Meet the Kiwis…

Population of kiwis…

Codes… Species Region GS-Great Spotted, NIBr-NorthIsland Brown, Tok-Southern Tokoeka NWN-North West Nelson, CW-Central Westland, EC-Eastern Canterbury StI-Stewart Island, NF-North Fiordland, SF-South Fiordland N-Northland, E-East North Island, W-West North Island

Kiwi Kapers 1 Take a handful of data cards and sort them Write some “I notice…” statements Look at what other people have done

Problem  I wonder what the median weight of New Zealand kiwis is?

I wonder what the median weight of New Zealand kiwis is?  What do you think the typical weight will be?  Why?  Sketch the shape of the distribution of weights of New Zealand kiwis.

Plan  What variable are we going to use to answer our question?  How are we going to gather our data?  Everyone?  Sample?  Simple random sample of 15 kiwis please.

Data  SRS of 15 kiwis  Make sure you don’t sample the same kiwi more than once

Analysis  Plot dot plot on axes  Add box plot above  Note the 5 point summary  {Minimum, lower quartile, median, upper quartile, maximum}

Analysis  Repeat three more times to complete 4 sets of 15 samples  Write (at least) three “I notice…” statements about your samples  Look at shape and spread – what do you notice?  Similarities? Differences? – between your sets of samples…  Make sure your statements include context  Would I be able to tell that you were looking at the weight of Kiwis?

Conclusion Use sample median to provide a point estimate of the population parameter  From my sample data I estimate that the median weight for all New Zealand kiwis is….

Conclusion  But they’re all different!  Who is right?  From my sample data I estimate that the median weight for all Stage 1 statistics students is….

Kiwi Kapers 1 Activity recaps… Language needed (eg population, sample, variables, etc) PPDAC cycle Question types Posing good investigative questions Sampling issues dot plot  box plot Describing distributions HANDOUTKiwi data cardsKiwi Kapers 1 lessons

Kiwi Kapers 1 What do you think the population distribution will look like? *most values are between ___ & ___ * the largest value is about ___ * the smallest value is about ___ * the middle is around ___ HANDOUTKiwi data cardsKiwi Kapers 1 lessons

Kiwi Kapers 1

Movies – one sample - summary Box plot with memory… n = 30 Sketch what you think the box plots with memory would look like for n = 10 n = 100 n = 1000 ..\..\Pip\Animations_WILD\b oxes_1samp_mem_30.pdf..\..\Pip\Animations_WILD\b oxes_1samp_mem_30.pdf

Movies – one sample - summary Box plot with memory…

We want to plant a reflex…

Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 10

Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 10

Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 30

Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 30

Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 100

Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 100

Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 300

Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 300

Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 1000

Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 1000

Sample size vs making the call… If the samples are larger, the difference between the two groups doesn’t have to be as big to make the call that there is a difference between them BACK IN THE POPULATION HANDOUTGuidelines for “How to make the call” L6 Guide – incorporates aspects of both spread and sample size

We want to plant a reflex…

Kiwi Kapers 2 Explores what sample size we want to take to be reasonably sure that the inference(s) we make are representative of the population. I wonder what are typical weights of kiwis? What is a sensible and reliable sample size to use for making inference about a population HANDOUTKiwi Kapers 2 lessonsKiwi Kapers 2 Fathom lessons

Go play on Fathom… … head down to the computer lab with your Kiwi Kapers 2 student fathom document…

TASK 1 – reflection What appears to be the effect of increasing the sample size on: (i) the median from sample to sample? (ii) the IQR from sample to sample? (iii) the range from sample to sample?

TASK 2 – reflection What is a sensible and reliable sample size to use to make inferences about a population?  Samples of 30 or 50 are ok  Samples of 15 are too variable  Samples of 100, while even better, are not so much better that we need to spend the extra time and energy (and $) collecting 100 kiwis when 30 or 50 will do  We want the smallest sample that should give us a reliable estimate of the population

Kiwi Kapers 3 Develops students’ understanding of the L7 guide & informal interval estimates

Kiwi Kapers 3 Kiwi population

Kiwi Kapers 3 Sample medians n = 30

Kiwi Kapers 3 Sample medians n = 400

Kiwi Kapers 3 Together population n=30 n=400 … ideas of how to put an interval estimate around our point estimate … is one IQR enough? … impact of sample size?

Lead into L7 guideline for informal interval estimate They cover the true population median approximately 9 out of 10 samples taken (shown with simulations)

Lead into L7 guideline for informal interval estimate Making the call at L7

Unit plan still under development…

And heading towards the assessment…