that are in different stages of development and discuss how they have been and might be used in statistics education research Comprehensive Assessment of Outcomes

in a Fist Statistics course (CAOS) Survey of Attitudes Toward Statistics

(SATS)

Assessment Resource Tools for Improving Statistical Thinking

Several online assessments ARTIST Topic Scales Comprehensive Assessment of

Outcomes in a First Statistics course (CAOS)

Statistics Thinking and Reasoning Test (START)

ARTIST Topic Scales

7-15 MC items Many topics

Data Collection Data Representation Measures of Center Measures of Spread Normal Distribution Probability Bivariate Quantitative Data Bivariate Categorical Data Sampling Distributions Confidence Intervals Significance Tests

CAOS Test

40 MC items Designed to assess students’

statistical reasoning after any first course in statistics.

CAOS test focuses on statistical literacy and conceptual understanding, with a focus on reasoning about variability.

Developed through a three-year process of acquiring and writing items, testing and revising items, and gathering evidence of reliability and validity.

CAOS Test

Reliability Analysis Sample of 10287 Cronbach’s alpha coefficient of .77

Content Validity Evidence 18 expert raters Unanimous agreement that CAOS measures

important basic learning outcomes All raters agreed with the statement “CAOS

measures outcomes for which I would be disappointed if they were not achieved by students who succeed in my statistics courses.”

Some raters indicated topics that they felt were missing from the scale - no agreement among these raters about the topics that were missing.

START Test

14 MC items Identified through a principal

components analysis performed on CAOS data gathered in Fall 2005 and Spring 2006 (n = 1470).

Alpha Coefficient from that data set was calculated to be 0.74.

Use of Quantitative Measures in a Phase 1 Study

Exploratory Studies What can we find out about

students’ understanding? Where are students having

difficulties? Are there inconsistencies in

students’ reasoning?

Example Item 1

Measured Learning Outcome

Understanding the interpretation of a median in the context of boxplots.

Example Item 1

The two boxplots below display final exam scores for all students in two different sections of the same course

Example Item 1

Which section has a greater percentage of students with scores at or above 80?

a) Section A

b) Section B

c) Both sections are about equal.

Example Item 1

How did students answer this item?

Example Item 1

Pretest Posttest Response (N = 754)

73.7% 65.6% Section A

6.6% 6.1% Section B

19.6% 28.2%Both sections are about equal.

Example Item 1

Is this surprising? What can we learn from

students’ responses to this item?

Implications/Directions for research? Teaching?

Example Item 2


Understanding that correlation does not imply causation.

Example Item 2

Researchers surveyed 1,000 randomly selected adults in the U.S. A statistically significant, strong positive correlation was found between income level and the number of containers of recycling they typically collect in a week. Please select the best interpretation of this result.

Example Item 2

a) We can not conclude whether earning more money causes more recycling among U.S. adults because this type of design does not allow us to infer causation.

b) This sample is too small to draw any conclusions about the relationship between income level and amount of recycling for adults in the U.S.

c) This result indicates that earning more money influences people to recycle more than people who earn less money.

Example Item 2


Example Item 2


54.6% 52.6%We can not conclude whether earning more money causes more recycling among U.S. adults because this type of design does not allow us to infer causation.

18.3% 11.4%This sample is too small to draw any conclusions about the relationship between income level and amount of recycling for adults in the U.S.

27.1% 35.9%This result indicates that earning more money influences people to recycle more than people who earn less money.

Example Item 2




Example Item 3


Ability to match a scatterplot to a verbal description of a bivariate

relationship.

Example Item 3

Bone density is typically measured as a standardized score with a mean of 0 and a standard deviation of 1. Lower scores correspond to lower bone density. Which of the following graphs shows that as women grow older they tend to have lower bone density?

Example Item 3

a) Graph A

b) Graph B

c) Graph C

Example Item 3


Example Item 3


90.5% 92.5% Graph A

6.1% 6.6% Graph B

3.3% 0.9% Graph C

Example Item 3




Example Item 4


Understanding of the purpose of randomization in an experiment.

