InfoVis:Wiki - User contributions [en]

Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 4

2009-01-04T18:41:48Z

UE-InfoVis0809 0426716:

== Aufgabenstellung ==
[http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws08/infovis_ue_aufgabe4.html Beschreibung der Aufgabe 4]

=== Gegebene Daten ===

'''Homer Simpson's Trinkverhalten in Abhängigkeit von seinen Lebensumständen''' 

...Visualisierung von Homer's Lebensabschnitten bzw. Ereignissen mit Einfluss auf sein
Trinkverhalten (zB.: Kindheit, Pubertät, Arbeitslosigkeit, Beziehungen, Hochzeit, Geburt
der Kinder, Liebeskummer, Alltag, etc.) von seiner Geburt bis Jetzt + mögliche
Zukunftsszenarien (mind. 3).
 
*Die Menge folgender Getränke soll für die jeweiligen Lebensumstände ablesbar sein
(ml oder Liter - je nachdem - pro Tag, Monat, Jahr (z.B.: Fokus+Kontext Methoden):
a) Wasser 
b) Milch 
c) Fruchtsaft 
d) Cola 
e) Kaffee (Würfelzucker?) 
f) Bier
(vereinfacht angenommen, Homer trinkt ausschließlich diese Getränke)
 
*Die folgenden Werte sollen abhängig von den konsumierten Getränken ablesbar sein:
1) g oder kg konsumierter Zucker (aus Getränken) + empfohlene Maximaldosis pro Tag, Monat, Jahr
(empfohlene Maximaldosis/Tag: 50g; enthaltener Zucker: 10g/100 ml Cola; 10g/100 ml Fruchtsaft; 3g/Würfelzucker). 
2) mg konsumiertes Coffein + empfohlene Maximaldosis pro Tag, Monat, Jahr
(empfohlene Maximaldosis/Tag: 600mg; enthaltenes Coffein: 10 mg/100 ml Cola; 80 mg/100 ml Kaffee). 
3) g konsumierter Alkohol + empfohlene Maximaldosis pro Tag, Monat, Jahr
(empfohlene Maximaldosis/Tag: 20g; enthaltener Alkohol: 3,6 g/100ml Bier)
 
*Die Daten sollen zur medizinischen/psychologischen Analyse visualisiert werden. 
*Die bisher erlernten Design-Prinzipien sollen umgesetzt werden (z.B.: Optimierung der Data-ink ratio). 
*Die Mockups sollten zumindest 1) Homer's Leben im Überblick 2) und eine Detailansicht wiedergeben. 
*Alle nicht angeführten Daten können frei erfunden werden.

=Description of the application field and the given dataset=

The given data should show the connection between the different periods of homer's life and his drinking behavior. We want to figure out
which periods of life affected the drinking behavior in a good/bad way.
The data is useful for a few different fields of application: Medical analysis, psychologically analisis and for nutritional advice.
For the application we are dealing with two different tables. We need both of them in order to get meaningful results.

===The nutrition panel===

[[Image:Nutritionalpanel.JPG]]

The nutrition panel contains a list of all the ingredients of a certain beverage. The data is multidimensional and metrical. Here
we are dealing with a ratio scale.
The unit for all ingredients (except for the sugar in the coffee where it is measured by piece) is 100 ml. There are beverages
like milk and water which have no entry in the table. This is because in this case we are only interested in the amount of sugar,
alcohol and coffein. If we would like to take also fat or protein into account, milk would play a different roll.
We can look at this table in two different ways. If we only look at a column (for example "Zucker") we can compare how much sugar
each beverage contains. If we take a look at a horizontal entry (e.g. "Cola") we can determine which ingredients this entry contains.
An additional value for each ingredient tells us about the maximal dosis per day.

===The list of amount===

[[Image:Amount.JPG]]

This table contains the amount of every beverage homer drank on a certain day. For the application we need the table of amount for each
day. Such a daily table contains the amount of beverages and the amount of the different ingredients of the beverages based on the information stored in the nutritional panel. As the nutritional panel the amount table is multidimensional and metrical. The structure of the data is also equal to the structure in the nutritional panel.

