Post on 23-Dec-2015
Time Series –from Achieved to
Excellence
http://www.nzchildren.co.nz/child_poverty.php
What will be coveredTechniques and data that gets students engaged in the topic
Help with the research component
A discussion on forms of assessment
Strategies for ensuring good report writing
AS: Time SeriesUsing the statistical enquiry cycle to investigate time series data involves:
• using existing data sets
• selecting a variable to investigate
• selecting and using appropriate display(s)
• identifying features in the data and relating this to the context
• finding an appropriate model
• using the model to make a forecast
• communicating findings in a conclusion.
Excellence!Investigate time series data, with justification and statistical insight involves integrating statistical and contextual knowledge throughout the statistical enquiry cycle, and may include reflecting about the process; considering other relevant variables; evaluating the adequacy of any models; or showing a deeper understanding of models.
Statistical insight involves integrating statistical and contextual
knowledge
http://www.nzchildren.co.nz/child_poverty.php
Road to excellence?
Students need to:
understand/relate to the context
research it properly and write with insight.
They need a structure to work to in order to organise their brains.
They need to be familiar with the language of statistics.
http://www.point8td.com/perfection-vs-excellence
Fake it until they make it
Understand and relate to context
http://www.bbc.co.uk/blogs/theoneshow/consumer/2009/03/25/truancy-should-the-kids-or-the.html
How do they get here?Students need to start with something that is very familiar that they feel confident talking about.
School!
Relating to the contextStart with something that gets them talking and looking at various issues.
Seed the things you want students to notice and develop especially things like where is the information coming from.
http://members.ebay.com/ws/eBayISAPI.dll?ViewUserPage&userid=boehmer98
Attendance in New Zealand Schools
2012Something they are familiar with
A little about me
Attendance in New Zealand Schools
2012
Get students to use a yellow highlighter
when reading material
Why are we interested in this investigation?
“There has been increasing community, political, and education sector concern over absence from school.”
(Mallari, Loader, 2013)
http://cityview.worcesterschools.org/modules/cms/pages.phtml?sessionid=&pageid=300890
Use referencing in
material given to students
BackgroundA national survey of state primary and secondary schools in New Zealand in 1977 (Taylor, Sturrock and White 1982) reported that the unjustified absence rate in primary schools was 0.69%, and in secondary schools it was 1.4%. Berwick-Emms (1987).
http://studentwork.hss.uts.edu.au/wnm08/scars/source/prischool.html
Broader context – Underlying issue - Referencing
The problem of truancy is shared throughout the world (see Reid 1987, Andrews 1986). Whitney (1994:15), a British researcher, notes that ‘Truancy, like poverty, has a lengthy past history, and the two have always been closely related.
“Chronic absenteeism is most prevalent among low income students.”
Balfanz, 2012
Data Sourcehttp://www.educationcounts.govt.nz/publications
/series/2503
Survey DetailsThe Ministry of Education survey on attendance was carried out in the week 11-15 June, 2012
The response rate was 88%
Schools recording absences on the paper form were required to make their own judgement as to whether a student was absent for all or part of a day, and whether that absence was justified based on the definitions and instructions supplied.
Are comparisons valid?The survey was carried out in the week of 11-15 June 2012, close to the middle of the second school term. This week was the same week of term as the 2009 and 2011 surveys.
By analysing data from a similar time of year, factors such as winter illness would have been at broadly similar levels.
Perspective - numbersIn 2012, approximately 62,000 students were absent from school for all or part of a day during the survey week. Of these, 15,000 students were unjustifiably absent from school.
Tables to visual
Not very good for the messages we want from the data
2004 2006 2009 20110.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
Unjustified Absence Rate (%)Intermittent Unjustified Absence Rate (%)Justified Absence Rate (%)Total Absence Rate (%)Total Unjustified Absence Rate (%)
Who would be interested and why?
2004 2006 2009 2011 20120.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
Percentage absent
Unjustified Absence Rate (%) Intermittent Unjustified Absence Rate (%)Justified Absence Rate (%) Total Absence Rate (%)Total Unjustified Absence Rate (%)
Is this a real decrease or is it pressure on schools by the Ministry to deal with
absences?
