Excellence Skills: All of the below are included.

  • Statistical insight (Link statistics to research is the key to showing your statistical insight.)
  • further depth of thinking demonstrated with clear contextual links
  • greater understanding of sampling variability (explain how bootstrapping works)
  • understanding of coverage of the confidence interval(s)
  • no errors demonstrated in understandings, interpretation or explanation of findings/data.
http://2013stats.wikispaces.com/3.10+Merit shows how you could end up with Merit.
Please note the standard of excellence will increase, as you now have some experience with this type of assessment.



Problem

  • Research into background of context to give purpose to the investigation
  • Comparison question includes:
  • Variable that is being examined (eg. height in cm)
  • Groups that are being compared (eg. Year 11 boys and Year 11 girls)
  • Population that inferences are being made about (eg. New Zealand Year 11 boys and New Zealand Year 11 girls)
  • Population Parameter / Sample Statistic (eg. DIFFERENCE in median and mean heights between boys and girls. Choose the best measure and compare the two)
  • Prediction of what students expect to see in their analysis and why
  • Note: you are using a sample statistic to estimate a population parameter (median)

Plan

  • as per 3.8 and 3.9

Data

  • State the source and explain the units etc

Analysis

  • iNZight graphs (Code extra variables, perhaps remove outliers IF they are ERRORS!)
  • Comparative statements will include discussion about the difference in medians AND means
  • Justify your choice of mean or median, do BOTH and compare.
  • Comparative statements will make contextual links back to the population and initial research (the “so what?” factor)
  • Randomisation could be used as another way of checking there is a difference.

Conclusion

  • Interpretation of formal confidence interval
  • Sample TO=> population link strong
  • Some level of uncertainty evident (“pretty sure”)
  • Population parameter identified
  • Correct call, with justification
  • Should reflect investigative question
  • Call based on whether zero is contained within the interval or not - Direction of evidence (if zero outside of interval)
  • Linking back to the context and using initial research to help explain what this means (the “so what?” factor)
  • Explain what bootstrap confidence intervals are http://en.wikipedia.org/wiki/Bootstrapping_(statistics)

http://learnandteachstatistics.wordpress.com/2013/04/29/median/



Some extra activities for Excellence Students to develop their understanding





The blog about the median from Dr. Nic suggests this video...
http://learnandteachstatistics.wordpress.com/2013/04/29/median/


Language: http://www.stats.gla.ac.uk/steps/glossary/basic_definitions.html#param

Marking a Students Work





StatisticalConcepts.jpg
The above is for Year 10: What we are up against is that students do not remember doing it in Year 10!
The table is from: http://new.censusatschool.org.nz/wp-content/uploads/2013/02/TSG12_Arnold.pdf
Just a random note: If the Median and Mean are different then the data is skewed.