==Target group==

The target group for this application could be both medical staff (psychologists, doctors, nutritionists, ...) and the patient. The visualization
is very simple so everybody is able to deal with the application but also contains all the sufficient data to make medical analysis possible.
The ideal case would be if the doctor and his patient would evaluate the data with each other. The doctor or nutritionist gets a general idea of the drinking
behavior of the patient and is so able to determine whether his behavior is healthy or not. In a second step a psychologist is able to see in what
kind of situation the patient is at a risk of drinking too much sugared beverages or too much alcohol. The final step would be to elaborate a diet
plan by taking into account the data and the psychological cognitions.

==Goal of the visualization==

The main goals for this visualization are:
* Demonstration of the consumption of beverages and the resulting consumption of nutrients for different periods of time.
* Comparisons (increase/decrease) of the consumption of beverages and nutrients over different longer periods of time.
* Comparisons of the consumption of nutrients at different non-connected periods of time (e.g. different periods of life).

= Concept =

To allow both professionals (doctors, psychologists ...) and patients to easily access information, our visualization concept provides 3 views, each one presenting some specific information. The 3 view are presented in a smalll toolbox, allowing the user to easily switch between the views and personalize the visualization.

The toolbox provides three button for choosing the three views, and below the desired view is visualized.

=== The ''Gesamt'' view ===

This view shows the total amount of each drink for a certain amount of time.

There is a timeline located on the bottom of the window. The user can select the exact period of time he wants to visualize. On startup, the maximum time span is Homer's whole life (1950 - 2008), but the user can zoom in using the zoom buttons on the right border for an accurate time span selection. This time span selection allows the user to control which exact period of the patient's life to be visualized. The currently selected period of time is always displayed above the diagrams.

The selected period of time is then visualized in the main window. This area is divided into two blocks: The large diagram on the left side shows the total amount of consumed drinks, summed up over the whole time span that is currently selected. The three diagrams on the right side show the amount of consumed sugar, coffein and alcohol during the selected period of time, including both the total amount as well as a break down to the drinks containing sugar, coffein and alcohol. The recommended maximum dose is dynamically calculated for the current time span and displayed as horizontal red line.

The ''Speichern'' button on the upper right border of the window allows the user to add a specific visualization the the ''Vergleich'' view, which will be presented later.

The following three images show the ''Gesamt'' view for Homers whole life, a time span of a few months and one single day respectively:

[[Image:homer0426716_gui_1a.png]]

[[Image:homer0426716_gui_1b.png]]

[[Image:homer0426716_gui_1c.png]]

=== The ''Verlauf'' view ===

This view shows the alteration of the amount of consumed drinks as well as sugar, coffein and alcohol over a certain period of time. Similar to the ''Gesamt'' view, the user can select a time span using the time line. The left diagram shows the amount of consumed drinks for each day, month or year (depending on the currently selected period of time). The three small diagrams show the same for sugar, coffein and alcohol, but summing up all drinks that contain sugar, coffein or alcohol. Again, the recommended maximum dose for the current unit (day, month or year) is shown as a horizontal red line. When moving the cursor over the diagrams, detailed infomation is shown in a tool-tip box.

The following two images show the ''Verlauf'' view for Homers whole life and for a time span of a few months:

[[Image:homer0426716_gui_2a.png]]

[[Image:homer0426716_gui_2b.png]]

=== The ''Vergleich'' view ===

This view is structured diffently, allowing the user to personalize the visualization and compare analyses from different points of time.

In the ''Gesamt'' view, the ''Speichern'' buttons adds the currently shown sugar, coffein and alcohol visualization to the ''Vergleich'' view. Here all sugar, coffein and alcohol diagrams are normalized and shown next to each other, allowing comparisons between the consumption at different points of time in the patient's life.

The diagrams can be sorted by clicking the arrow-buttons at the bottom of the window, and diagrams can be removed from the ''Vergleich'' view using the small delete buttons.

The following image shows the comparison of three days in Homer's life using the ''Vergleich'' view:

[[Image:homer0426716_gui_3a.png]]

== Links ==

* [[Teaching:TUW_-_UE_InfoVis_WS_2008/09|InfoVis:Wiki UE Homepage]]

* [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws08/ UE InfoVis]

*[[Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05|Gruppe 05]]

Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 4

2009-01-04T13:49:44Z

UE-InfoVis0809 0426716:

Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 4

2009-01-03T13:16:35Z

UE-InfoVis0809 0426716:

Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 4

2009-01-03T13:14:10Z

UE-InfoVis0809 0426716:

Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 4

2009-01-03T13:07:09Z

UE-InfoVis0809 0426716:

Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 4

2009-01-03T12:58:55Z

UE-InfoVis0809 0426716:

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2009-01-02T21:50:29Z

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2009-01-02T21:50:19Z

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2009-01-02T21:50:06Z

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2009-01-02T21:49:47Z

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2009-01-02T21:49:31Z

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2009-01-02T21:49:15Z

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Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 4

2009-01-02T21:49:00Z

UE-InfoVis0809 0426716:

Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 4

2009-01-02T21:47:44Z

UE-InfoVis0809 0426716:

Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 4

2008-12-30T15:01:51Z

UE-InfoVis0809 0426716:

Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 3

2008-12-05T10:14:08Z

UE-InfoVis0809 0426716:

== Aufgabenstellung ==
[http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws08/infovis_ue_aufgabe3.html Beschreibung der Aufgabe 3]

=== Zu beurteilende Grafik ===
[[Image:Klimafaktor-vieh die-zeit 04-2007.jpg|600px]] 
Treibhausgas-Emissionen durch tierische Gase und Dung in den Weltregionen

== Critical comments ==

== Adapted graphic ==

[[Image:diagramm0426716.gif|800px]]

== Adaptions ==

== Links ==

* [[Teaching:TUW_-_UE_InfoVis_WS_2008/09|InfoVis:Wiki UE Homepage]]

* [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws08/ UE InfoVis]

* [[Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05|Gruppe 05]]

File:Diagramm0426716.gif

2008-12-05T10:13:39Z

UE-InfoVis0809 0426716: New page: == Summary == == Copyright status == == Source ==

== Summary ==

== Copyright status ==

== Source ==

Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 3

2008-12-05T10:12:40Z

UE-InfoVis0809 0426716:

== Aufgabenstellung ==
[http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws08/infovis_ue_aufgabe3.html Beschreibung der Aufgabe 3]

=== Zu beurteilende Grafik ===
[[Image:Klimafaktor-vieh die-zeit 04-2007.jpg|600px]] 
Treibhausgas-Emissionen durch tierische Gase und Dung in den Weltregionen

== Critical comments ==

== Adapted graphic ==

[[Image:diagramm0426716.gif|600px]]

== Adaptions ==

== Links ==

* [[Teaching:TUW_-_UE_InfoVis_WS_2008/09|InfoVis:Wiki UE Homepage]]

* [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws08/ UE InfoVis]

* [[Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05|Gruppe 05]]

Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 3

2008-12-05T09:02:57Z

UE-InfoVis0809 0426716:

== Aufgabenstellung ==
[http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws08/infovis_ue_aufgabe3.html Beschreibung der Aufgabe 3]

=== Zu beurteilende Grafik ===
[[Image:Klimafaktor-vieh die-zeit 04-2007.jpg|600px]] 
Treibhausgas-Emissionen durch tierische Gase und Dung in den Weltregionen

== Critical comments ==

== Adapted table ==

== Adaptions ==

== Links ==

* [[Teaching:TUW_-_UE_InfoVis_WS_2008/09|InfoVis:Wiki UE Homepage]]

* [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws08/ UE InfoVis]

* [[Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05|Gruppe 05]]

File:Ue2 adaptedtable 0426716.gif

2008-11-17T18:38:23Z

UE-InfoVis0809 0426716: New page: == Summary == == Copyright status == == Source ==

== Summary ==

== Copyright status ==

== Source ==

Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 2

2008-11-17T18:38:07Z

UE-InfoVis0809 0426716:

== Aufgabenstellung ==
[http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws08/infovis_ue_aufgabe2.html Beschreibung der Aufgabe 2]

=== Zu beurteilende Tabelle ===

[[Image:AnimalsKilledforFood.jpg|600px]]

== Critical comments ==

* Too many colors where white space would be sufficient
* The comparison column ''07/06'' is placed between the two columns it refers to (''2006'' and ''2007''), but this is not true for the comparison column ''06/05''
* In the columns ''06/05'' and ''07/06'' the numbers / decimal points are not aligned
* A comma is placed to the left of every three digits in the ''Total'' row, but not in the table body
* In the ''%died'' column, a % sign is missing after each number
* In the column headers, years are sometimes formatted using four digits (e.g. ''2005''), and sometimes using two digits (e.g. ''06/05'')
* Columns ''06/05'' and ''07/06'' use a higher precision / more digits after the comma
* Different fonts are used in the table body and the column / row headers
* Some column headers are set to bold font and some are not
* All numbers in the ''2007'' column are bold just like the numbers in the ''Total'' row, although the ''2007'' numbers do not summarize anything
* Columns are separated from each other using colors, which makes it difficult to scan through the rows and compare numbers from one row to each other
* The spanner header ''2005'' is not aligned to the center, while all other spanner headers are center-aligned
* The outer grid is not necessary
* More categories are available in the ''2006'' section than in the ''2005'' and ''2007'' section

== Adapted table ==

[[Image:ue2_adaptedtable_0426716.gif]]

== Adaptions ==

TODO

== Links ==

* [[Teaching:TUW_-_UE_InfoVis_WS_2008/09|InfoVis:Wiki UE Homepage]]

* [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws08/ UE InfoVis]

*[[Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05|Gruppe 05]]

Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 2

2008-11-17T18:34:33Z

UE-InfoVis0809 0426716:

== Aufgabenstellung ==
[http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws08/infovis_ue_aufgabe2.html Beschreibung der Aufgabe 2]

=== Zu beurteilende Tabelle ===

[[Image:AnimalsKilledforFood.jpg|600px]]

== Critical comments ==

* Too many colors where white space would be sufficient
* The comparison column ''07/06'' is placed between the two columns it refers to (''2006'' and ''2007''), but this is not true for the comparison column ''06/05''
* In the columns ''06/05'' and ''07/06'' the numbers / decimal points are not aligned
* A comma is placed to the left of every three digits in the ''Total'' row, but not in the table body
* In the ''%died'' column, a % sign is missing after each number
* In the column headers, years are sometimes formatted using four digits (e.g. ''2005''), and sometimes using two digits (e.g. ''06/05'')
* Columns ''06/05'' and ''07/06'' use a higher precision / more digits after the comma
* Different fonts are used in the table body and the column / row headers
* Some column headers are set to bold font and some are not
* All numbers in the ''2007'' column are bold just like the numbers in the ''Total'' row, although the ''2007'' numbers do not summarize anything
* Columns are separated from each other using colors, which makes it difficult to scan through the rows and compare numbers from one row to each other
* The spanner header ''2005'' is not aligned to the center, while all other spanner headers are center-aligned
* The outer grid is not necessary
* More categories are available in the ''2006'' section than in the ''2005'' and ''2007'' section

== Adapted table ==

TODO

== Adaptions ==

TODO

== Links ==

* [[Teaching:TUW_-_UE_InfoVis_WS_2008/09|InfoVis:Wiki UE Homepage]]

* [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws08/ UE InfoVis]

*[[Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05|Gruppe 05]]

Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 2

2008-11-16T10:02:32Z

UE-InfoVis0809 0426716:

== Aufgabenstellung ==
[http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws08/infovis_ue_aufgabe2.html Beschreibung der Aufgabe 2]

=== Zu beurteilende Tabelle ===

[[Image:AnimalsKilledforFood.jpg|600px]]

== Critical comments ==

* Too many colors where white space would be sufficient
* The comparison column ''07/06'' is placed between the two columns it refers to (''2006'' and ''2007''), but this is not true for the comparison column ''06/05''
* In the columns ''06/05'' and ''07/06'' the numbers / decimal points are not aligned
* A comma is placed to the left of every three digits in the ''Total'' row, but not in the table body
* In the ''%died'' column, a % sign is missing after each number
* In the column headers, years are sometimes formatted using four digits (e.g. ''2005''), and sometimes using two digits (e.g. ''06/05'')
* Columns ''06/05'' and ''07/06'' use a higher precision / more digits after the comma
* Different fonts are used in the table body and the column / row headers
* Some column headers are set to bold font and some are not
* All numbers in the ''2007'' column are bold just like the numbers in the ''Total'' row, although the ''2007'' numbers do not summarize anything
* Columns are separated from each other using colors, which makes it difficult to scan through the rows and compare numbers from one row to each other
* The spanner header ''2005'' is not aligned to the center, while all other spanner headers are center-aligned
* The outer grid is not necessary

== Adapted table ==

TODO

== Adaptions ==

TODO

== Links ==

* [[Teaching:TUW_-_UE_InfoVis_WS_2008/09|InfoVis:Wiki UE Homepage]]

* [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws08/ UE InfoVis]

*[[Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05|Gruppe 05]]

Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 2

2008-11-16T09:59:38Z

UE-InfoVis0809 0426716:

== Aufgabenstellung ==
[http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws08/infovis_ue_aufgabe2.html Beschreibung der Aufgabe 2]

=== Zu beurteilende Tabelle ===

[[Image:AnimalsKilledforFood.jpg|600px]]

== Critical comments ==

* Too many colors where white space would be sufficient
* The comparison column "07/06" is placed between the two columns it refers to ("2006" and "2007"), but this is not true for the comparison column "06/05"
* In the columns 06/05 and 07/06 the numbers / decimal points are not aligned
* A comma is placed to the left of every three digits in the "Total" row, but not in the table body
* In the "%died" column, a % sign is missing after each number
* In the column headers, years are sometimes formatted using four digits (e.g. 2005), and sometimes using two digits (e.g. 06/05)
* Columns 06/05 and 07/06 use a higher precision / more digits after the comma
* Different fonts are used in the table body and the column / row headers
* Some column headers are set to bold font and some are not
* All numbers in the "2007" column are bold just like the numbers in the "Total" row, although the "2007" numbers do not summarize anything
* Columns are separated from each other using colors, which makes it difficult to scan through the rows and compare numbers from one row to each other
* The spanner header "2005" is not aligned to the center, while all other spanner headers are center-aligned
* The outer grid is not necessary

== Adapted table ==

TODO

== Adaptions ==

TODO

== Links ==

* [[Teaching:TUW_-_UE_InfoVis_WS_2008/09|InfoVis:Wiki UE Homepage]]

* [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws08/ UE InfoVis]

*[[Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05|Gruppe 05]]

Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 2

2008-11-16T09:49:50Z

UE-InfoVis0809 0426716:

Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 1 - Level (Scales) of Measurement

2008-11-14T10:28:03Z

UE-InfoVis0809 0426716:

== LEVELS OF MEASUREMENT ==

----

===DEFINITION===

{{Quotation| [...] measurement, in the broadest sense, is defined as the assignment of numerals to objects or events according to rules.| [Stevens, 1946]}}

{{Quotation| Measurement of some attribute of a set of things is the process of assigning numbers or other symbols to the things in such a way that relationships of the numbers or symbols reflect relationships of the attributes of the things being measured. A particular way of assigning numbers or symbols to measure something is called a scale of measurement. |[Sarle, 1995]}}

----

===INTRODUCTION===

Different levels of measurement refer to different relationships among the values that are assigned to the attributes for a variable. Knowing the level of measurement helps when interpreting the data that variable contains.

There are four levels of measurement defined: nominal, ordinal, interval and ratio. These levels are ordered increasingly, different levels of measurements use different mathematical structures, and on higher levels more operations and relations are defined. Each higher level of measurement includes the measurement principle of the lower level of measurement.

----

===LEVELS OF MEASUREMENT===

====NOMINAL====

At the nominal level of measurement, names are assigned to observations. In most cases numbers are used as names, but also other symbols are possible names. The purpose of this naming is to label or classify the observations.

Two things are assigned the same name if they have the same value of the attribute. Two variable values can only be compared to each other to define if they are equal or not, there are no other relations among the categories such as "less than" or "greater than", and there are no operations such as addition or subtraction.

It is important to mention that these attributes do not imply any ordering among the observations. For example, when numbers are used to represent the different categories, this does not imply anything about the quantitative difference between the categories.

Examples for variables measured on a nominal scale are gender, religion, favorite color, etc.

====ORDINAL====

At the ordinal level of measurement, all observations are classified in several ordered categories and numbers are assigned to these categories. The categories are orderes from low to high, which is encoded in the numbers assigned to each category. These numbers are called "ordinals". However, the difference betweeen tho categories is not defined at this scale of measurement.

Comparisons like "less than" and "greater than" can be made, and also equality and inequality are defined. However, operations such as addition and subtraction are undefined.

