1. Time Series – from Achieved to Excellence
I am interested in ‘high’ excellence as I teach a scholarship class and I want their learning to last.

2. What will be covered
Techniques 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

3. Time Series
Using 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.

4. 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.

5. Statistical insight involves integrating statistical and contextual knowledge

6. Fake it until they make it
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.
Fake it until they make it

7. Understand and relate to context
Understand and relate to context

8. How do they get here?
Students need to start with something that is very familiar that they feel confident talking about.

9. School!

10. Relating to the context
Start 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.
i.e.

11. Attendance in New Zealand Schools 2012
Something they are familiar with
A little about me

12. Attendance in New Zealand Schools 2012
Get students to use a yellow highlighter when reading material
Emphasis on date and who it applies to. Get students to use a highlighter

13. Why are we interested in this investigation?
“There has been increasing community, political, and education sector concern over absence from school.” (Mallari, Loader, 2013)
Use referencing in material given to students
Highlight the reference

14. Background
A 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).
Highlight the date

15. 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.
Put some ideas behind what you are researching
“Chronic absenteeism is most prevalent among low income students.”
Balfanz, 2012

16. Data Source
2503
Always include the data source

17. Survey Details
The Ministry of Education survey on attendance was carried out in the week 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.
Survey details are always important

18. Are comparisons valid?
The survey was carried out in the week of 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.
Is comparison between data sets valid?

19. Perspective - numbers
In 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.

20. Tables to visual
Reading tables is pretty meaningless

21. Not very good for the messages we want from the data
Bar charts are common but do not adequately show the message.

22. Who would be interested and why?
This tells the story.
Questions to ask: Does it matter to teachers whether the absence is justified or not?
Total is the most important as if a student isn’t in class, no matter the reason, they are missing out on the lesson.

23. Is this a real decrease or is it pressure on schools by the Ministry to deal with absences?
Left to right: what is happening and why? Possible causes for the changes.

24. 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
Not a times series graph. We have straight lines between the data so we cannot be sure the peak wasn’t higher.

25. Similarities/Differences/Reasons What other questions should be asked?
But this is across all schools: secondary, intermediate and primary.
Would this look the same in any other week during the year or is it special to this week.
Are absences higher at this time of year?

26. What might be different in the previous graphs if we just looked at secondary?
Beyond what is presented

27. or Decile

28. Gender and year level
What about gender and year level. Does it seem correct in your experience? Differences and similarities?
Why is there a steady climb from secondary Year 9 to Year 13 and a steeper rise from Year 12 to Year 13?

29. Ethnicity
New Category: MELAA-Middle Eastern, Latin American and African which were previously included in ‘Other’. 
Does this tell us anything?

30. Regions – is there a link with poverty
What do you notice? Cities, poor regions (Gisborne and Northland),

31. Time Series Questions: What term do they think this is?
What are some of the features of this graph?

32. Always ask questions about it.
What would it look like at our school? What might be different?

33. Other topics Cell phone usage Births Marriage and divorce rates
House prices
Alcohol consumption
Dramatic events like people killed by cows/sharks

34. All births in the US 1978

35. A snippet Interesting discussion:
What are the peaks and troughs and why?

36. Why is this Thursday lower than usual?
A snippet
Why is this Thursday lower than usual?
Thanksgiving is the 4th Thursday of November in the US

37. Births in NZ 2011 Why does it seem more erratic than the US data?
Do we see see equivalent patterns?

38. September Yellow = Saturdays Red = 13th
Note: Tuesday is still the highest except for the 13th.

39. December births
Red dot = 13th
Green dots = 24th, 25th, 26th

40. Researching and Referencing

41. NOTE
Correct referencing is NOT REQUIRED but research sources must be clear so they can be followed up e.g. url of websites used

42. 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.

43. Style
I encourage my students to use APA referencing as it is often used in university courses.

44. Mobile Data Usage
September 9, 2013
September 16, 2013

45. Researching
Research skills need to be taught. There are lesson plans available from sons.html

46. Research skills
I think the plans need to be adapted to specifically statistics

47. Good site for starting

48. You can search by dates

50. Google search tools

51. “Wikipedia acknowledges
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.