2004 2006 2009 2011 20120.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
Unjustified Absence Rate (%)Intermittent Unjustified Absence Rate (%)Justified Absence Rate (%)Total Absence Rate (%)Total Unjustified Absence Rate (%)
Main features:Time periods are not at equal intervals
Total: Between about 10% and 12%Peak: ≈12% in 2009
Drop or leveling out since 2009
2004 2006 2009 2011 20120.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
Percentage absent
Unjustified Absence Rate (%) Intermittent Unjustified Absence Rate (%) Justified Absence Rate (%)Total Absence Rate (%) Total Unjustified Absence Rate (%)
Similarities/Differences/ReasonsWhat other questions should be asked?
Monday Tuesday Wednesday Thursday Friday0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
Total Absence: Day of the week
200920112012
% A
bse
nt
What might be different in the previous graphs if we just looked at secondary?
Full
Prim
ary
inclu
ding
Kur
a Te
ina
Inte
rmed
iate
Seco
ndar
y (Y
ear 7
-15)
Seco
ndar
y (Y
ear 9
-15)
inclu
ding
TPU
and
Kur
a Te
ina
0.02.04.06.08.0
10.012.014.016.0
School Type
Total Unjustified Absence Rate (%)Justified Absence Rate (%)
or Decile
1 2 3 4 5 6 7 8 9 100.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
Absence and school decile
Total Unjustified Absence Rate (%)Justified Absence Rate (%)
Decile
Gender and year level
Ethnicity
2006 2009 2011 20120.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
Ethnicity
NZ EuropeanMāoriPasifikaAsianOther*
Absence %
Regions – is there a link with poverty
2009 2011 20128
9
10
11
12
13
14
15
16
Regions absence rate
NorthlandAucklandWaikatoGisborneWellingtonCanterbury*Otago
Time Series
Wed Fr
i
Tues
Thur
sm
on wed fritu
es
thur
sm
on wed fritu
es
thur
sm
on wed fritu
es
thur
sm
on wed fri0
10
20
30
40
50
60
70
80
Number absent from School
Nu
mb
er
Ab
se
nt
Always ask questions about it.
What would it look like at our school?
What might be different?
Other topicsCell phone usage
Births
Marriage and divorce rates
House prices
Alcohol consumption
Dramatic events like people killed by cows/sharks
All births in the US 1978
12/2
/73
1/1/
74
1/31
/74
3/2/
74
4/1/
74
5/1/
74
5/31
/74
6/30
/74
7/30
/74
8/29
/74
9/28
/74
10/2
8/74
11/2
7/74
12/2
7/74
1/26
/75
0
2000
4000
6000
8000
10000
12000
Babies born in the US in 1978
Date
Num
ber
of
babie
s b
orn
A snippetBabies born in the US in 1978
10/28/74 11/2/74 11/7/74 11/12/74 11/17/74 11/22/74 11/27/74 12/2/747500
8000
8500
9000
9500
10000
10500
A snippetBabies born in the US in 1978
10/28/74 11/2/74 11/7/74 11/12/74 11/17/74 11/22/74 11/27/74 12/2/747500
8000
8500
9000
9500
10000
10500
Why is this Thursday lower
than usual?
Births in NZ 2011
11/18/10 1/7/11 2/26/11 4/17/11 6/6/11 7/26/11 9/14/11 11/3/11 12/23/11 2/11/120
50
100
150
200
250
Distinct number of Babies- 2011
September
8/30/11 9/4/11 9/9/11 9/14/11 9/19/11 9/24/11 9/29/11 10/4/110
50
100
150
200
250
September
December births
11/28/11 12/3/11 12/8/11 12/13/11 12/18/11 12/23/11 12/28/11 1/2/120
50
100
150
200
250
December
Researching and Referencing
http://csmaster.sxu.edu/caviles/images/
NOTE
Correct referencing is NOT REQUIRED but research sources must be clear so they can be followed up e.g. url of websites used
Why Reference? Referencing is necessary to avoid plagiarism.
It allows others to follow up and read what other researchers (writers) have to say about the topic.
It will become part of the students’
university life.
http://writecite.com/swsi.nsw/
StyleI encourage my students to use APA referencing as it is often used in university courses.
http://owll.massey.ac.nz/referencing/apa-reference-list.php
Mobile Data UsageSeptember 9, 2013 September 16, 2013
ResearchingResearch skills need to be taught.
There are lesson plans available from
http://www.google.co.nz/insidesearch/searcheducation/lessons.html
Research skills
Good site for starting
You can search by dates
www.nzherald.co.nz
Google search tools
With sites like wikipedia, reddit etc., I encourage students to go to the referenced sites.
“Wikipedia acknowledges that it should not be used as a primary source for research.”