An examples for variables measured on an ordinal scale are academic grades (1, 2, 3, 4, 5).

====INTERVAL====

Variables measured at the interval level also encode the distance between attributes. All distances between two neighbouring attributes are equal. This means for example that it is possible - and makes sense - to calculate the average of an interval variable, in contrast to ordinal variables where average numbers can not be used. However, ratios can not be applied to interval scales, for example when measuring temparature 30 degrees is not twice as warm as 15 degrees.

As in ordinal scales, relations such as less, greater or equal are defined. Operations such as multiplication and division cannot be calculated, but ratios of differences can be expressed.

{{Quotation| "If it's twice as cold today as it was yesterday," runs a popular joke, "and it was zero degrees yesterday, how cold is it today?" This illustrates the limitation of interval measurements such as Celsius and Fahrenheit temperature: by setting zero at an arbitrary point, they make it impossible to multiply and divide meaningfully. | [Wikipedia, 2008]}}

Examples for variables measured on an interval scale are temperature measured in degrees Celsius or Fahrenheit, or calendar years.

====RATIO====

The main difference to the interval scale is that at the ratio level of measurement, the ratio between two measurements is meaningful. Therefore there must be an absolute zero value. In that case, operations such as multiplication and division can be carried out as well.

Most physical measures can be used as examples for variables measured on an interval scale, such as weight or height. Other examples are age or amounts of money.

====COMPARISON====

The four levels of measurement are defined in a hierarchical way. Each level of measurement provides certain qualities, and in addition every level includes all qualities provided by the level below.

[[Image:hierarchy0426716.gif]]

[Trochim, 2006]

====EXAMPLES====

The following table shows some measurements and their level of measurement:

[[Image:examples0426716.gif]]

[Wharrad, 2004]

----

===REFERENCES===

[Stevens, 1946] Stanley Smith Stevens: On the Theory of Scales of Measurement. Science, New Series, Vol. 103, No. 2684. (Jun. 7, 1946), pp. 677-680.

[Sarle, 1995] Warren Sarle. Measurement theory: Frequently asked questions. In the Disseminations of the International Statistical Applications Institute, volume 1, edition 4, 1995, Wichita: ACG Press, pp. 61-66.

[Becker, 1997-1999] Lee A. Becker, 1997-1999. Scales of Measeurement. University of Colorado. Retrieved at: 30.10.2008. http://web.uccs.edu/lbecker/SPSS/scalemeas.htm

[Lane, 2003] David Lane. Levels of Measurement. Connexions, June 20, 2003. Retrieved at: 30.10.2008. http://cnx.org/content/m10809/2.4/

[Wharrad, 2004] Heather Wharrad. Levels of Measurement. University of Cambridge. Retrieved at: 30.10.2008. http://www.ucel.ac.uk/showroom/levels_of_measurement/downloads/levels_notes.pdf

[Trochim, 2006] William M. K. Trochim. Levels of Measurement. Research Methods Knowledge Base. Retrieved at: 30.10.2008. http://www.socialresearchmethods.net/kb/measlevl.php

[Wikipedia, 2008] Wikipedia.org, Level of measurement. Retrieved at: 30.10.2008. http://en.wikipedia.org/wiki/Level_of_measurement

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UE-InfoVis0809 0426716: New page: == LEVELS OF MEASUREMENT == ---- ===DEFINITION=== {{Quotation| [...] measurement, in the broadest sense, is defined as the assignment of numerals to objects or events according to rules...

== LEVELS OF MEASUREMENT ==

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===DEFINITION===

{{Quotation| [...] measurement, in the broadest sense, is defined as the assignment of numerals to objects or events according to rules.| [Stevens, 1946]}}

{{Quotation| Measurement of some attribute of a set of things is the process of assigning numbers or other symbols to the things in such a way that relationships of the numbers or symbols reflect relationships of the attributes of the things being measured. A particular way of assigning numbers or symbols to measure something is called a scale of measurement. |[Sarle, 1995]}}

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===INTRODUCTION===

Different levels of measurement refer to different relationships among the values that are assigned to the attributes for a variable. Knowing the level of measurement helps when interpreting the data that variable contains.

There are four levels of measurement defined: nominal, ordinal, interval and ratio. These levels are ordered increasingly, different levels of measurements use different mathematical structures, and on higher levels more operations and relations are defined. Each higher level of measurement includes the measurement principle of the lower level of measurement.