Example Item 4

A recent research study randomly divided participants into groups who were given different levels of Vitamin E to take daily. One group received only a placebo pill. The research study followed the participants for eight years to see how many developed a particular type of cancer during that time period. Which of the following responses gives the best explanation as to the purpose of randomization in this study?

Example Item 4

a) To increase the accuracy of the research results.

b) To ensure that all potential cancer patients had an equal chance of being selected for the study.

c) To reduce the amount of sampling error.

d) To produce treatment groups with similar characteristics.

e) To prevent skewness in the results.

Example Item 4


Example Item 4


41.4% 31.8% To increase the accuracy of the research results.

13.5% 19.8%To ensure that all potential cancer patients had an equal chance of being selected for the study.

22.7% 29.4% To reduce the amount of sampling error.

8.5% 12.3% To produce treatment groups with similar characteristics.

13.9% 6.6% To prevent skewness in the results.

Example Item 4




How Can We Use the Results?

Begin to look for underlying reasons students are having difficultiesExamine the research literature Interview students to gain a more in-

depth understanding of their reasoning

Compare results with data from other classes (other teachers, schools)

How Can We Use the Results?

They can inform our instruction Reconsider how difficult or easy some

concepts are for students Rethink how we currently teach these ideas Add new activities or tools Re-allocate classroom time

Change the way we assess students Assessment items better aligned with

learning outcomes Assessment items that probe students

reasoning

SATS

Survey of Attitudes Towards Statistics Candace Schau and Tom Dauphinee (http://www.unm.edu/~cschau/satshomepage.htm)

Twenty-eight item survey Seven point Likert scale response

Strongly Neither agree Strongly

Disagree nor disagree Agree

1 2 3 4 5 6 7

SATS

Original four subscales Value (9 items; α range .80 - .90 )

“Statistics is worthless.” Affect (6 items; α range .80 - .85)

“I like statistics.” Cognitive Competence (6 items; α range .77

- .85)

“I have no idea of what’s going on in statistics.” Difficulty (7 items; α range .64 - .79)

“Statistics is a complicated subject.”

SATS

Two additional subscales Interest (4 items)

“I am interested in using statistics.”

Effort (4 items)

“I plan to complete all of my statistics assignments.”

SATS

Attitude is multi-faceted outcome

Issues to consider Pre-existing attitudes Direction and magnitude of

changes over a semester Relevance of items to study

Using the SATS: A Case Study

Assessment of a project-rich introductory statistics course

Fall 2004, at Cleveland State University

Class 1: 30 students Pre/Post Class 2: 16 students Pre/Post SATS administered first day and

final exam day

Class 1: Projects - Rich

4 team projects that used/requiredReal dataComputer SoftwareCollaborationWriting

Individualized Mid-Term and Take-home Data Analysis Exams

http://academic.csuohio.edu/holcombj/eku/index.html Login: holcomb pwd: projects22

Class 2

Ti – 83 In – Class demos Homework and Exams

Comparison of Pre Data

No significant difference between Class1 and Class2

Class

Pre

AFF

ECT

21

7

6

5

4

3

2

1

PreAFFECT vs Class

Class

Pre

COGCOM

P

21

7

6

5

4

3

2

1

PreCOGCOMP vs Class

Class

Pre

VA

LUE

21

7

6

5

4

3

2

1

PreVALUE vs Class

Class

Pre

DIF

FICULT

Y

21

7

6

5

4

3

2

1

PreDIFFICULTY vs Class

Class

Pre

INTE

RES

T

21

7

6

5

4

3

2

1

PreINTEREST vs Class

Class

Pre

EFFO

RT

21

7

6

5

4

3

2

1

PreEFFORT vs Class

Class 1 Change from Pre to Post(2 – sided tests)

