meet the kiwis…
DESCRIPTION
Meet the Kiwis…. Population of kiwis…. Species Weight (kg)Height (cm) Region/gender. 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, - PowerPoint PPT PresentationTRANSCRIPT
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Meet the Kiwis…
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Population of kiwis…Species
Weight (kg) Height (cm)
Region/gender
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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
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Kiwi Kapers 1Take a handful of data cards and sort themWrite some “I notice…” statementsLook at what other people have done
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Problem
I wonder what the median weight of New Zealand kiwis is?
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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.
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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.
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Data
SRS of 15 kiwis Make sure you don’t sample the
same kiwi more than once
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Analysis
Plot dot plot on axes Add box plot above Note the 5 point summary
{Minimum, lower quartile, median, upper quartile, maximum}
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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?
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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….
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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….
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Kiwi Kapers 1Activity recaps…•Language needed (eg population, sample, variables, etc)•PPDAC cycle•Question types•Posing good investigative questions•Sampling issues•dot plot box plot•Describing distributions HANDOUT
Kiwi data cardsKiwi Kapers 1 lessons
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Kiwi Kapers 1What 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 ___
HANDOUT Kiwi data cardsKiwi Kapers 1 lessons
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Kiwi Kapers 1
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Movies – one sample - summaryBox plot with memory…
n = 30
Sketch what you think the box plots with memory would look like for
n = 10n = 100n = 1000
..\..\Pip\Animations_WILD\boxes_1samp_mem_30.pdf
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Movies – one sample - summaryBox plot with memory…
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We want to plant a reflex…
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Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 10
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Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 10
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Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 30
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Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 30
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Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 100
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Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 100
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Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 300
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Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 300
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Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 1000
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Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 1000
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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
HANDOUT Guidelines for “How to make the call”
L6 Guide – incorporates aspects of both spread and sample size
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We want to plant a reflex…
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Kiwi Kapers 2Explores 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 HANDOUT
Kiwi Kapers 2 lessonsKiwi Kapers 2 Fathom lessons
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Go play on Fathom…
… head down to the computer lab with your Kiwi Kapers 2 student fathom document…
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TASK 1 – reflectionWhat 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?
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TASK 2 – reflectionWhat is a sensible and reliable sample size to use to make inferences about a population?
Samples of 30 or 50 are okSamples of 15 are too variableSamples 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
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Kiwi Kapers 3Develops students’ understanding of the L7 guide & informal interval estimates
Under development
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Kiwi Kapers 3Under development
Kiwi population
weight1.5 2.0 2.5 3.0 3.5 4.0 4.5
Kiw ipop Dot Plot
1.5 2.0 2.5 3.0 3.5 4.0 4.5weight
Kiw ipop Box Plot
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Kiwi Kapers 3Under development
Sample mediansn = 30
sample_median1.5 2.0 2.5 3.0 3.5 4.0 4.5
Measures from Sample of Kiw ipop (n=30) Dot Plot
sample_median1.5 2.0 2.5 3.0 3.5 4.0 4.5
Measures from Sample of Kiw ipop (n=30) Box Plot
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Kiwi Kapers 3Under development
Sample mediansn = 400
sample_median1.5 2.0 2.5 3.0 3.5 4.0 4.5
Measures from Sample of Kiw ipop (n=400) Dot Plot
1.5 2.0 2.5 3.0 3.5 4.0 4.5sample_median
Measures f rom Sample of Kiw ipop (n=400) Box Plot
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Kiwi Kapers 3Under development
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?
2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
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Lead into L7 guideline for informal interval estimate
They cover the true population median approximately 9 out of 10 samples taken (shown with simulations)
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Lead into L7 guideline for informal interval estimate
Making the call at L7
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Unit plan still under development…
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And heading towards the assessment…