Guide to Fathom and E-STAT Statistics Canada has prepared a special website for students, called ESTAT (estat.statcan.ca), containing not only vast amount of data but also articles, lessons, and a wealth of other material. Fathom Dynamic Statistics Software will enable you to organize, display and analyze data with incredible ease and flexibility. As you can imagine, it takes a bit of practice to become comfortable with these tools. The purpose of this guide is to give you a series of recipes employing E-STAT and the Statistics Canada websites as sources of data and Fathom as a tool for analyzing the data. Tourism deals with one-variable statistics. Braking Distance takes up twovariable data. Education and Income offers a novel way of viewing the least squares regression line. Poverty and Crime shows how to investigate possible cause-and-effect relationships. Beer Consumption provides practice in manipulating data in order to show a trend. If you get lost, refer to appendix B in your textbook.
Tourism Use E-STAT to investigate patterns of international tourism in Canada. Procedure: 1. At the E-STAT Table of Contents, select Data. 2. Under the heading of People, select Travel and tourism 3. Under CANSIM II, select International travel. 4. At the Search results, select Table 427-0001—Number of international travelers entering or returning to Canada by type of transport, monthly. 5. At the Subset selection under Geography (267 items), select Canada. 6. Under Traveller characteristics (91 items), select Total non-resident travelers. 7. Select Jan 1972 to Dec 1972 from the drop down menu: 8. Click Retrieve as individual Time Series 9. At the Output specification screen, under Screen Output format selection, Line Graph (max.12 series) is the default selection. Click Retrieve now. Answer the following questions: A. Describe what you see on the screen. What do you think causes this pattern? B. Reduce the data range displayed to the last 12 months by returning to the Output specification and changing the years. Now describe what is displayed. C. Which month registered the highest number of international tourists? Which month registered the lowest? Are these months the same every year? Do you think this pattern is the same in each province? D. Does this pattern surprise you? Why or why not? E. Is the long-term trend in the number of international tourists obvious? Describe the trend. F. Now describe the long-term trend, identifying the peaks and troughs. Compare to the first graph you produced. Which of these graphs would you use if you were planning on opening a bed and breakfast, a fish camp and a ski resort? Explain. Extension G. Using the computer instructions given above, retrieve and analyze data for your own province. H. Describe what you see for your province. Compare the graphs for your region with those of Canada.
I. List some factors drawing tourists to your region.
Travellers to Canada 6500000 6000000 5500000 5000000 4500000 4000000 3500000 3000000 2500000 2000000 0 2 4 6 8 Month 10 12 14 Scatter Plot
Patterns of International Tourism in Canada and Ontario Month 1 = April
Travellers to Ontario 3800000 3600000 3400000 3200000 3000000 2800000 2600000 2400000 2200000 2000000 1800000 1600000 1400000 0 2 4 6 8 Month 10 12 14 Scatter Plot
T ravellers
T ravellers
Education and Income Is it worth going to university? Investigate the association between the proportion of people with a completed university degree and average census tract income (i.e., the average income in a each geographical section of the census) using Census of Canada data for Oshawa, Ontario. Using census tract data on E-STAT, create a scatter plot of the relationship between average income versus the percent of the population with a university degree. Import the data into Fathom and then compute the regression equation and correlation statistics. Procedure: Access Census Data 1. Start up E-STAT 2. From the left tool bar click Search Census. 3. Under Census, select “2001 Census” and click “Go!” 4. Select “2001 Census, 46 Large Urban Centres, Census Tracts (neighbourhoods)” and click “Go!” 5. Under Profile selection, select “2001 School Attendance, Education, Field of Study, Highest Level of Schooling and Earnings” and click “Go!” 6. Under Geography, select “Large Urban Centres in Ontario—2001— Oshawa (68 areas)” or another urban centre without too many census tracts. Toronto is too big, but you might want to try Barrie. 7. Under Characteristics, click “View Checklist” 8. Select the following variables from the checklist: “Total population 20 years and over by highest level of schooling” “With bachelor’s degree or higher, university, population 20 years and over by highest level of schooling” “Average employment income, $, worked full year, full time, population 15 years and over with employment income” [Be sure not to click the “part time” box or you will get very strange results.] Tip: Because the list of variables is long, use the “Find on this page” key from the Edit pull-down menu on your browser. For example, do a find on „schooling‟ and then on „income‟. 9. Click the Home or End keys, and click on “Back to Main Selection Form”
10. To see the geographic distribution of the first variable as a percent of the total population, we first click the “Table, Areas as rows” icon at the bottom of the screen. We then click the radio button under the table “Data as % of 1st characteristic” and click the “Redisplay As”: tab. This produces a table showing the schooling level as a percentage of the total population. Load the Data into Fathom 11. Click and drag in the table so that you have selected all the data, but not the Legend at the top of the page, or the source line at the bottom of the page. Click Ctrl-C. 12.Switch to Fathom. (If Fathom isn’t already running, you will need to launch it.) 13.In a new document, make a new empty collection. 14.With the collection selected, choose Paste Cases from the Edit menu. (Or just Ctrl-V). 15. Make a case table for the collection (for example by choosing Case table form the Object > New menu). 16.Edit the names of the attributes to “census_tract”, “University_degree_or_higher” and “Avg_Employment-incomefulltime.” 17. Change the name of the collection to “Education and Income” 18. Save your Fathom document by choosing Save from the File menu. Graphing the Data 19.Make a graph showing the variation in average income versus the schooling level. 20. Using the Graph pull-down menu, overlay a Show Squares line. Move the line around until you think you have made the total areas of the squares a minimum. To see the actual line of best fit, overlay a “Least-Squares Line” from the menu. Analysis 21.Write a description of the pattern you see on this graph. Write a possible explanation for the shape observed in this distribution, using the Text tool on the shelf. 22. You may wish to add a residual plot to help you assess the quality of the fit of the least squares line. Extension Repeat the entire process and analysis using the percent of the population with less than grade 9 education.