52. Encourage students to create references as they go.

53. Form of Assessment

54. Forms of assessment Timed test over several periods Assignment
Cumulative project
Portfolio
Presentation
Key word: Authenticity

55. Most common forms of assessment
Timed test over several periods
Assignment
Cumulative project
Portfolio
Presentation
Key word: Authenticity

56. 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

57. Timed test
Disadvantages:
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.

58. Timed test
Disadvantages:
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.

59. Timed test
Disadvantages:
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.

60. Assignments
Advantages: 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.

61. Assignment
Advantages: 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.

62. Assignment Students are learning whilst completing the assignment.
Advantages:
Students are learning whilst completing the assignment.
Weaker students have time to clarify understanding.

63. Assignment Some students will not produce an assessment.
Disadvantages:
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.

64. Structure

65. Structure
Students 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.

66. Briefly Concise sentences
Passive form (avoid “I”), use impersonal verbs.
Correct tense
Use a writing frame
Vocabulary

68. PROBLEM and PLAN
Understanding 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.

69. Introduction State the investigation.
Research related to choosing particular variables- not just general research.

70. Background Data source Description of variables
Important aspects of survey details
Most important factors affecting trends (from research)

71. Data and analysis Overview Trend Seasonal Effects Residuals
Irregularities
Variation
Forecast

72. Overview – add labels

73. Overview Start with an overview of what they see.
Can include maximum and minimum values and average increase / decrease
Useful words:
Rapid/steady/gradual/plateau, increase/decrease, fallen/risen, weekly/monthly/quarterly/annual

74. Trend
Monthly visitor arrivals – Holiday; Jan 2000 to Oct 2012

75. Description from left to right
Include numbers and gradients
“The graph shows that the trend for the number of holiday visitors was increasing from about in the beginning of 2000 up to about visitors in the beginning of This means there is a rise of approximately 300 holiday travellers every month.”
Emphasize words that are important
Model good writing

76. 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).”

77. 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 This is reflected by the research “The International Visitor Survey from 2004 found that six percent of visitors to New Zealand (around 120, ,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)”

78. Description from left to right
Next section
“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.”

79. Student’s own thoughts about what is happening
Insight!
“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.”
Student adding their own thoughts on the situation.

80. Last section
“At the beginning of 2012, especially in February, there was a sudden decrease in holiday visitors to New Zealand.”

81. 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 …….”

82. Seasonal Effects

83. “There is very clear seasonality in this series
“There is very clear seasonality in this series. The patterns can be clearly seen in the following graphs.”

84. 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.”

85. Relates back to the investigative question
Identify and quantify high and low seasons in context with reasons and insight.
Relates back to the investigative question
“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.”

86. Identify and quantify high and low seasons in context with reasons.
Not always in February- student notices this.
“….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.”

87. 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)”

88. Student’s own thoughts on why
“…. The number of visitors troughed in June (about 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.”

89. 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 …”

90. 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.”

91. Variation and residuals

92. 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 This unusual residual was probably caused by….”

93. Components (ball park)
Variation in data: – = 77000
Variation in Trend: – = 22000
22/77 = 0.29 i.e. 29% of the variation in the data is the trend

94. Seasonal component Variation in data: = 77000
Variation in Seasonal Effects: = 60000
60/77 = 0.78 i.e. 78% of the variation in the data is the seasonal component

95. Residual Component
Variation in residuals = 15000
15/77 = 19%

96. Approx. % of Contribution
Summary
Holiday Visitors to NZ
Min (000)
Max (000)
Range (000)
Approx. % of Contribution
Raw Data 21 98 77
Trend 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.

97. Approx. % of Contribution
Summary
Holiday Visitors to NZ
Min (000)
Max (000)
Range (000)
Approx. % of Contribution
Raw Data 21 98 77
Trend 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.

98. Prediction Intervals

99. 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.”

100. Rounded values
Creates a new chart from the iNZight output

101. Make an actual prediction
“I predict that the average number of holiday visitors to NZ in August 2013 will be between and Hence, in the near future, my model predicts that there will be a decreasing trend in 2013.”

102. 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 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.”

103. Limitations of forecasting
Discusses what the data does not tell you in relation to the investigative question
“…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.”

104. Etc. etc.
Second analysis: Visitors of family and friends. The student then compares the two series.

105. Similarities and differences with reasons

106. Etc. etc
Forms a new series and discusses the contributions made and effects of key events on the new series.

107. Conclusion
Student gives a concise summary of the investigation which links back to the original purpose of the investigation.