Statistical Problem
Solving for nonspecialists
John Marriott
RSS Centre for Statistical Education
University of Plymouth
John.Marriott@rsscse.org.uk
Summary
i.
Introductory statistics modules
ii. Engaging students
iii. Using a problem solving approach
iv. Some examples
v. Concluding remarks
Introductory statistics modules
The first semester
• EDA
• Graphical presentation of data
The usual suspects
• Descriptive statistics
Location
spread
Attention and attendance
The lectures
Why?
Students talking in lectures
(if they are there)
Two crucial questions
1. Why are they talking
2. What are they talking about ……………
if it isn’t about statistics?
Why are they talking?
Introductory statistics modules
• EDA
• Graphical presentation of data
The usual suspects
• Descriptive statistics
Location
spread
Why are they talking?
Introductory statistics modules
• Not intellectually challenging
 They have been doing this since they were 11!
 Boredom
• The result?
 Poor attendance
 Both lectures and classes/labs
• If we must cover this material how can we make
it more interesting?
Why are they talking?
A solution?
• Include relevant context?
 Parachuting in ‘context’??
 It doesn’t work for introductory courses!
 Students say it appears contrived to them
• What do students want to talk about?
Engaging students
• What are they talking about?
 Themselves and their friends
• What topics interest them?
 Their accommodation
 The neighbourhood that live in/crime
• Can we use this to get students to talk
about statistics?
Engaging students
• We should ask them to talk about
 Themselves and their friends
• We could choose as topics
 How good is their accommodation
 How safe is the place they live in?
Engaging students
• Can we use this to get students to
learn introductory statistics?
• YES
if we use real data that is relevant to
the students
• YES
if we use a problem solving approach
(PSA)
Using a Problem Solving Approach
Problem solving approach (PSA)
We report back what
we found – and
compare it with what
we expected.
Plan
Discuss
Then we examine
our data and make it
easier to understand.
First we decide
what problem to
solve and what
data we need
Collect
Process
Then we collect
suitable data.
Engaging students – the PSA
• PSA can counter dominance of mathematical
thinking. Stuart (1995, 2003)
• Use of PSA improves students’ skills
Garfield (1995),
Garfield and Ben-Zvi (2007)
 esp. if real data used
Cobb (1992), Cobb and Moore (1997)
• GAISE, ASA advocate active learning pf stats
using PSA and real data Franklin and Mewborn (2006)
• Use of PSA a benefit to teachers and learners
Rossman et al (2006), Groth (2006)
Economic and Social Research Council Response
Economic and Social Research Council Response
In 2006 there were calls for proposals to develop
undergraduate curricula that:
• use real data to show the value of quantitative methods
• show students they have the foundation skills that can build
on their school experience
• encourage students to collect their own data and analyse
them
• encourage students to carry out their own research projects
using data
Motivating/engaging new undergraduates
• New undergraduates will be concerned about the
town where they are attending university
•
‘HowScience
safe is your
neighbourhood?’
• A
Social
students
will, at some problem
stage,
will
be ofthe
interest
all undergraduates
:
consider
socialtoeffects
of crime
– Mathematics; statistics; biosciences;
medicine; health sciences; business/finance;
economics; sociology/social admin;
psychology; geography; built environment;
engineering; leisure and sport; legal studies;
…..
The first introductory stats lecture
•
•
•
•
•
Introduce the problem
Discussion
Student questions
Discuss choice of data
Reminder of the PSA
The Second and Subsequent Lectures
• From the start the students have been involved in
– the formulation of the problem being investigated
– their own data being collected
• The impetus is maintained by
– reminding the students of the PSA
– using their data to illustrate the Process and
Discuss stages of the PSA
– introducing the statistical tools/techniques they
need in the context of their data and at the time
it is required
Some examples
1. Introductory statistics
How safe is your neighbourhood?
Setting the Scene
Collecting Data
Data Downloaded from Website
Processing the Data
Discussing the Results
The First Seminar/Workshop
- Collect
• The students complete a short questionnaire (online)
• The questionnaire comprises?
– Three demographic questions including date of birth
– Four questions taken from the British Crime Survey
(www.statistics.gov.uk/ssd/surveys/british_crime_survey.asp)
The First Seminar/Workshop
– Process and Discuss
• Students revise data summary presentation
– use their collective seminar data for this
– summarise their seminar group’s perceptions
• Students draw tentative conclusions
– limitations of the seminar ‘sample’ discussed
– possibility of using the whole module group’s
responses in next seminar session discussed
The Second and Subsequent Lectures
• From the start the students have been involved in
– the formulation of the problem being investigated
– their own data being collected
• The impetus is maintained by
– reminding the students of the PSA
– using their data to illustrate the Process and
Discuss stages of the PSA
– just introducing the statistical tools/techniques
they need in the context of their data and at the
time it is required
Some examples
1. For introductory statistics
2. For two sample topics
1. Chi-squared test
2. ANOVA
Where now?
• Online survey tools
– SNAP
http://www.snapsurveys.com/software/
– Limesurvey http://www.limesurvey.org/
– SurveyMonkey
http://www.surveymonkey.com/
• Fast turnaround of data
– Real time results to stats lab/class
Conclusions
• Engage students
– using what they want to talk about
• Use the PSA
– Evidence this works
– It is what statisticians ‘do’
• Online survey tools
• Need exemplar resources
– 3 available
– PSA PowerPoint template
The last slide
Really the last slide!