Education and Income 80000
Scatter Plot
70000
AverageIncome
60000
50000
40000
30000 0 5 10 15 Education 20 25 30
AverageIncome = 959Education + 35500; r^2 = 0.70
Poverty and Crime Some people do not see “law-and-order” policies as the best way to reduce crime. They claim that there are many social and demographic factors that are related to crime and that understanding these might help us work to reduce crime rates. We will investigate two possible factors that might be related to crime: poverty and unemployment. Access Statistics Canada Website: 1. Go to: estat.statcan.ca 2. Click in sequence: Justice > under CANSIM II select Crime and offences > 252-0001 (under the “Terminated” area) (This sequence selects the matrix for “Crimes, by actual offences, annual” 3. Select in sequence: Canada> All offences, total> 1983 > 2000 4. Select: Retrieve as Individual Time Series > Manipulate Data > Add more series 5. Select: Browse by subject < Subject 6. Select a category for your second series (Personal finance and household finance) and a subcategory (income) if necessary 7. Select a matrix for your second series (202-0802 Persons with low income before and after tax, showing prevalence and estimated number, annual) 8. Select the characteristics of the data required as in (4) above: (Canada > low income cut-offs after tax > number of persons in low income > all persons > 1983 > 1998) 9. Select: Retrieve as Individual Time Series 10. Check that the two series indicated are those that you wish to retrieve 11. Set Output Format to: HTML Table, time as rows 12.Click: Go 13.Highlight the three columns of data in the table, but not the legend at the top or the sources at the bottom. 14.Click Copy from the Edit menu (or just Ctrl-C) Fathom Analysis: Copying and Pasting the Data 15. Switch to Fathom. (If Fathom isn’t already running, you will need to launch it.) 16.In a new document, make a new empty collection. 17. With the collection selected, choose Paste Cases from the Edit menu (or just Ctrl-V).
18. Make a case table for the collection (for example by choosing Case table from the Object menu, or just drawing a Case table from the shelf). 19.Edit the attribute names by double-clicking on the attribute and renaming it: e.g., Poverty (x-axis), Crime (y-axis) (Note: You may not use spaces in attribute names). 20. Save your Fathom document by choosing Save from the File menu. Graphing the Data 22.Make a graph showing the variation in crime rate by year. 23. Make a graph showing the variation in poverty by year. 24. Make a scatter plot with poverty on the x-axis and crime on the yaxis. 23. Write a description of the pattern you see on this graph. If you have any explanation for the shape in this distribution, write that as well. Poverty does not appear to be a very good explanation for crime. Repeat the exercise using unemployment as a possible factor. You may wish to limit the population to young males. Does unemployment seem like a stronger explanatory factor?