The main problem is the lack of authority.
http://downwithtyranny.blogspot.co.nz/2011/08/is-wikipedias-real-problem-really-that.html
Encourage students to create references as they go.
Form of Assessment
Forms of assessmentTimed test over several periods
Assignment
Cumulative project
Portfolio
Presentation
Key word: Authenticity
Most common forms of assessment
Timed test over several periods
Assignment
Cumulative project
Portfolio
Presentation
Key word: Authenticity
Timed test (over several periods)
Advantages:
Students can be monitored the whole time
The work is their own
Generally, all students will produce an assessment
Timed testDisadvantages:
Unless data is different, students can easily see what another student is producing on computer.
They need more than a period for assessment and hence students can discuss with others between assessment periods and learn responses.
Timed testDisadvantages:
The assessment tends to be the same for everyone which makes it easier to discuss responses.
Teachers may teach to the assessment or standardise teaching to suit.
Timed testDisadvantages:
Weaker students do not have the time to show what they are capable of.
It is more difficult for English as a second language students.
AssignmentsAdvantages:
These give students the chance to go deeper with the material to put the knowledge they’ve acquired to use or create something new from it.
This type of assessment also gives students who do not test well a chance to shine.
AssignmentAdvantages:
Students have time to develop ideas and research well.
Students have time to test their ideas and change them if need be.
Students have time to write good in-depth reports.
AssignmentAdvantages:
Students are learning whilst completing the assignment.
Weaker students have time to clarify understanding.
AssignmentDisadvantages:
Some students will not produce an assessment.
Unless data is different, students can easily discuss with others.
Generally need more datasets.
Teachers can be tempted to help too much.
Structure
StructureStudents have not been taught how to write
reports in their English class (or any other class).
We need to teach them how.
I suggest you download Lucy Edmond’s talk and material on this.
BrieflyConcise sentences
Passive form (avoid “I”), use impersonal verbs.
Correct tense
Use a writing frame
Vocabulary
PROBLEM and PLANUnderstanding and defining the problem.
Time series is essentially an investigation into ‘what has already happened and what then is likely to happen’ with consideration of how valid it all is.
IntroductionState the investigation.
Research related to choosing particular variables- not just general research.
BackgroundData source
Description of variables
Important aspects of survey details
Most important factors affecting trends (from research)
Data and analysisOverview
Trend
Seasonal Effects
Residuals
Irregularities
Variation
Forecast
Overview – add labels
OverviewStart with an overview of what they see.Can include maximum and minimum values and average increase / decreaseUseful words:Rapid/steady/gradual/plateau, increase/decrease, fallen/risen, weekly/monthly/quarterly/annual
Trend
Monthly visitor arrivals – Holiday; Jan 2000 to Oct 2012
Description from left to
right
“The graph shows that the trend for the number of holiday visitors was increasing from about 35000 in the beginning of 2000 up to about 59000 visitors in the beginning of 2007. This means there is a rise of approximately 300 holiday travellers every month.”
Include numbers and gradients
Model good writing
Reasons from research
“During this period, we noticed a sharp increase in the year 2000, this could be caused by multiple international events happening around that time, “Visitors to several international events - America’s Cup, APEC summit, World Netball Championship, Under-17 Soccer World Cup - contributed to this large increase” (as cited in External Migration January 2000).”
Detail – In-depth research
“The prominent increase in the end of 2003 could be partly contributed to the success of “The Lord of the Rings” trilogy which is completed in December 2003. This is reflected by the research “The International Visitor Survey from 2004 found that six percent of visitors to New Zealand (around 120,000 - 150,000 people) cited The Lord of the Rings as being one of the main reasons for visiting New Zealand.” (as cited in Marketing destination New Zealand through the Hobbit trilogy, 2012)”
Description from left to
right
“However, from the start of 2007 to the end of 2011, the trend remains to be relatively stable with a very slight decrease over time.”
Next section
“This change in trend could be explained by the global economical recession starting from roughly 2008, ………The change is understandable as people will first cut their budget in recreational activities like holiday travel.”
Insight!
Student’s own
thoughts about what
is happening
“At the beginning of 2012, especially in February, there was a sudden decrease in holiday visitors to New Zealand.”
Last section
Holiday effect“This could be due to a number of reasons, such as the moving holiday effect of Chinese New Year, “There were fewer arrivals from Hong Kong and China …….”
Seasonal Effects
“There is very clear seasonality in this series. The patterns can be clearly seen in
the following graphs.”
