Difficulties in learning about
sampling and approaches to
overcoming these (AS1.10 & 2.9)
Jared Hockly - Western Springs College
hocklyj@wsc.school.nz
Overview of this session:
- Discuss the standards 1.10 and 2.9 briefly
(some clarifications)
- Focus on developing understanding of
sampling variability
- Look at a few activities that develop this
understanding
- Discuss how to get the best out of the
learning and assessment of this topic
Achievement Objectives -Explanatory note 3
AS1.10 Investigate a given multivariate data set using the
statistical enquiry cycle
Students need to be familiar with the statistical enquiry cycle to
investigate a given multivariate data set, which involves:
P
• investigating data that has been collected from a survey
situation
• posing an appropriate comparison question using a given
multivariate data set
AS2.9 Use statistical methods to make an inference
Using the statistical enquiry cycle to make an inference
involves:
• posing an appropriate investigative comparison
question from a given set of population data
• selecting random samples
P
D
A
C
• selecting and using appropriate display(s)
• giving summary statistics such as the five summary values (minimum,
maximum, median, quartiles)
• discussing features of distributions comparatively, such as shape,
middle 50%, shift, overlap, spread, unusual or interesting features
• selecting and using appropriate displays and measures
• communicating findings, such as informal inference and
• discussing sampling variability, including the variability
of estimates
• making an inference
• communicating findings in a conclusion.
supporting evidence, in a conclusion.
• discussing sample distributions
Questions for you
1) Why do we teach this topic/standard?
(What are our beliefs, What do/should
students get out of it)
2) Are we turning students off stats by doing
these standards?
3)
What do you think it is about sampling
variability that makes it tricky?
Question about
population
(problem)
Answer about
population.
“making the call”
(conclusion)
Get/organise your
sample data
(plan, data)
Compare the two
groups using graphs
and summary stat
(Analysis)
a few off topic points before we get into it
● technology should be used (but not exclusively in the
teaching)
● Beware, some data is tricky to ask worthwhile questions
about (titanic, world at a glance)
● 1.10: don’t need a random process for selecting the data
● Students should be given opportunities to understand
the context they are investigating (they need this at
higher grades)
● 2.9 is a bit odd, sampling from a “population database”...
Kinda off topic still - How sampling really
works
- (If possible) generate a list of the population:
a sampling frame. (e.g electoral roll, register
of schools, list of students)
- then randomly choose units for your sample
- then you gather the data for those in the
sample
Some of my beliefs about teaching stats
- Compartmentalising the skills makes it hard for students
to understand what they are really doing
- More effective learning of skills is teaching them when
there is a need.
- Use interesting data, data they may be invested in.
- This is hard but: don’t always be critical or accuracy. Let
the intuitive statements have some air
A suggested overview of teaching this topic
1. Do some investigations where you have the whole population to
investigate.
e.g are boys better at robot unicorn attack than girls in our class. (Get
to do the PPDAC cycle without too much complexity)
2. Move onto situations where it is impractical to have/use/collect the whole
population.
data cards (similar to karekare college 2009 stats day)
census at school samples/dataviewer
The idea of a sample will develop. Do we all get the same result when we
sample?
A suggested overview of teaching this topic
(cont)
3. Develop the idea of sampling variability before they learn rules.
The effect of sample size, the effect of the spread of the dataset(s), iNZight
could make an appearance here
a
1 variable variation of sample median (how different can out answers be,
looking around the class)
- 2 variable comparisons of sample medians. Use intuition.
3. They are probably wanting to know when there is a big enough difference for
us to make a call
1.10 the rules for making a call
2.9 the formula for confidence interval and the idea of overlap
Are they correct with their calls? A mixture of knowing the population results (to see
if they got it right and provide closure) and not knowing (because thats the way it
really is)
And back to assessment
1.10 Why not get the students to create the
sample, this will ensure they are well informed
about the context
2.9 does say “from a given set of population
data”. Can we still get them to sample the data
in a more real way?
Takeaways
- A desire to adjust the teaching of these topics to:
-
be engaging in the use of data
uses a range of activities
have multiple investigations developing in complexity
develops understanding of sampling variability (rather than an
emphasis on rules and canned statements)
A desire to create better assessments that involve
students in the context/data
Level 6
• plan and conduct surveys and experiments
using the statistical enquiry cycle
- determining appropriate variables
- cleaning data
- using multiple displays, and re-categorising
data to find patterns, variations, in multivariate
data sets
- comparing sample distributions visually, using
measures of centre, spread, and proportion
- presenting a report of findings;
• plan and conduct investigations using the
statistical enquiry cycle
- justifying the variables used
- identifying and communicating features in
context (differences within and
between distributions), using multiple displays
- making informal inferences about populations
from sample data
- justifying findings, using displays and
measures.
Level 7
• carry out investigations of phenomena,
using the statistical enquiry cycle:
− using existing data sets
− evaluating the choice of sampling and
data collection methods used
− using relevant contextual knowledge,
exploratory data analysis, and statistical
inference
• make inferences from surveys:
− using sample statistics to make point
estimates of population parameters
− recognising the effect of sample size on
the variability of an estimate