{"id":47,"date":"2018-10-31T16:45:17","date_gmt":"2018-10-31T20:45:17","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/simplestats\/?post_type=chapter&p=47"},"modified":"2019-09-09T15:03:17","modified_gmt":"2019-09-09T19:03:17","slug":"1-3-levels-of-measurement","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/simplestats\/chapter\/1-3-levels-of-measurement\/","title":{"raw":"1.3 Levels of Measurement","rendered":"1.3 Levels of Measurement"},"content":{"raw":" \r\n\r\nNow that you know there are different ways to operationalize concepts, let me introduce another term in respect to variables: level of measurement<\/em>. Each and every variable has a level of measurement. Knowing, or being able to identify, the level of measurement of a variable tells us how it has been operationalized and vice versa: knowing how an existing variable has been operationalized gives us information about its level of measurement.\r\n\r\n \r\n\r\nMore importantly, however, knowing and being able to identify a variables's level of measurement allows us to determine what we can do with that variable in terms of statistical methods and procedures<\/strong>. This last point is key to doing statistical analysis in a correct and meaningful way. The flip side is also true: misidentifying a variable's level of measurement will inevitably end in erroneous analysis and conclusions (that is, if the analysis can even be performed, as in many cases the statistical software will give an error message).[footnote]The more dangerous -- and quite frequent -- scenario, however, is when the software will execute the analysis and produce results. In that case, without an error message to warn them, the researchers would trust their analysis and results without realizing both are bogus. [\/footnote]\r\n\r\n \r\n\r\nWhy is the level of measurement so important for statistical analysis?\r\n\r\n \r\n\r\nSimply put, variables are not created equal when it comes to levels of measurement. Due to differences in the nature of the information contained within, you can do very little with some variables\u00a0in terms of analysis<\/span>\u00a0<\/span>while you can do a whole lot more with others.\u00a0<\/span>\r\n\r\n \r\n
\r\n

Do it!<\/em> 1.2. Measuring Different Types of Variables<\/em><\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nImagine you have to analyze the following (individual-level) variables:\r\n\r\na) religious affiliation,\r\n\r\nb) educational attainment,\r\n\r\nc) exam test scores,\r\n\r\nd) age.\r\n\r\n \r\n\r\nThink of what type of information would be contained within the categories of each of the four variables above. (It might help to imagine the possible answers respondents -- say, university students -- could give if asked questionnaire questions about each.)\r\n\r\n \r\n\r\nWhat more (beyond collecting it), if anything, can you do with that information? For example, can you say that one answer is more\/bigger than another? Can you identify answers as different or the same as others? Can you do some calculations with the answers?\r\n\r\n<\/div>\r\n<\/div>\r\n \r\n\r\nThe exercise above gives you a clue: there are four\u00a0<\/em>levels of measurement<\/strong>.\u00a0They are called nominal<\/em>, ordinal<\/em>, interval<\/em>, and ratio<\/em>. Each and every variable has only one level of measurement once it's operationalized.[footnote]Recall, however, that sometimes -- though not always -- one and the same variable can be operationalized in different ways. These different ways can sometimes be at different levels of measurement, depending on the type of information we want to have.[\/footnote] A variable's level of measurement is sometimes also called its measurement\u00a0scale<\/em>.\r\n\r\n \r\n\r\nThe following sub-sections provide details about each measurement scales.\r\n\r\n ","rendered":"

 <\/p>\n

Now that you know there are different ways to operationalize concepts, let me introduce another term in respect to variables: level of measurement<\/em>. Each and every variable has a level of measurement. Knowing, or being able to identify, the level of measurement of a variable tells us how it has been operationalized and vice versa: knowing how an existing variable has been operationalized gives us information about its level of measurement.<\/p>\n

 <\/p>\n

More importantly, however, knowing and being able to identify a variables’s level of measurement allows us to determine what we can do with that variable in terms of statistical methods and procedures<\/strong>. This last point is key to doing statistical analysis in a correct and meaningful way. The flip side is also true: misidentifying a variable’s level of measurement will inevitably end in erroneous analysis and conclusions (that is, if the analysis can even be performed, as in many cases the statistical software will give an error message).[1]<\/sup><\/a><\/p>\n

 <\/p>\n

Why is the level of measurement so important for statistical analysis?<\/p>\n

 <\/p>\n

Simply put, variables are not created equal when it comes to levels of measurement. Due to differences in the nature of the information contained within, you can do very little with some variables\u00a0in terms of analysis<\/span>\u00a0<\/span>while you can do a whole lot more with others.\u00a0<\/span><\/p>\n

 <\/p>\n

\n
\n

Do it!<\/em> 1.2. Measuring Different Types of Variables<\/em><\/p>\n<\/header>\n

\n

Imagine you have to analyze the following (individual-level) variables:<\/p>\n

a) religious affiliation,<\/p>\n

b) educational attainment,<\/p>\n

c) exam test scores,<\/p>\n

d) age.<\/p>\n

 <\/p>\n

Think of what type of information would be contained within the categories of each of the four variables above. (It might help to imagine the possible answers respondents — say, university students — could give if asked questionnaire questions about each.)<\/p>\n

 <\/p>\n

What more (beyond collecting it), if anything, can you do with that information? For example, can you say that one answer is more\/bigger than another? Can you identify answers as different or the same as others? Can you do some calculations with the answers?<\/p>\n<\/div>\n<\/div>\n

 <\/p>\n

The exercise above gives you a clue: there are four\u00a0<\/em>levels of measurement<\/strong>.\u00a0They are called nominal<\/em>, ordinal<\/em>, interval<\/em>, and ratio<\/em>. Each and every variable has only one level of measurement once it’s operationalized.[2]<\/sup><\/a> A variable’s level of measurement is sometimes also called its measurement\u00a0scale<\/em>.<\/p>\n

 <\/p>\n

The following sub-sections provide details about each measurement scales.<\/p>\n

 <\/p>\n

  1. The more dangerous -- and quite frequent -- scenario, however, is when the software will execute the analysis and produce results. In that case, without an error message to warn them, the researchers would trust their analysis and results without realizing both are bogus. ↵<\/a><\/li>
  2. Recall, however, that sometimes -- though not always -- one and the same variable can be operationalized in different ways. These different ways can sometimes be at different levels of measurement, depending on the type of information we want to have. ↵<\/a><\/li><\/ol><\/div>","protected":false},"author":533,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-47","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/simplestats\/wp-json\/pressbooks\/v2\/chapters\/47","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/simplestats\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/simplestats\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/simplestats\/wp-json\/wp\/v2\/users\/533"}],"version-history":[{"count":24,"href":"https:\/\/pressbooks.bccampus.ca\/simplestats\/wp-json\/pressbooks\/v2\/chapters\/47\/revisions"}],"predecessor-version":[{"id":1993,"href":"https:\/\/pressbooks.bccampus.ca\/simplestats\/wp-json\/pressbooks\/v2\/chapters\/47\/revisions\/1993"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/simplestats\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/simplestats\/wp-json\/pressbooks\/v2\/chapters\/47\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/simplestats\/wp-json\/wp\/v2\/media?parent=47"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/simplestats\/wp-json\/pressbooks\/v2\/chapter-type?post=47"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/simplestats\/wp-json\/wp\/v2\/contributor?post=47"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/simplestats\/wp-json\/wp\/v2\/license?post=47"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}