ordinal data

Examples of ordinal data in the following topics:

• Collecting and Measuring Data

  • There are four main levels of measurement: nominal, ordinal, interval, and ratio.
  • There are four main levels of measurement used in statistics: nominal, ordinal, interval, and ratio.
  • Data is collected about a population by random sampling .
  • Examples of ordinal data include dichotomous values such as "sick" versus "healthy" when measuring health, "guilty" versus "innocent" when making judgments in courts, "false" versus "true", when measuring truth value.
  • Distinguish between the nominal, ordinal, interval and ratio methods of data measurement.

• Levels of measurement: Binary, signed, and valued graphs

  • When our data are collected this way, we can graph them simply: an arrow represents a choice that was made, no arrow represents the absence of a choice.
  • This kind of data is called "signed" data.
  • The graph with signed data uses a + on the arrow to indicate a positive choice, a - to indicate a negative choice, and no arrow to indicate neutral or indifferent.
  • Yet another approach would have been to ask: "rank the three people on this list in order of who you like most, next most, and least. " This would give us "rank order" or "ordinal" data describing the strength of each friendship choice.
  • With either an ordinal or valued graph, we would put the measure of the strength of the relationship on the arrow in the diagram.

• When to Use These Tests

  • "Ranking" refers to the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted.
  • In statistics, "ranking" refers to the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted.
  • In another example, the ordinal data hot, cold, warm would be replaced by 3, 1, 2.
  • The upper plot uses raw data.
  • Indicate why and how data transformation is performed and how this relates to ranked data.

• Scales of measurement

  • Summing nominal data about the presence or absence of multiple types of ties gives rise to an ordinal (actually, interval) scale of one dimension of tie strength.
  • That is, the scores reflect finer gradations of tie strength than the simple binary "presence or absence. " This would seem to be a good thing, yet it is frequently difficult to take advantage of ordinal data.
  • Many have been adapted to continuous data -- but for interval, rather than ordinal scales of measurement.
  • Alternatively, ordinal data are sometimes treated as though they really were interval.
  • Of course, it is also possible to group the rank order scores into groups (i.e. produce a grouped ordinal scale) or dichotomize the data (e.g. the top three choices might be treated as ties, the remainder as non-ties).

• Averages of Qualitative and Ranked Data

  • The central tendency for qualitative data can be described via the median or the mode, but not the mean.
  • In order to address the process for finding averages of qualitative data, we must first introduce the concept of levels of measurement.
  • On the other hand, the median, i.e. the middle-ranked item, makes no sense for the nominal type of data since ranking is not allowed for the nominal type.
  • The ordinal scale allows for rank order (1st, 2nd, 3rd, et cetera) by which data can be sorted, but still does not allow for relative degree of difference between them.
  • An opinion survey is an example of a non-dichotomous data set on the ordinal scale for which the central tendency can be described by the median or the mode.

• Types of Data

  • Primary data is original data that has been collected specially for the purpose in mind.
  • Secondary data is data that has been collected for another purpose.
  • When the categories may be ordered, these are called ordinal categories.
  • Categorical data that judge size (small, medium, large, etc. ) are ordinal categories.
  • Attitudes (strongly disagree, disagree, neutral, agree, strongly agree) are also ordinal categories; however, we may not know which value is the best or worst of these issues.

• Basic Descriptive Statistics

  • The mean is the average value of a data set.
  • In the data set (1, 3, 3, 4, 5, 6), the average would be the sum of all of the values of the data set (22), divided by the total number of values (6), which gives a mean of 3.66 for this data set.
  • Thus the median of this data set is 3.5.
  • The median can be computed for ordinal, interval, and ratio data.
  • A data set involves a range of values.

• Types of Variables

  • A variable may also be called a data item.
  • Variables are so-named because their value may vary between data units in a population and may change in value over time.
  • Categorical variables may be further described as ordinal or nominal.
  • An ordinal variable is a categorical variable.
  • Distinguish between quantitative and categorical, continuous and discrete, and ordinal and nominal variables.

• Introduction to kinds of graphs

  • Figure 3.2 is an example of a binary (as opposed to a signed or ordinal or valued) and directed (as opposed to a co-occurrence or co-presence or bonded-tie) graph.
  • Figure 3.4 is an example of one method of representing multiplex relational data with a single graph.

• Describing Qualitative Data

  • When the categories may be ordered, these are called ordinal variables.
  • Categorical variables that judge size (small, medium, large, etc.) are ordinal variables.
  • Attitudes (strongly disagree, disagree, neutral, agree, strongly agree) are also ordinal variables; however, we may not know which value is the best or worst of these issues.
  • It is more sophisticated in qualitative data analysis.
  • Summarize the processes available to researchers that allow qualitative data to be analyzed similarly to quantitative data.