### Dru Rose - CensusAtSchool New Zealand

```Evaluate Statistically Based
Reports ( AS 3.12)
Workshop 1
Margin of Error and Testing Claims in the Media
Dru Rose (Westlake Girls High School, Ministry of Education Study Award)
What does AS 3.12 cover?
i. Polls and Surveys


Non-sampling errors and survey concerns (Workshop 2)
Sampling error :Workshop 1
margin of error, 95% confidence intervals for proportions,
“rules of thumb”, testing claims
ii.
Experimental and Observational Studies
(Workshop 2)
Dru Rose
The purpose of this workshop
 To demonstrate the power of technology for
developing the concept of margin of error (making the
topic accessible to a wider diversity of students than a
theoretical approach relying on the central limit theorem
and the normal distribution).
 To give you a snap-shot of the teaching approach I
developed and trialled with a small group of students.
Dru Rose
Resource Pack Contents (available from
www.censusatschool.org.nz after today)
The 6 to 7 lesson teaching sequence for sampling error,
with teaching notes
2. Power-point slides (sampling error , political polls)
3. 6 media reports
4. Students worksheets and resource materials linked to the
teaching sequence
5. 3 csv data files to import into iNZight
1.
Dru Rose
Margin of error
Media Reports have a dual role:
• They provide a purpose for developing the
concepts
•
They provide a real life-context with
claims to be tested after developing the
concepts
Dru Rose
C1, L2, S5
Dru Rose
C1, L2, S6
3 types of claim and rules of thumb:
• Single poll %
51% of young people agree there is too much
1
sex, violence and bad language on TV MoE ≈ √
• Comparison within one group
Young people are more likely to agree than
disagree
MoE for the difference ≈ 2 x MoE
• Comparison between independent groups
Young women are more likely to agree than young
men MoE for the difference
≈ 1.5 x Average MoE
Dru Rose
C1, L2, S7
Conceptualising a Margin of Error
• Margin of error involves the sampling
variability of a proportion (%) –a categorical
parameter
• Before using a computer simulation, do a
concrete activity which mimics what will later
be seen in the software
Dru Rose
C1, L2, S8
3 types of claim and rules of thumb:
• Single poll %
51% of young people agree there is too much
1
sex, violence and bad language on TV MoE ≈ √
• Comparison within one group
Young people are more likely to agree than
disagree
MoE for the difference ≈ 2 x MoE
• Comparison between independent groups
Young women are more likely to agree than young
men MoE for the difference
≈ 1.5 x Average MoE
Dru Rose
C1, L2, S9
I wonder what percentage of all 600 Kare
Kare College students travel to school by
car? (“motor” on the cards)
Population 600
students
Sample
n = 25
Dru Rose
C1, L2, S10
For small sample sizes (n=30), sample
proportions (categorical data) are much more
variable than sample means or medians
(quantitative data)
See Wild’s animations
Dru Rose
C1, L2, S11
Looking at the world using
data is
Like looking through a window with ripples
in the glass
“What I see …
is not quite the way it really is”
C1, L2, S12
• Although imperfect, each sample should give a reasonable
picture of the population as a whole.
• In the real world, we usually only have one sample. We want
to use this sample to estimate the population parameter.
(make an inference)
e.g. estimate the percentage of students at Kare Kare College
who travel to school by car.
• Since the sample is representative of the population, we will
re-sample from the sample (with replacement) to estimate the
sample-to-sample variability ie sampling error or margin of
error.
• Re-sampling from the sample is called Bootstrapping
C1, L2, S13
n=100
CI half as long
MoE ≈ 10%
C1, L2, S14
• Repeat coverage module with n=100
n × 4 halves length of CI , MoE =10%
• Repeat bootstrap module with n=500
from whole census at school database
CI length = 9%, MoE = 4.5%
1
1
1
=0.2=20%,
=0.1=10%,
=0.045=4.5%,
√100
√500
√25
Rule of thumb to estimate MoE =
1
√
C1, L2, S15
“Opinion Divided on NZ-US exercises”
Margin of error
=
1
750
= 3.7%
% who support resumption
= 47.6%
47.6%
95% CI:
43.9%
51.3%
With 95% confidence, we can infer that
Meaning:
the % of Nzers who support the
resumption of exercises is somewhere
between 43.9% and 51.3%
Judgement: Claim is supported (CI captures 50%)
C1, L2, S16
Broadcasting Standards Poll
Can it be claimed that:
“More young people agree than disagree
that there is too much sex, violence and
bad language on TV” ?
Dru Rose
C1, L2, S17
Dru Rose
Difference in Poll %s
Consider this scenario:
MoE = 4%
sample
50%
50%
% who agree could be somewhere between
46% and 54%
A likely new sample 46% 54%
Difference in new sample poll %s = 8perct. pts
= 2 × MoE
• A difference of more than 2 × MoE would be
needed to disprove a claim of 50% agree
C1, L2, S18
Broadcasting Standards Poll (1)
Dru Rose
Can it be claimed that more young people agree
than disagree?
Sample Size
Poll MoE
n = 600
MoE difference 2 x 4.1
= 8.2 perc. pts
-1.2
95% CI difference
1
√600
= 4.1%
Difference 51-44
7
= 7 perc. pts
15.2
[ -1.2 perc pts. , 15.2 perc. pts.]
Meaning More young people may disagree than agree by
up to 1.2 perc.pts and more young people may
agree than disagree by up to 15.2 perc. pts
Judgement
Claim Not Supported
C1, L2, S19
MoE for difference = 8.6% (half CI)
MoE Males
1
=6.5%
235
=
MoE Females =
Average MoE =
1
265
=6.1%
6.5+6.1
(
)
2
= 6.3%
Rule of thumb for MoE difference
= 1.5 x Av MoE = 1.5 x 6.3 =9%
We can show that this works about 95% of the time
Dru Rose
C1, L2, S20
Broadcasting Standards Poll (2)
Can it be claimed that young women were more
likely to agree than young men ?
1
1
=
=
5.8%
MoE women =
=5.7%
MoE men
Av MoE
=
307
5.7+5.8
(
)
2
293
= 5.75%
Difference =57-45 = 12 perc. pts
95% CI difference
MoE difference
1.5 x 5.75 = 8.6%
12
3.4
20.6
[3.4 perc pts. , 20.6 perc. pts.]
The % of Young women who agreed was
meaning
somewhere between 3.4 and 20.6 perc. pts more
than the % of young men
Dru Rose
Judgement
Claim is supported
C1, L2, S21
Why teach AS3.12 ?






Statistical Literacy is an essential life-skill to function
effectively in the information age (Wallman, 1993; Gal, 2002)
Broadens students’ horizons, taking statistical understanding
beyond the classroom into the real world (a motivational
aspect for students in the trial)
Accessible to less academic students
External standard
Only pre-requisite is AS2.9 (possibly just 1.10)
Links to other standards students may be taking (formal
inference AS3.10, experiments AS3.11, bi-variate data AS 3.9)
Dru Rose
```