Introduction to making an inference

Examples in the media

Idea of sampling

Learn Box and Whisker plot

Inzight is the software to analyse data

How to get it and install?

An activity from Census At School: Kiwi Kaper

Key words:

Achievement Standard clarification

91264 Use statistical methods to make an inference

Problem

Plan and Data

Analysis

Conclusion

Plan

Data

Analyse

Interpret Box Plot

Making a statistical ‘call’  (inference)

Exemplar: report writing

Problem: question

Plan: sampling (why did you choose this sampling process?)

Data: display

Data: Summary Statistics

Analysis:

(Obvious-Specific-Evidence-Meaning) (Acronym: OSEM)

(Acronym: SSSOU)

Inference:

Conclusion (answer to your posed question)

Sampling variability statement: ( you must write)

Note:

NZ Grapher: instruction

Introduction to making an inference

Following are address of links.  To easily view the video clips go to the individual page of this site.

Examples in the media

Watch the videos on Video_sampling page.

Idea of sampling

What is inference in statistics?

Data and statistics_Khan Academy

Dancing Statistics  (https://www.youtube.com/watch?v=5fGu8hvdZ6s)

Dancing Statistics: variance_measure of variation

(https://www.youtube.com/watch?v=pGfwj4GrUlA)

Take a sample: khan Academy

(https://www.youtube.com/watch?v=k5EbijWu-Ss)

Why sample?

(https://www.youtube.com/watch?v=IOBYsdgGhVw)

More on sample

(https://www.youtube.com/watch?v=xt9LB5l3O8g)

The Island_video_sampling & other considerations

Learn Box and Whisker plot

Easy way to learn Box Plot

(https://www.youtube.com/watch?v=7Y74etZRIp4)

Khan Academy explains how to interpret with box plot

(https://www.youtube.com/watch?v=oBREri10ZHk)

Inzight is the software to analyse data

How to get it and install?

InZight site address

Or use NZGrapher

NZ Grapher server address_RC  (only can be accessed within RC network)

An activity from Census At School: Kiwi Kaper

Census At School link

2016-04-10-0004.jpg

2016-04-10-0004.jpg

Key words:

Data, Inference, sample size, sampling variability

snag it sample.png

boxes_2samp_mem_10_600.gif

boxes_2samp_mem_30_600.gif

boxes_2samp_mem_100_600.gif

boxes_2samp_mem_1000_600.gif

Achievement Standard clarification

91264 Use statistical methods to make an inference

Updated August 2015. This document has been updated to address issues that have arisen from moderation.

Problem

The investigative question that is posed must involve a comparison and needs to include the variable, the population groups being compared,r the population parameter  the inference will be about and the direction of the comparison. A suitable question would be Is the median height of NZ year 12 boys greater than the median height of NZ year 12 girls?

Plan and Data

The investigation involves selecting random samples from the population groups and using information from the samples to make an inference about the population groups. Students must demonstrate an understanding of the population from which the sample will be taken.

Analysis

The informal confidence intervals for the population medians must be used to answer the investigative comparison question. At Merit and above the informal confidence intervals must be interpreted in context. For example, ‘I am pretty sure that the median height for NZ year 12 boys is somewhere between xxx and yyy’.

The discussion of the sample distributions must be about the distributions of the variables, for example the heights of NZ year 12 boys and NZ year 12 girls, and needs to include numerical values and associated units. The basis of the discussion will be the visual evidence, so students need to be looking at the sample distributions and discussing distinctive features of the distributions.

Sample statistics could be used to justify the observations made from the visual interpretation.

Conclusion

Students must make an inference, which will be a conclusion about the population medians based on the samples taken from the population.

The conclusion must be consistent with the analysis. It will answer the posed investigative question and will involve making a call about the population medians. The informal confidence intervals need be used to make an inference about the population medians.

If there is no overlap in the informal confidence intervals, an appropriate inference is that the population median for ‘A’ is greater than/less than the population median for ‘B’. If there is an overlap in the intervals there is not enough evidence to make a call that the population median for ‘A’ is greater than/less than the population median for ‘B’.

An understanding relating to sampling variability and variability of estimates must be evident. Another sample could give different statistics and different informal confidence intervals. For the inference, the informal confidence intervals are still likely to capture the population parameter.

Posing a statistical question is an important skill which should be learnt in depth.

Scroll up…..

Statistical questions can be of many types. Primarily, we come across two types of questions.

Relationship type,   pose a  question about two variables of a person.

smiling-young-man-standing-hands-pockets-full-length-portrait-isolated-white-background-34741867.jpg

Plan

Data

Analyse

Interpret Box Plot

Making a statistical ‘call’  (inference)

Google Slide: making a statistical 'call'

Level 1 (Year 11) Knowledge review

Sampling variations and developing the concept of confidence interval

picture 1.jpg

picture 1.jpg

Informal Confidence interval (outcome of sampling variability)

  • One sample is shown below with the Median total fat of 33
  • Each student collects a sample i.e may be about 30 samples in a class of 30 students.
  • What will happen to the individual median?
  • Do you think it will be always 33?
  • Note the ‘blue’ band inside the box.
  • The purple box shows the ‘footprints’ which ranges from approximately 31 to just over 33.
  • In statistics we say, ‘we are fairly confident to say the medians will be between 31 to 33’. Usually the level of confidence is about 95%.
  • We have introduced a level of ‘uncertainty’ into our result.

Short clip from Chris Wild's video on Sampling variability

                                                           footprint-trail-clipart-1.jpgFootprints can be imagined showing the movements of the ‘medians’. Medians of different samples.

Total fat footprint final.jpg

Uncertainty of our measurement

=

gives rise to the variability of measurement outcomes

=

confidence interval

=

margin of ‘error’

For example, your teacher says, ‘that measurement is 1.67 m’. Do you think it is exactly 1.67m?

Answer is ‘NO’.

Better statement would be , ‘that measurement is ‘close’ to 1.67m.

Exemplar: report writing

Problem: question

Plan: sampling (why did you choose this sampling process?)

Data: display

Data: Summary Statistics

Analysis:

(Obvious-Specific-Evidence-Meaning) (Acronym: OSEM)

(Acronym: SSSOU)

Analysis:

Analysis:

Analysis:

Analysis:

Inference:

Conclusion (answer to your posed question)

Animation clips on Sampling variability with sample size=10 & 100

Sampling variability statement: ( you must write)

Note:

(During the final report writing students tend to forget to write about the sampling variability)

NZ Grapher: instruction

NZGrapher: instruction

Other important site links for information

Nayland College Maths site

PSSS   and  OSEM (describing distribution of data)

Main features of analysis

Levels of analysis in categories

Notes

Position  (shift)

Obvious

Mean, median or mode.

(relative position)

Median is better for data affected by extreme values.

Specific

Evidence

Numerical values

Meaning

Spread

Obvious

Inter-quartile range (IQR)

Do not use RANGE (affected by extreme values).

Specific

Wide or narrow

Evidence

Numerical values

Meaning

Link it to context, insightful comments.

Shape

Obvious

Skew or symmetric. Very high peak or low peak.

Specific

Further clarification .

Evidence

Numerical value.

Meaning

Link it to the context.

Special

Obvious

Cluster, groups, extreme values, outliers.

Specific

Comparison between groups.

Evidence

Numerical values.

Meaning

Link it to the context.