Section 1.1 - Levels of Measurement Flashcards
Nominal, Ordinal, Interval, Ratio
a. Identify the individuals of the study and the variable from the following example:
“How important is music education in school (K–12)? The Harris Poll did an online survey of 2286 adults (aged 18 and older) within the United States. Among the many questions, the survey asked if the respondents agreed or disagreed with the statement “Learning and habits from music education equip people to be better team players in their careers.” In the most recent survey, 71% of the study participants agreed with the statement.”
The individuals are the 2286 adults who participated in the online survey. The variable is the response agree or disagree with the statement that music education equips people to be better team players in their careers.
b. Do the data comprise a sample? If so, what is the underlying population?
“How important is music education in school (K–12)? The Harris Poll did an online survey of 2286 adults (aged 18 and older) within the United States. Among the many questions, the survey asked if the respondents agreed or disagreed with the statement “Learning and habits from music education equip people to be better team players in their careers.” In the most recent survey, 71% of the study participants agreed with the statement.”
The data comprise a sample of the population of responses from all adults in the United States.
c. Is the variable qualitative or quantitative?
“How important is music education in school (K–12)? The Harris Poll did an online survey of 2286 adults (aged 18 and older) within the United States. Among the many questions, the survey asked if the respondents agreed or disagreed with the statement “Learning and habits from music education equip people to be better team players in their careers.” In the most recent survey, 71% of the study participants agreed with the statement.”
Qualitative—the categories are the two possible responses: agrees or disagrees with the statement that music education equips people to be better team players in their careers.
d. Identify a quantitative variable that might be of interest.
“How important is music education in school (K–12)? The Harris Poll did an online survey of 2286 adults (aged 18 and older) within the United States. Among the many questions, the survey asked if the respondents agreed or disagreed with the statement “Learning and habits from music education equip people to be better team players in their careers.” In the most recent survey, 71% of the study participants agreed with the statement.”
Age or income might be of interest.
e. Is the proportion of respondents in the sample who agree with the statement regarding music education and effect on careers a statistic or a parameter?
“How important is music education in school (K–12)? The Harris Poll did an online survey of 2286 adults (aged 18 and older) within the United States. Among the many questions, the survey asked if the respondents agreed or disagreed with the statement “Learning and habits from music education equip people to be better team players in their careers.” In the most recent survey, 71% of the study participants agreed with the statement.”
Statistic—the proportion is computed from sample data.
The _____ level of measurement applies to data that consist of names, labels, or categories. There are no implied criteria by which the data can be ordered from smallest to largest.
nominal
The _____ level of measurement applies to data that can be arranged in order. However, differences between data values either cannot be determined or are meaningless.
ordinal
The ____ level of measurement applies to data that can be arranged in order. In addition, differences between data values are meaningful.
interval
The ____ level of measurement applies to data that can be arranged in order. In addition, both differences between data values and ratios of data values are meaningful. Data at the ratio level have a true zero.
ratio
Is the following nominal, ordinal, interval, or a ratio level of measurement?
Taos, Acoma, Zuni, and Cochiti are the names of four Native American pueblos from the population of names of all Native American pueblos in Arizona and New Mexico.
These data are at the nominal level.
Notice that these data values are simply names. By looking at the name alone, we cannot determine if one name is “greater than or less than” another. Any ordering of the names would be numerically meaningless.
Is the following nominal, ordinal, interval, or a ratio level of measurement?
In a high school graduating class of students, Jim ranked 25th, June ranked 19th, Walter ranked 10th, and Julia ranked 4th, where is the highest rank.
These data are at the ordinal level.
Ordering the data clearly makes sense. Walter ranked higher than June. Jim had the lowest rank, and Julia the highest. However, numerical differences in ranks do not have meaning. The difference between June’s and Jim’s ranks is 6, and this is the same difference that exists between Walter’s and Julia’s ranks. However, this difference doesn’t really mean anything significant. For instance, if you looked at grade point average, Walter and Julia may have had a large gap between their grade point averages, whereas June and Jim may have had closer grade point averages. In any ranking system, it is only the relative standing that matters. Computed differences between ranks are meaningless.
Is the following nominal, ordinal, interval, or a ratio level of measurement?
Body temperatures (in degrees Celsius) of trout in the Yellowstone River.
These data are at the interval level.
We can certainly order the data, and we can compute meaningful differences. However, for Celsius-scale temperatures, there is not an inherent starting point. The value 0 degrees may seem to be a starting point, but this value does not indicate the state of “no heat.” Furthermore, it is not correct to say that 20 degrees is twice as hot as 10 degrees.
Is the following nominal, ordinal, interval, or a ratio level of measurement?
Length of trout swimming in the Yellowstone River.
These data are at the ratio level.
An 18-inch trout is three times as long as a 6-inch trout. Observe that we can divide 6 into 18 to determine a meaningful ratio of trout lengths.
What is a suitable calculate for Nominal Data?
We can put the data into categories.
What is a suitable calculate for Ordinal Data?
We can order the data from smallest to largest or “worst” to “best.” Each data value can be compared with another data value.
What is a suitable calculate for Interval Data?
We can order the data and also take the differences between data values. At this level, it makes sense to compare the differences between data values. For instance, we can say that one data value is 5 more than or 12 less than another data value.
What is a suitable calculate for Ratio Data?
We can order the data, take differences, and also find the ratio between data values. For instance, it makes sense to say that one data value is twice as large as another.
Is the following nominal, ordinal, interval, or a ratio level of measurement?
The senator’s name is Sam Wilson.
Nominal
Is the following nominal, ordinal, interval, or a ratio level of measurement?
The senator is 58 years old.
Ratio level.
Notice that age has a meaningful zero. It makes sense to give age ratios. For instance, Sam is twice as old as someone who is 29.
Is the following nominal, ordinal, interval, or a ratio level of measurement?
The years in which the senator was elected to the Senate are 2000, 2006, and 2012.
Interval level.
Dates can be ordered, and the difference between dates has meaning. For instance, 2006 is 6 years later than 2000. However, ratios do not make sense. The year 2000 is not twice as large as the year 1000. In addition, the year 0 does not mean “no time.”
Is the following nominal, ordinal, interval, or a ratio level of measurement?
The senator’s total taxable income last year was $878,314
Ratio level. It makes sense to say that the senator’s income is times that of someone earning $878,314.
Is the following nominal, ordinal, interval, or a ratio level of measurement?
The senator surveyed his constituents regarding his proposed water protection bill. The choices for response were strongly support, support, neutral, against, or strongly against.
Ordinal level.
The choices can be ordered, but there is no meaningful numerical difference between two choices.
Is the following nominal, ordinal, interval, or a ratio level of measurement?
The senator’s marital status is “married.”
Nominal level
Is the following nominal, ordinal, interval, or a ratio level of measurement?
A leading news magazine claims that the senator is ranked seventh for his voting record on bills regarding public education.
Ordinal level.
Ranks can be ordered, but differences between ranks may vary in meaning.
