Inference+AS+3.10

=Final summing up:= AS 3.10 Statistical Inference – getting a smooth flow in your assessment

Brief notes

Question

Sample Graphs

Features:

Finish these off with talking about the difference between the sample medians and how they can vary when another sample it taken?

Therefore why is it we form a bootstrapping interval? Eg: I've used bootstrapping because the data was not normally distributed.

Bootstrapping:

Inference comment: I am confident that the difference in medians between -- ---for males and their --- and­­lies between -- and from the NZ Secondary School students at census at schools (population). OR I am reasonably confident that for this population of NZ Sec School students from census at schools the median footlength of - -males and -females - is between and ---2.4  and ---4.9cm--
 * Make sure you use units **

Explain what it means. From these samples, I am reasonably confident that the median footlength of males from. the NZ sec school students on census at school is somewhere between 2.4 and 4.9cm longer than the median footlength of females from the NZ sec school students on census at school

OR As 0 is contained in the interval for the difference of two medians between ---for --- and­­­­­­­­-, from (population) then there is insufficient evidence to make a call. Explain what it means.

Because zero lies in the CI for the difference of two medians between...... and ........ for............, it means that I do not have enough evidence to make a call for as the median could be below zero or above zero.

Conclusion Why select medians? Because the range is larger due to skewed data (or abnormally distributed data) hence those outer values will not affect the median but would affect the mean. Re-iterate the confidence interval - see above What backs up my inference? - research you've done Is it what I expected? refer to your prediction if you made one at the beginning, OR just comment on whether this is what you expected. Is there any research which backs up my inference (agrees with my inference)

=Putting it all together= Use the statistical enquiry cycle!! Make sure you discuss each stage!

Purpose of Investigation Pose a comparison investigation question Make sure you clearly define the comparison and the population. Clearly identify your variables

Outline your plan

Analysis Identify the size of your sample Calculate statistics sample statistics that reflect centre and spread Display as appropriate graphs eg. overall visual comparison using Box and Whisker, dot plot Discuss graphs and statistics Centres Shape Shift, overlap and spread – is the median inside both boxes Look at difference between medians and the overall visible spread. Any unusual features Sampling variability Do confidence intervals using bootstrapping Make a statistical inference

Conclusion

=Exemplars:= =Practice exams/answer schedules=

=Make sure you include in your assessment:=

Produce a report that shows used each component of the statistical enquiry cycle.: 1. Pose a **comparison investigation question** using a given multivariate data set that clearly identifies the comparison and the population(s).
 * Use statistical methods to make a formal inference – Student summary**


 * Example: I will investigate whether there is a difference between the female and male median foot lengths for NZ Secondary School students from Census at schools. The data has been provided by Census at School. **

2. Select and use **appropriate displays and summary statistics**. - Dotplots and Boxplots are drawn for each set of data - Summary statistics - Calculate the point estimate of difference between the two population medians. ** Eg: State the difference between the sample medians. Explain that this gives an estimate but it is better to use 'bootstrapping' to find a confidence interval where the population median may lie between. ** 3. ** Identify and compare ** (**at least two**) features of their sample distributions using features of their displays and their summary statistics. This could involve comparing: 4. ** Discuss the sampling variability **, including the variability of their estimates. They should: - Identify the size of their sample(s) - Identify whether they will use the mean(s) or the median(s) to estimate the difference ** (We are only using Medians, so communicate this) ** - Use a statistical method that takes into account sampling variability and the variability of estimates ** Eg: we are using bootstrapping to find a CI because the sample did not produce a perfectly normally distributed graph ** 6. ** Communicate their findings in a conclusion ** (formal inference) by taking their results from the resampling method to answer the question they initially posed. // . //
 * Shift/centre
 * Spread
 * Shape
 * Unusual features
 * 5. **** Describe how to estimate the difference ** by using a formal inference and then make an appropriate formal statistical inference. This will be done using a resampling (bootstrapping) method to construct a confidence interval.

=Lessons:=


 * 5 September 2013 - Your HW (due on Monday) is to read and complete pgs 17-20 of your booklet**
 * You will be using computers and data sets from Ex 6.03 and Ex 6.04 today (worksheets we've been using this week).
 * You will find these data sets in the 'shared docs' under '13MS' You will need to open up each file and save it to your documents first. Or open them here:[[file:Ex 6.03.xlsx]][[file:Ex6.04.xlsx]]
 * The aim of this lesson is to ensure you can use the inzight programme, describe features of graphs and find statistical information (eg: LQ, median, mean etc.).
 * ** Note: when you open inzight select 'Run Inzight' near the top **
 * Work through Ex. 6.03 of your work sheet (it has pg 41 at the top of it). Do numbers 4 to 6 on inzight. Then, over the page, work through Ex 6.04 of your work sheet and do numbers 1-4.
 * Now we will work on the 3.10 booklets you were given, pg's 11 to 16 using inzight (Note: this time you will select 'Run selected VIT module' near the bottom'). Follow all the steps in the book.


 * 6 September 2013 **
 * Work through Ex. 6.03 of your work sheet (it has pg 41 at the top of it). Do numbers 4 to 6 on inzight. Then, over the page, work through Ex 6.04 of your work sheet and do numbers 1-4.
 * Now we will work on the 3.10 booklets you were given, pg's 11 to 16 using inzight (Note: this time you will select 'Run selected VIT module' near the bottom'). Follow all the steps in the booklets.
 * Now start on Confidence Intervals from your booklets. pg 21 to 26. Read pg 21, then you will need to use inzight for pgs 22 onwards


 * 9 September (Monday)**

Ensure you have covered the work from the two previous lessons (5 & 6 Sep). HW is due today too (pgs 17-20 of your booklet)
 * Today we are using InZight and we will be displaying Confidence Intervals. Read pg 27 of your booklet to see what to expect. The nulake data we are using is here:[[file:Nulake data Formal Inference IAS3_10.xlsx]]
 * Read and do Pg 28 (using the data above)
 * Skip pg 29, and work through pg 30 and 31


 * 10 September, Tuesday**
 * Work through the worksheet on bootstrapping manually
 * Today we are 'Resampling using Bootstrapping' p53-63. You will need this data: [[file:pg 60 take 2.xlsx]]


 * 16 September, Monday - Finish this practice we started on Friday - email it to me for marking: nathans@freyberg.ac.nz.**
 * Check out the 'student summary' hand out for what you must cover to Achieve in this assessment (it's also near the top of this page)
 * Using inzight data (Census at Schools) we are going to do a practice assessment, **comparing male and female arm span lengths** (always use medians). The data is collect from Census at Schools.


 * HERE IS YOUR TASK**
 * Census at Schools collects data from students all over NZ; hence, the data sets you are using are from NZ Secondary School students. For the purposes of this practice assessment your variables have been selected for you (You will have to select your own in the assessment AND do background research).

Use the statistical enquiry cycle to conduct your investigation and to write a report describing the investigation. 1. 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. 2. Identify the variables you wish to investigate, and establish a related investigative comparison question. 3. Conduct your investigation and write a report containing: As you write your report, take care to link your discussion to the context and to support your statements by referring to statistical evidence.
 * your comparison investigative question
 * 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.


 * 17 September (Tuesday) - PRACTISE ASSESSMENT**




 * 18 September**

Now do this practice assessment from NZQA:


 * 19 September**
 * Try the practice Internal Assessment task on page 64 & 65 of your booklet. The data you need is here: [[file:Practice Task in IAS Book.xlsx]]