Poverty&Crime 3000000 2900000 2800000 Scatter Plot
Poverty&Crime 4200 4000 3800
Scatter Plot
CrimeCases
2600000 2500000 2400000 2300000 2200000 1982 1986 1990 1994 Year 1998 2002
Poverty
2700000
3600 3400 3200 3000 2800 2600 1982 1986 1990 1994 Year 1998 2002
Poverty&Crime 3000000 2900000 2800000
Scatter Plot
CrimeCases
2700000 2600000 2500000 2400000 2300000 2200000 2600 3000 3400 Poverty 3800 4200
Youth Unemployment & Crime 150000 140000 130000 120000
Scatter Plot
Crime
110000 100000 90000 80000 70000 60000 180 200 220 240 260 280 300 320 340 360 Unemployment
Beer Consumption
This exercise will investigate the claim that the greatest consumers of domestic beer are young men ages 20 to 24. During the 1980s this age group experienced great growth. We can investigate the hypothesis by creating time series plots for the 20 to 24 age male group and beer consumption in Canada between 1971 and 2001. Procedure: Access Beer Consumption data 1. Startup E-STAT 2. Retrieve data from the CANSIM databases on E-STAT by clicking “Search CANSIM II” on the left side bar. It is the 4th button on the left side bar. 3. Under Search: enter “beer consumption” 4. Under Active tables select “002-0011 Apparent per capita food consumption in Canada, annual” 5. Under Commodity scroll down and select “Ale, beer, tout and porter, retail weight (Litres per year)” 6. Select the time frame from “1971” to “2001” 7. Click on “Retrieve as individual Time Series” tab. 8. Click on “Manipulate Data” 9. Click on “Add more series” Access 20 to 20 age cohort data 10. Select “Search by Subject” 11. Click on the yellow box for “Population and demography” 12.Click on “Population characteristics” 13.Select “Table 051-0001 Estimates of population, by age group and sex, Canada, provinces and territories, annual” 14.Under Geography select “Canada” 15. Under Sex select “Male” 16.Under Age group select 2 different time series. First select “All ages”, then scroll down and (while holding down the Ctrl key) select also “20-24 years” 17. Select the time frame from “1971” to “2001”, the same time frame as for the previous series 18. Click on “Retrieve as individual Time Series” tab. 19.In the Output format selection box select “Plain text, time as rows” 20. Click on “Retrieve Now”
Fathom Analysis: Copying and Pasting the Data 21.Click and drag in the table so that you have selected all the data, but not the Legend at the top of the page, or the source line at the bottom of the page. 22. Choose Copy from the Edit menu (or just Ctrl-C). 23. Switch to Fathom. (If Fathom isn’t already running, you will need to launch it.) 24. In a new document, make a new empty collection. 25. With the collection selected, choose Paste Cases from the Edit menu (or just Ctrl-V). 26. Make a case table for the collection (for example by choosing Case table from the Object menu, or just drawing a Case table from the shelf). 27. Edit the attribute names by double-clicking on the attribute and renaming it: Year, TotalPopulation, Pop20-24, Beerconsumption. (Note: You may not use spaces in attribute names). 28. Change the name of the collection to “Beer Consumption” by double-clicking on the collection sign. 29. Save your Fathom document by choosing Save from the File menu. Graphing the Data 30. Make a graph showing the variation in beer consumption per capita versus the years. 31.Write a description of the pattern you see on this graph. If you have any explanation for the shape in this distribution, write that as well. Manipulating the Data—Converting to Percentages Now we will check if this pattern can be explained by the variation in the 20-24 year old cohort, as we think this cohort may be the largest beer drinkers on average. Since beer consumption is measured in average number of litres consumed per year over the entire population, we need to convert the 20-24 year old cohort to a percentage of the total population. 32. To do this, we need to define a new attribute. We do this by opening the Case table and clicking the attribute labeled (new) at the top right of the case table. 33. We need to give this new attribute a name. Let’s call it Pop20_24asPercent. Type in this name. 34. Now we want to assign it values, which will be computed using our existing attributes. Highlight the new attribute column. From the Edit menu, select Edit formula/
35. In the formula box, expand the Attribute list by clicking on the word Attribute. Type in the following formula using the buttons and the list of attributes: 100*(Pop20_24/Totalpop) 36. When you click Apply, the formula is applied and the values are computed for the new attribute for all the years. Looking for Possible Relationships using Graphing techniques 37. Make a graph showing BeerConsumption (y-axis) against this new computed variable, Pop20_24/Totalpop (x-axis). 38. Using the Graph pull-down menu, overlay a Least-Squares line. 39. You can also add a residual plot to help you assess the quality of the fit of the least squares line. Analysis Write one sentence explaining the meaning of the equation computed for the least-squares line (or line of best fit). Is this line a good fit? Look at the r2 value. A value of 1.0 indicates an exact linear correlation between the x and the y values of points on the graph. In other words from the x-value and the equation you can accurately predict the corresponding y-value. What happens as the percentage of 20-24 year olds increases in the population? How could marketing specialists use this information on consumption related to age? Extensions Examine the relationship of average beer consumption to other age cohorts, such as 15-19 and 25-29. Investigate the consumption of another food or beverage (e.g., wine, milk, oatmeal, ice cream) using the same E-STAT data table and identify which, if any, age cohorts are most highly related to high consumption of the selected product. Fathom calculates the correlation coefficient for the scatter plot as 0.91. What does this mean. Explain what the residual plot under the scatter plot shows us. Scatter plot showing the relationship between average beer consumption in Canada in litres per year (on the y-axis) against the percentage of the total Canadian population who are 20 to 24 years old (on the x-axis)
Beer Consumption 86 84 82 80 78 76 74 72 70 68 66 3.4 3.6 3.8 4.0 4.2 4.4 Pop20_24asPercent 4.6 4.8
Scatter Plot
BearPerCapita
5.0
5.2
Residual
2 -1 -4 3.4 3.6 3.8 4.0 4.6 4.8 5.0 5.2
4.2 4.4 Pop20_24asPercent BearPerCapita = 9.73Pop20_24asPercent + 35.2; r^2 = 0.91