Identify and quantify high and low seasons in context with reasons.
“From the estimated seasonal effect, it shows that holiday visitors are considerably higher in January and February with the peak in February at about 35,000 visitors above the trend.”
Identify and quantify high and low seasons in context with reasons and insight.
“This is important for the New Zealand economy and tourism dependent industries, as that is the time where they can maximize their profits. Hence we can see that tourism industry in New Zealand is a heavily seasonally dependent market.”
Relates back to the investigative
question
Identify and quantify high and low seasons in context with reasons.
“….Moreover, we notice that the peak is normally in February: this is possibly due to the fact that New Zealand is sometimes visited after going to Australia in January.”
Use of language
“An increasing population of Chinese holiday visitors to New Zealand also supports the February peak, as their holiday of Chinese New Year usually starts between early and mid February. This is justified by, “Tourism is set to recover from its current slowdown due to the continuing strength of Australia and a growing Chinese market.” (as cited in Forecast commentary, 2012)”
Student’s own thoughts on why
“…. The number of visitors troughed in June (about 25000 people below the trend line) but raised slightly in July. The trough in June can be caused by the decreasing temperature as New Zealand goes to winter and the increasing amount of rainfall which makes a holiday less favourable.”
Detail
“July, however, seems to favour more visitor numbers than June; one would expect this because July is when the summer holiday of the Northern Hemisphere starts. Hence we would see an increase in holiday visitors from UK and China. This explanation is supported by …”
Unusual season(s)
“…In particular, there is an outlier in the seasonality for September in 2011, which reaches to about 50,000 instead of the usual 30,000 visitors. This change is caused by positive influence brought by the Rugby World Cup of 2011.”
Variation and residuals
Variation and residuals“After a visual inspection of the graph, the residual is relatively small with most of the variations being below 10% of the overall range (±4000) However, at the beginning of 2011, there is a large residual of about 7500. This unusual residual was probably caused by….”
Components (ball park)
Variation in data: 98000 – 21000 = 77000Variation in Trend: 58000 – 36000 = 2200022/77 = 0.29 i.e. 29% of the variation in the data is the trend
Seasonal component
Variation in data: = 77000Variation in Seasonal Effects: 35000 + 25000 = 6000060/77 = 0.78 i.e. 78% of the variation in the data is the seasonal component
Residual Component
Variation in residuals = 1500015/77 = 19%
SummaryHoliday Visitors to NZ
Min (000)
Max (000)
Range (000)
Approx. % of Contribution
Raw Data 21 98 77Trend 36 58 22 29%Seasonal -25 35 60 78%Residual -5 10 15 19%
NOTE: These are ball-park figures read off the graphs and don’t add up to 100%. The main source of variation comes from the seasonal component which contributes around 78% of the overall variation in the data.
SummaryHoliday Visitors to NZ
Min (000)
Max (000)
Range (000)
Approx. % of Contribution
Raw Data 21 98 77Trend 36 58 22 29%Seasonal -25 35 60 78%Residual -5 10 15 19%
What we are interested in is what is driving this series- in this case the seasonal component.
Prediction Intervals
Prediction Intervals“After a visual inspection of the plot I am confident that the model provides a good fit as differences (white spaces) between the fitted data and the raw data are very small.”
Rounded values
Make an actual prediction“I predict that the average number of holiday visitors to NZ in August 2013 will be between 17400 and 44600. Hence, in the near future, my model predicts that there will be a decreasing trend in 2013.”
Check robustness of the prediction
Take out the last 3 months of data, re-analyse and check against predictions.
“The model does not work particularly well for Sept 2012. There was an unusual decrease in visitor numbers, as opposed to the expected increase. The actual value of Sept 2012 does not even fall into the prediction interval.”
Limitations of forecasting“…the data captures a period of economical downturn at the near end, hence predictions are generally decreasing and this will be inaccurate if the economy becomes better in the future.”
“In addition, the data only covers the total number of visitors and it does not signify the visitor spending and the length of stay. Hence it cannot give a very accurate reading of the tourism’s contribution to the New Zealand economy.”
Discusses what the data does not tell you in relation
to the investigative
question
Etc. etc.Second analysis: Visitors of family and friends.
The student then compares the two series.
Similarities and differences with reasons
Etc. etcForms a new series and discusses the contributions made and effects of key events on the new series.
ConclusionStudent gives a concise summary of the investigation which links back to the original purpose of the investigation.