Informal Inference Revisited ^ The eyes have it Maxine - PowerPoint PPT Presentation

The eyes have it The ideas in this talk have developed …. through a long series of brainstorming sessions about informal inference with: about informal inference with: Informal Inference Revisited ^ The eyes have it Maxine Pfannkuch Matt Regan Nick Horton U. of Auckland, NZ Smith College, MA, USA Chris Wild Dept of Statistics, University of Auckland p , y New Zealand “Informal statistical inference” “Informal statistical inference” • important new element of the new We will … curriculum i l • Start with the big ideas of statistical inference What is it? • Describe simple methods for students to apply when looking at their own data h l ki t th i d t • plain old statistical inference, but … f – Minimise steps that lead students to take their – operated simply enough for young students p p y g y g eyes off the data – “ Exploit the power of the visual sense ”

The eyes have it The eyes have it Let’s look at some data the eyes have it ! the eyes have it ! from http://www.censusatschool.org.nz/ How did they travel to school ? y How did they travel to school ? y Sample of size 100 Sample of size 100 50 50 40 40 4 4 30 30 cent cent Perc Perc 20 20 10 10 Sample of size 100 50 0 0 bike bus car other train walk bike bus car other train walk 40 30 Percent 20 10 0 bike bus car other train walk

How did they travel to school ? y Comparing heights of boys and girls at age 12 Sample of size 100 Sample of size 100 Heights of boys and girls aged 12 50 50 from samples of size 30 40 40 30 3 4 Percent 20 Boys 30 10 cent Perc 0 20 bike bus car other train walk Girls 10 Sample of size 100 50 0 bike bus car other train walk 80 100 120 140 160 180 200 40 30 Percent 20 10 0 bike bus car other train walk Comparing heights of boys and girls at age 12 Comparing heights of boys and girls at age 12 Heights of boys and girls aged 12 Heights of boys and girls aged 12 from samples of size 30 from samples of size 30 Boys Boys Girls Girls 80 100 120 140 160 180 200 80 100 120 140 160 180 200

Heights of boys and girls aged 12 Population distributions Boys Girls Armspan vs Height: Samples of size 200 Armspan vs Height: Samples of size 200 00 00 20 20 150 150 span span arms arms 100 100 50 50 100 100 120 120 140 140 160 160 180 180 200 200 100 100 120 120 140 140 160 160 180 180 200 200 height height

Armspan vs Height: Samples of size 200 Armspan vs Height: Samples of size 200 00 00 20 20 150 150 span span arms arms 100 100 50 50 100 100 120 120 140 140 160 160 180 180 200 200 100 100 120 120 140 140 160 160 180 180 200 200 height height Armspan vs Height: Samples of size 200 Armspan vs Height: Samples of size 200 200 200 150 150 an n armspa armspa 100 100 0 50 0 50 100 120 140 160 180 200 100 120 140 160 180 200 height height Armspan vs Height: Samples of size 200 Armspan vs Height: Samples of size 200 00 00 20 20 150 150 span pan arms arms 100 100 50 50 100 120 140 160 180 200 100 120 140 160 180 200 height height

Description versus inference p • Description is what I see in the data in hand – Theme: “ Right here, right now ” – Fat Boy Slim Th “ Ri ht h i ht ” F t B Sli • Inference is what I think is likely to be Inference is what I think is likely to be The nature of statistical inference happening back in the populations, back where these data came from back where these data came from – Theme: “ Back in the USSR ” – Beatles – We have a natural propensity to move early to inference inference • Many unclear in their thinking & communication when they are describing and when inferring h th d ibi d h i f i . Description theme Inference Theme How do we make inferences? We will be concentrating on inference but We will be concentrating on inference, but … • Often from coming to believe that something I see in these data is a reflection of I i th d t i fl ti f something occurring back in the populations To see the richness of the interplay between description y and inference at work • Always know that what we see is, at best, an imperfect reflection of the way it really i f t fl ti f th it ll is back in the populations see Handout 2 ( on the website )

Armspan vs Height: Samples of size 200 But … But … Armspan vs Height: Samples of size 200 200 200 150 150 an n armspa armspa 100 100 50 0 50 0 100 120 140 160 180 200 100 120 140 160 180 200 height height Armspan vs Height: Samples of size 200 Armspan vs Height: Samples of size 200 00 00 20 20 150 150 span pan arms arms 100 100 50 50 100 120 140 160 180 200 100 120 140 160 180 200 height height Armspan vs Height: Samples of size 200 Armspan vs Height: Samples of size 200 200 200 150 150 an n armspa armspa 100 100 0 50 50 0 100 120 140 160 180 200 100 120 140 160 180 200 height height Armspan vs Height: Samples of size 200 Armspan vs Height: Samples of size 200 00 00 20 20 150 150 span pan arms arms 100 100 50 50 100 120 140 160 180 200 100 120 140 160 180 200 height height

“What I see is not quite the way it really is” y y Metaphor to set the stage for statistical inference Metaphor to set the stage for statistical inference “ What I see … is not quite the way it really is ” “What I see is not quite the way it really is” y y “What I see is not quite the way it really is” y y More Allows me to make more precise claims Bigger sample size information about what is happening back in the population

How did they travel to school ? y Sample of size 100 Sample of size 100 50 50 40 Let’s look at some sampling Let s look at some sampling 40 30 3 4 Percent 20 variation 30 10 cent Perc 0 20 bike bus car other train walk 10 Sample of size 100 50 0 bike bus car other train walk 40 30 Percent 20 10 0 bike bus car other train walk Play movie Bar Chart Animations “What I see is not quite the way it really is” Play Play • Samples of 1000 p • Samples of 200 • Samples of 100 S l f 100 • Samples of 50 p • Samples of 30 • Samples of 30 without jitter S l f 30 ith t jitt

“What I see is not quite the way it really is” Comparing heights of boys and girls at age 12 • What can we learn from proportions taken from samples of size 30? p – Very little !! Heights of boys and girls aged 12 Heights of bo s and girls aged 12 from samples of size 30 • Information content of category data points category data points Boys “Do you fall into this category? Yes/No” is very small Girls • Need very large samples b f before can say anything hi very useful 80 100 120 140 160 180 200 – Unfortunate fact of life! Unfortunate fact of life! Play movie – Situation better with measurement data

Dot and Boxplot Animations Boxplots with a Memory I Play Play 1-sample build-up, n=30 1 sample build up n=30 Play • Original 2-sample • Original 2-sample • Effect of sample size Boxplots with a Memory II Want to plant a reflex p “Whenever I see … “I remember … “ b Play • 1-sample build-up n=30 • 1-sample build-up, n=30 “Mine could even be like this …” • 2-sample build-up, n=30 • 1-sample build-up, n=200 • 2 sample build up n=200 • 2-sample build-up, n=200 “Or even this …” “I must take this uncertainty I must take this uncertainty about where it really should be into account when I make comparisons!”

Want to plant a reflex p But must ensure students don’t just see it as … “Whenever I see … Computer Computer Computer Computer M M Mag agic i i “I remember … “ b “Mine could even be like this …” Must securely anchor Must securely anchor to something real and believable and believable “Or even this …” -- Maxine & Pip have great ideas “I must take this uncertainty I must take this uncertainty about where it really should be into account when I make comparisons!”