Stats-Day22-Nov-AS3.12-MoE-presentation

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 ≈ √𝑛

• 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 ≈ √𝑛

• 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 √𝑛 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 of 50% support for resumption of excercises NOT supported since support could be as low as 43.9%.

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