Significant Differences for: Cognitive Competence Value Difficulty* Interest

Insignificant Differences for: Affect Effort

*(Not Significant with Nonparametric Test)

diffAFFECTdiffCOGCOMP

diffVALUEdiffDIFFICULTY

diffINTERESTdiffEFFORT

-6.00

-4.00

-2.00

0.00

2.00

4.00

6.00

727

29

5

24

2

2

218

29

Six Components for Class1: Pre - Post

p = 0.541 p=0.018 p = 0.038 p = 0.049 p = 0.006 p = 0.881

Class 2: Change from Pre to Post (2- sided tests)

Significant Differences Affect (wrong direction)

Insignificant Differences Cognitive Competence Value Difficulty Interest Effort

diffAFFECTdiffCOGCOMP

diffVALUEdiffDIFFICULTY

diffINTERESTdiffEFFORT

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

43

31

32

42

40

p = 0.020 p = 0.522 p = 0.247 p = 0.303 p = 0.062 p = 0.051

Six Components for Class2: Pre - Post

Multivariate Analysis of Post DataClass Significant vs Insignificant

Significant Differences Affect Value Interest

Insignificant Differences Cognitive Competence Difficulty Effort

Does SATS Ask the Right Questions?

Value Component Questions Statistics is worthless. Statistics should be a required part of my

professional training. Statistical skills will make me more employable. Statistics is not useful to the typical professional. Statistical thinking is not applicable in my life outside

my job. I use statistics in my everyday life. Statistics conclusions are rarely presented in

everyday life. I will have no application for statistics in my

profession. Statistics is irrelevant in my life.

What are the Questions You Want to Ask?

ADD ANSWERS HERE

Instructors: Do try this at home!

But first, set your expectations Results may not be as high as you

desire by the end of your course (e.g., CAOS)

Results may not change from the beginning to the end of your course or in the direction you anticipate (e.g., SATS)

Same is true for other instruments, too

How might you use such data?

How might you use such data?

To better understand students’ learning of particular concepts and skills

To identify different patterns of student performance

To establish a starting point for further inquiry To make your teaching and students’ learning

more effective To assess where students start and to reveal

areas of difficulty during course

Some Practical Considerations

Motivating students to take these instruments seriously Grading? Feedback

Instrument integrity Time to administer Others?

INQUERI Project

INQUERI = Initiative for Quantitative Education Research Infrastructure To build a research infrastructure by

focusing on the development, deployment, user training, and archiving of high quality research methods, instruments, and data

To disseminate these methods and results

To catalyze research collaborations See www.inqueri.org

Back to the Big Picture

Focus on the question/goal you want to address and relate that to past research

Start small Using existing instruments is one

way Working within your own course to

start Share with colleagues, connect

with the literature, and then extend

References

delMas, R., Garfield, J., Ooms, A., & Chance, B. (2006). Assessing students' conceptual understanding after a first course in statistics. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, CA.

Garfield, J., delMas, R., & Chance, B. (n.d.). Assessment Resource Tools for Improving Statistical Thinking Retrieved May 8, 2007, from https://app.gen.umn.edu/artist/index.html.

References

http://www.unm.edu/~cschau/satshomepage.htm Dauphinee, T. L., Schau, C., & Stevens, J. J. (1997).

Survey of Attitudes Toward Statistics: Factor structure and factorial invariance for females and males. Structural Equation Modeling, 4, 129-141.

Schau, C., Stevens, J., Dauphinee, T. L., & Del Vecchio, A. (1995). The development and validation of the Survey of Attitudes Toward Statistics. Educational and Psychological Measurement, 55, 868-875.

Hilton, S. C., Schau, C., & Olsen, J. A. (2003). Survey of Attitudes Toward Statistics: Factor structure invariance by gender and by administration time. Structural Equation Modeling, 11, 92 – 109.

Contact Information

Sterling Hilton [email protected]

Andy Zieffler [email protected]

John Holcomb [email protected]

Marsha Lovett [email protected]

what can we learn from quantitative data in statistics education research?

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