Evaluate Statistically Based Reports ( AS 3.12)

Dru Rose (Westlake Girls High School, Ministry of Education Study Award)

Workshop 1Margin of Error and Testing Claims in the Media

What does AS 3.12 cover?i. Polls and SurveysNon-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 workshopTo 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)1. The 6 to 7 lesson teaching sequence for

sampling error, with teaching notes2. Power-point slides (sampling error , political

polls)3. 6 media reports4. Students worksheets and resource materials

linked to the teaching sequence5. 3 csv data files to import into iNZight

Dru Rose

C1, L2, S5

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, S6

Dru Rose

C1, L2, S7

3 types of claim and rules of thumb:• Single poll %51% of young people agree there is too much sex, violence and bad language on TV MoE ≈ • Comparison within one groupYoung people are more likely to agree than disagree MoE for the difference ≈ 2 x MoE• Comparison between independent

groupsYoung women are more likely to agree than young men MoE for the difference ≈ 1.5 x Average MoE

Dru Rose

C1, L2, S8

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, S9

3 types of claim and rules of thumb:• Single poll %51% of young people agree there is too much sex, violence and bad language on TV MoE ≈ • Comparison within one groupYoung people are more likely to agree than disagree MoE for the difference ≈ 2 x MoE• Comparison between independent

groupsYoung women are more likely to agree than young men MoE for the difference ≈ 1.5 x Average MoE

Dru Rose

C1, L2, S10

I wonder what percentage of all 600 Kare Kare College students travel to school by car? (“motor” on the cards)

Sample

n = 25

Population 600 students

Dru Rose

C1, L2, S11

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, S12

Like looking through a window with ripples in the glass

“What I see …is not quite the way it really is”

Looking at the world using data is

C1, L2, S13

• 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, S14

n=100

CI half as longMoE ≈ 10%

C1, L2, S15

• 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%

=0.2=20%, =0.1=10%, =0.045=4.5%,

Rule of thumb to estimate MoE =

C1, L2, S16

“Opinion Divided on NZ-US exercises” Margin of error

% who support resumption

95% CI:

Meaning:

Judgement:

47.6%51.3%43.9%

= = 3.7%

= 47.6%

With 95% confidence, we can infer that the % of Nzers who support the resumption of exercises is somewhere between 43.9% and 51.3%

Claim of 50% support for resumption ofexcercises NOT supported since supportcould be as low as 43.9%.

C1, L2, S17

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, S18

Difference in Poll %sConsider this scenario: MoE = 4% sample

% who agree could be somewhere between 46% and 54% A likely new sample

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

50% 50%

54%46%

Dru Rose

C1, L2, S19

Can it be claimed that more young people agree than disagree?

Broadcasting Standards Poll (1)

Sample Size Poll MoE

MoE difference Difference

95% CI difference

Meaning

Judgement

n = 600 = 4.1%

2 x 4.1 = 8.2 perc. pts

51-44= 7 perc. pts

[ -1.2 perc pts. , 15.2 perc. pts.]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

Claim Not Supported

7-1.2 15.2

Dru Rose

C1, L2, S20

MoE for difference = 8.6% (half CI)

MoE Males = =6.5%

MoE Females =6.1%

Average MoE = () = 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, S21

Broadcasting Standards Poll (2)Can it be claimed that young women were more likely to agree than young men ?

MoE women MoE men= =5.7% = =5.8%

Av MoE = () = 5.75% MoE difference1.5 x 5.75 = 8.6%

95% CI difference [3.4 perc pts. , 20.6 perc. pts.]Difference

meaning The % of Young women who agreed was somewhere between 3.4 and 20.6 perc. pts more than the % of young men

Judgement Claim is supported

123.4 20.6=57-45 = 12 perc.

pts

Dru Rose

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