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.

• 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.

• 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.

• Mann-Whitney U-Test

  • The responses are ordinal (i.e., one can at least say of any two observations which is the greater).
  • a measure of the central tendencies of the two groups (means or medians; since the Mann–Whitney is an ordinal test, medians are usually recommended)
  • $U$ remains the logical choice when the data are ordinal but not interval scaled, so that the spacing between adjacent values cannot be assumed to be constant.
  • For large samples from the normal distribution, the efficiency loss compared to the $t$-test is only 5%, so one can recommend Mann-Whitney as the default test for comparing interval or ordinal measurements with similar distributions.

• Types of variables

  • Examine the fed spend, pop2010, state, and smoking ban variables in the county data set.
  • A variable with these properties is called an ordinal variable.
  • To simplify analyses, any ordinal variables in this book will be treated as categorical variables.
  • Data were collected about students in a statistics course.

• 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.

• 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.

• Data basics exercises

  • There were 50 flowers from each species in the data set.
  • (b) How many numerical variables are included in the data?
  • (c) How many categorical variables are included in the data, and what are they?
  • If categorical, indicate if the variable is ordinal.
  • The data matrix displays a portion of the data collected in this survey.

• Levels of Measurement

  • This is what distinguishes ordinal from nominal scales.
  • Unlike nominal scales, ordinal scales allow comparisons of the degree to which two subjects possess the dependent variable.
  • Like an ordinal scale, the objects are ordered (in terms of the ordering of the numbers).
  • Some sample data are shown below.
  • Consider the following hypothetical data: