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# 3.10 Inference Practice Assessment

12

Putting it all together

You will be give a data set with quantitative and qualitative variables. Decide what are your two groups and what your comparative variable will be.
Assessment Checksheet Doc Class notes

You will then have to analyse the data and write a report - showing evidence of each component of the Statistical Cycle: Pose a Question, Plan, Display, Analysis, Conclusion.

Review: Achievement Objectives

Manipulating data in Excel
This can be a good idea, especially to combine groups together before doing analysis in iNZight
Practice combing lisence types or age groups in the Car crash data

Good practice data sets and material on http://www.mathsnz.com

Example assessments on TKI (car crash & elite athletes)

Exemplar, Elite Athletes,
Data set
Write up:
Assessment information
Introduction

Sample Discussion
Bootstrap Discussion
Conclusion

Car Crash Injury Practice:
Data set, csvVariable Info
Worksheet
NZQA annotated exemplars

3.10 Inference by Jeremy Brocklehurst
Video 1 - Getting Started

Video 2 - Analysis
Video 3 - Bootstrap Confidence Interval
Video 4 - Inference Conclusion

### Remember: You Have to run iNZight TWO times!

The iNZight tips page has information on ordering, removing, grouping, re-categorising, & exporting data, and creating variables, adding variables to create box plots and show summary statistics. (Adding another variable can also provide more information)

1) To Analyse the Sample

2) To make a Bootstrap Confidence Interval

Prior to the assessment you will be given information on the context.

You should do some research into to context to gain prior understanding to help during the assessment and have material to discuss in your report. You will be able to bring this contextual research into the assessment.

### 1) Generic Assessment Instructions: (get familiar with these)

Use the statistical enquiry cycle to conduct your investigation and to write a report describing the investigation.

Familiarise yourself with the data set provided. This will include doing research to help you understand the variables and develop a purpose for the investigation.

Identify the variables you wish to investigate, and establish a related investigative comparison question.

Conduct your investigation and write a report containing:
- appropriate displays and summary statistics
- a discussion of the sample distributions
- an appropriate formal statistical inference
- a conclusion communicating your findings, including discussing sampling variability, the variability of estimates, and reflecting on the process that has been used to make the formal inference.

As you write your report, take care to link your discussion to the context and to support your statements by referring to statistical evidence.

### 2) What is expected...(based on the PPDAC cycle)

Report Writing

(1) Pose a Question

Purpose of Investigation.

Variables Defined & Data Source.

Comparative Investigative Question.

Achieve
- Identify two groups to compare.
- Define the variable being compared (and units)
- Describe the purpose for the investigation.
- Some reference to own research done (could be infered)
- Comparative Research Question:
"Is there a difference between the MEDIAN of (group) and (group) in the (population)"

Merit
Achieve and...
- Explains the reasoning behind choice of variable.
- Make a prediction.
- References made to own research done

Excellence
Merit and...
- Justify the choice of variable(s) to investigate from the data set with respect to a clear purpose for the investigation.
- Explains choice for using the mean or median.
- Justify / reasoning for your prediction.

(2) Plan

Using existing data sets & selecting groups and an applicable variable to compare.

(3) Display

Graphs (with labels)

Summary (sample) Statistics

Achieve
- At least one appropriate graph.
- Add graph labels & Units.
- Sample Summary statistics table.
- The difference between appropriate sample statistics calculated.

Merit & Excellence
Achieve and...
- Dot & Box plots (easy using iNZight)

(4) Analysis:

Describing and Comparing Sample Distributions:
- Initial Visual Interpretation
- Shape (Skew, Tail, symmetry)
- Centre
- Shift/Overlap
- Unusual Features (outliers, gaps)

Discussion of Sample Distributions:

Achieve
- Sample distributions compared in context using features of displays and summary sample statistics. (use numbers)

Merit
Achieve and...
- Links discussion to population or investigative question.
- Is clearly showing the difference between sample and population in discussion.

Excellence
Merit and...
- Seeks explanations for features and considers impact of these on context or question.
- Refers to knowledge from research.

(5) Analysis:

Sample Variability

Achieve / Merit / Excellence
- Recognises sampling variability, including variability of estimates.
- Discussion of Sample variability
- Some argue that this is recognised by using bootstrapping to construct a confidence interval and using the interval to make a formal inference about difference between the two groups population medians.

(6) Analysis:

Statistical inference

Achieve
- Correctly interprets inclusion (or not) of zero in difference of means/medians confidence interval.
- Population parameter identified (mean or median)

Merit
Achieve and...
- contextually explains the interpretation. What does this mean?
- Some level of uncertainty shown, "I can be reasonably sure that..."

Excellence
Merit and...
- Relates confidence interval to whether the original sample is representative.
- Discussion of assumptions.

(5) Conclusion

Achieve

Merit
Achieve and...
- Formal inference used to answer question with justification and links to context.
- Includes interpretation of the confidence interval.
- An understanding of sampling variability is also evident.