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===LEVELS OF MEASUREMENT===

====NOMINAL====

At the nominal level of measurement, names are assigned to observations. In most cases numbers are used as names, but also other symbols are possible names. The purpose of this naming is to label or classify the observations.

Two things are assigned the same name if they have the same value of the attribute. Two variable values can only be compared to each other to define if they are equal or not, there are no other relations among the categories such as "less than" or "greater than", and there are no operations such as addition or subtraction.

It is important to mention that these attributes do not imply any ordering among the observations. For example, when numbers are used to represent the different categories, this does not imply anything about the quantitative difference between the categories.

Examples for variables measured on a nominal scale are gender, religion, favorite color, etc.

====ORDINAL====

At the ordinal level of measurement, all observations are classified in several ordered categories and numbers are assigned to these categories. The categories are orderes from low to high, which is encoded in the numbers assigned to each category. These numbers are called "ordinals". However, the difference betweeen tho categories is not defined at this scale of measurement.

Comparisons like "less than" and "greater than" can be made, and also equality and inequality are defined. However, operations such as addition and subtraction are undefined.

An examples for variables measured on an ordinal scale are academic grades (1, 2, 3, 4, 5).

====INTERVAL====

Variables measured at the interval level also encode the distance between attributes. All distances between two neighbouring attributes are equal. This means for example that it is possible - and makes sense - to calculate the average of an interval variable, in contrast to ordinal variables where average numbers can not be used. However, ratios can not be applied to interval scales, for example when measuring temparature 30 degrees is not twice as warm as 15 degrees.

As in ordinal scales, relations such as less, greater or equal are defined. Operations such as multiplication and division cannot be calculated, but ratios of differences can be expressed.

{{Quotation| "If it's twice as cold today as it was yesterday," runs a popular joke, "and it was zero degrees yesterday, how cold is it today?" This illustrates the limitation of interval measurements such as Celsius and Fahrenheit temperature: by setting zero at an arbitrary point, they make it impossible to multiply and divide meaningfully. | [Wikipedia, 2008]}}

Examples for variables measured on an interval scale are temperature measured in degrees Celsius or Fahrenheit, or calendar years.

====RATIO====

The main difference to the interval scale is that at the ratio level of measurement, the ratio between two measurements is meaningful. Therefore there must be an absolute zero value. In that case, operations such as multiplication and division can be carried out as well.

Most physical measures can be used as examples for variables measured on an interval scale, such as weight or height. Other examples are age or amounts of money.

====COMPARISON====

The four levels of measurement are defined in a hierarchical way. Each level of measurement provides certain qualities, and in addition every level includes all qualities provided by the level below.

[[Image:hierarchy0426716.gif]]

[Trochim, 2006]

====EXAMPLES====

The following table shows some measurements and their level of measurement:

[[Image:examples0426716.gif]]

[Wharrad, 2004]

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===REFERENCES===

[Stevens, 1946] Stanley Smith Stevens: On the Theory of Scales of Measurement. Science, New Series, Vol. 103, No. 2684. (Jun. 7, 1946), pp. 677-680.

[Sarle, 1995] Warren Sarle. Measurement theory: Frequently asked questions. In the Disseminations of the International Statistical Applications Institute, volume 1, edition 4, 1995, Wichita: ACG Press, pp. 61-66.

[Becker, 1997-1999] Lee A. Becker, 1997-1999. Scales of Measeurement. University of Colorado, http://web.uccs.edu/lbecker/SPSS/scalemeas.htm

[Lane, 2003] David Lane. Levels of Measurement. Connexions, June 20, 2003, http://cnx.org/content/m10809/2.4/

[Wharrad, 2004] Heather Wharrad. Levels of Measurement. University of Cambridge. http://www.ucel.ac.uk/showroom/levels_of_measurement/downloads/levels_notes.pdf

[Trochim, 2006] William M. K. Trochim. Levels of Measurement. Research Methods Knowledge Base, http://www.socialresearchmethods.net/kb/measlevl.php

[Wikipedia, 2008] Wikipedia.org, Level of measurement. Retrieved at: 30.10.2008. http://en.wikipedia.org/wiki/Level_of_measurement

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