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Difficulties in learning about sampling and approaches to overcoming these (AS1.10 & 2.9) Jared Hockly - Western Springs College hocklyj@wsc.school.nz hocklyj@wsc.school.nz

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Overview of this session: -Discuss the standards 1.10 and 2.9 briefly (some clarifications) -Focus on developing understanding of sampling variability -Look at a few activities that develop this understanding -Discuss how to get the best out of the learning and assessment of this topic

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Achievement Objectives -Explanatory note 3 AS1.10 Investigate a given multivariate data set using the statistical enquiry cycle Students need to be familiar with the statistical enquiry cycle to investigate a given multivariate data set, which involves: AS2.9 Use statistical methods to make an inference Using the statistical enquiry cycle to make an inference involves: P investigating data that has been collected from a survey situation posing an appropriate comparison question using a given multivariate data set posing an appropriate investigative comparison question from a given set of population data P selecting random samples D A selecting and using appropriate display(s) giving summary statistics such as the five summary values (minimum, maximum, median, quartiles) discussing features of distributions comparatively, such as shape, middle 50%, shift, overlap, spread, unusual or interesting features selecting and using appropriate displays and measures discussing sample distributions C communicating findings, such as informal inference and supporting evidence, in a conclusion. discussing sampling variability, including the variability of estimates making an inference communicating findings in a conclusion.

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Questions for you 1)Why do we teach this topic/standard? (What are our beliefs, What do/should students get out of it) 2)Are we turning students off stats by doing these standards? 3)What do you think it is about sampling variability that makes it tricky?

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Question about population (problem) Answer about population. “making the call” (conclusion) Get/organise your sample data (plan, data) Compare the two groups using graphs and summary stat (Analysis)

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a few off topic points before we get into it ●technology should be used (but not exclusively in the teaching) ●Beware, some data is tricky to ask worthwhile questions about (titanic, world at a glance) ●1.10: don’t need a random process for selecting the data ●Students should be given opportunities to understand the context they are investigating (they need this at higher grades) ●2.9 is a bit odd, sampling from a “population database”...

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Kinda off topic still - How sampling really works -(If possible) generate a list of the population: a sampling frame. (e.g electoral roll, register of schools, list of students) -then randomly choose units for your sample -then you gather the data for those in the sample

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Some of my beliefs about teaching stats -Compartmentalising the skills makes it hard for students to understand what they are really doing -More effective learning of skills is teaching them when there is a need. -Use interesting data, data they may be invested in. -This is hard but: don’t always be critical or accuracy. Let the intuitive statements have some air

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A suggested overview of teaching this topic 1.Do some investigations where you have the whole population to investigate. -e.g are boys better at robot unicorn attack than girls in our class. (Get to do the PPDAC cycle without too much complexity)robot unicorn attack 2.Move onto situations where it is impractical to have/use/collect the whole population. - data cards (similar to karekare college 2009 stats day)karekare college -census at school samples/dataviewer The idea of a sample will develop. Do we all get the same result when we sample?

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A suggested overview of teaching this topic (cont) 3.Develop the idea of sampling variability before they learn rules. The effect of sample size, the effect of the spread of the dataset(s), iNZight could make an appearance here a1 variable variation of sample median (how different can out answers be, looking around the class) -2 variable comparisons of sample medians. Use intuition. 3.They are probably wanting to know when there is a big enough difference for us to make a call 1.10 the rules for making a call 2.9 the formula for confidence interval and the idea of overlap Are they correct with their calls? A mixture of knowing the population results (to see if they got it right and provide closure) and not knowing (because thats the way it really is)

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And back to assessment 1.10 Why not get the students to create the sample, this will ensure they are well informed about the context 2.9 does say “from a given set of population data”. Can we still get them to sample the data in a more real way?

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Takeaways -A desire to adjust the teaching of these topics to: -be engaging in the use of data -uses a range of activities -have multiple investigations developing in complexity -develops understanding of sampling variability (rather than an emphasis on rules and canned statements) -A desire to create better assessments that involve students in the context/data

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Level 6 plan and conduct surveys and experiments using the statistical enquiry cycle - determining appropriate variables - cleaning data - using multiple displays, and re-categorising data to find patterns, variations, in multivariate data sets - comparing sample distributions visually, using measures of centre, spread, and proportion - presenting a report of findings; plan and conduct investigations using the statistical enquiry cycle - justifying the variables used - identifying and communicating features in context (differences within and between distributions), using multiple displays - making informal inferences about populations from sample data - justifying findings, using displays and measures. Level 7 carry out investigations of phenomena, using the statistical enquiry cycle: − using existing data sets − evaluating the choice of sampling and data collection methods used − using relevant contextual knowledge, exploratory data analysis, and statistical inference make inferences from surveys: − using sample statistics to make point estimates of population parameters − recognising the effect of sample size on the variability of an estimate

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