Excellence
Merit and...
- Findings clearly communicated and linked to population and context.
- Further reflection on process or further explanations for findings.

Notes:

For the assessment students will be provided with a data set containing multiple variables.

Background information related to the data set will be provided. There should be sourcing of relevant contextual knowledge about the situation under investigation from places such as the internet, the school or local library, newspapers and magazines. These sources should be referenced in their report.

## Achieve

(1) Pose a Question
- Identify two groups to compare.
- Define the variable being compared (and units)
- Describe the purpose for the investigation.
- Some reference to own research done (could be infered)
- Comparative Research Question:
"Is there a difference between the MEDIAN of (group) and (group) in the (population)"

(3) Display
- At least one appropriate graph.
- Add graph labels & Units.
- Sample Summary statistics table.
- The difference between appropriate sample statistics calculated.

(4) Analysis:
Describing and Comparing Sample Distributions:
- Initial Visual Interpretation, Shape (Skew, Tail, symmetry), Centre, Spread, Shift/Overlap, Unusual Features (outliers, gaps)
- Sample distributions compared in context using features of displays and summary sample statistics. (use numbers)

(5) Analysis: Sample Variability
- Recognises sampling variability, including variability of estimates.
- Discussion of Sample variability
- Some argue that this is recognised by using bootstrapping to construct a confidence interval and using the interval to make a formal inference about difference between the two groups population medians.

(6) Analysis: Statistical inference
- Correctly interprets inclusion (or not) of zero in difference of means/medians confidence interval.
- Population parameter identified (mean or median)

(5) Conclusion

## Merit

(1) Pose a Question
- Identify two groups to compare.
- Define the variable being compared (and units)
- Describe the purpose for the investigation.
- Comparative Research Question:
"Is there a difference between the MEDIAN of (group) and (group) in the (population)"
- Explains the reasoning behind choice of variable.
- References made to own research done
- Make a prediction.

(3) Display
- At least one appropriate graph.
- Add graph labels & Units.
- Sample Summary statistics table.
- The difference between appropriate sample statistics calculated.
- Dot & Box plots (easy using iNZight)

(4) Discussion of Sample Distributions:
Describing and Comparing Sample Distributions:
- Initial Visual Interpretation, Shape (Skew, Tail, symmetry), Centre, Spread, Shift/Overlap, Unusual Features (outliers, gaps)
- Sample distributions compared in context using features of displays and summary sample statistics. (use numbers)
- Links discussion to population or investigative question.
- Is clearly showing the difference between sample and population in discussion.

(5) Analysis: Sample Variability
- Recognises sampling variability, including variability of estimates.
- Discussion of Sample variability
- Some argue that this is recognised by using bootstrapping to construct a confidence interval and using the interval to make a formal inference about difference between the two groups population medians.

(6) Analysis: Statistical inference
- Correctly interprets inclusion (or not) of zero in difference of means/medians confidence interval.
- Population parameter identified (mean or median)
- contextually explains the interpretation. What does this mean?
- Some level of uncertainty shown, "I can be reasonably sure that..."

(5) Conclusion
- Formal inference used to answer question with justification and links to context.
- Includes interpretation of the confidence interval.
- An understanding of sampling variability is also evident.

## Excellence

Merit and...

(1) Pose a Question
- Identify two groups to compare.
- Define the variable being compared (and units)
- Describe the purpose for the investigation.
- Comparative Research Question:
"Is there a difference between the MEDIAN of (group) and (group) in the (population)"
- Explains the reasoning behind choice of variable.
- Make a prediction.
- Justify the choice of variable(s) to investigate from the data set with respect to a clear purpose for the investigation.
- Explains choice for using the mean or median.
- Justify / reasoning for your prediction.

(3) Display
- At least one appropriate graph.
- Add graph labels & Units.
- Sample Summary statistics table.
- The difference between appropriate sample statistics calculated.
- Dot & Box plots (easy using iNZight)

(4) Discussion of Sample Distributions:
Describing and Comparing Sample Distributions:
- Initial Visual Interpretation, Shape (Skew, Tail, symmetry), Centre, Spread, Shift/Overlap, Unusual Features (outliers, gaps)
- Sample distributions compared in context using features of displays and summary sample statistics. (use numbers)
- Links discussion to population or investigative question.
- Is clearly showing the difference between sample and population in discussion.
- Seeks explanations for features and considers impact of these on context or question.
- Refers to knowledge from research.

(5) Analysis: Sample Variability
- Recognises sampling variability, including variability of estimates.
- Discussion of Sample variability
- Some argue that this is recognised by using bootstrapping to construct a confidence interval and using the interval to make a formal inference about difference between the two groups population medians.

(6) Analysis: Statistical inference
- Correctly interprets inclusion (or not) of zero in difference of means/medians confidence interval.
- Population parameter identified (mean or median)
- contextually explains the interpretation. What does this mean?
- Some level of uncertainty shown, "I can be reasonably sure that..."
- Relates confidence interval to whether the original sample is representative.
- Discussion of assumptions.

(5) Conclusion