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Nominal is categorical in nature a. b. c. d. Name of schools Car model you drive Types of books people read Easy to remember because nominal sounds like name because they have the same Latin root. Ordinal refers to quantities that have a natural ordering, rankings a. b. c. d. Favorite sports Peoples place in line Order of runners finishing a race Choice on a scale of 1 to 5, a. On a scale the difference between 9 and 10 not the same as a difference between 6 and 7. or 2 and 3, and, 4 and 5 differences aren’t the same. b. Easy to remember as ordinal sounds like order. Interval data is like ordinal except we can say the intervals between each value equally split, so the differences would be the same. a. Temperature in Celsius or Fahrenheit (the differences between 29 and 30 degrees F is the same magnitude as the difference between 78 and 79 degrees Fahrenheit. b. One step up from an ordinal data. Ratio Data is interval data with a natural zero point. a. Time is a ratio since 0 time is meaningful. Maybe no movement at zero time. b. Ratio is all of the above plus a 0 as part of the data Who Cares? Where did this all come from you ask and why do we care? Well, the short answer is, we should care most about identifying nominal data--which is categorical data. If it isn't nominal, then it's quantitative. So why all the fuss? In the 1940's when behavioral science was in its infancy, there was much concern about trying to make the practice as legitimate as possible. Psychology and other Social and Behavioral Sciences are considered soft sciences as opposed to the hard sciences of Chemistry and Physics. It was thought that by applying some of the same thinking from the hard sciences, it would improve the legitimacy of these soft sciences--as well as the veracity of the claims made. Levels of Measurement part 2 1 What is the Difference Between Nominal and Ordinal Data? Nominal and Ordinal Data are two of the major four types of data. They’re different ways to classify and express information. Each type tells you different information about what you are trying to measure and allows for various types of statistics. Choosing the most appropriate type of data for your research is an important first step in Statistics. Nominal Data is based on labeling or “coding” information into categories. Generally, you are creating names for the information based on characteristics of the category. For example, you could classify hair colors into brunette, blonde, red, or black. When entering your data, you assign a code, or number, to each category. For example, brunette = 1, blonde = 2. This number is simply a shorthand that means brunette. Ordinal Data describes the order of data based on a scale. In the scale, there’s no way to tell the relative difference among the groups. For example, we can say something or someone arrives 1st, 2nd, 3rd, or last, but we don’t know the time between each place without more information. Scales are often used for attitudes --- for example, satisfied to unsatisfied. Interval Data is when we know the difference between groups. We know the exact time differences between places assigned in a race, or the exact difference between earning $20,000 and $30,000 per year. Difference Between Types Nominal data is only about labels, whereas ordinal data provides more information about the rank, preference or order of the evidence. With ordinal data, you can infer the range of opinion or order. Nominal data can not make inferences because numbers are only codes for the assigned lables, they don’t mean anything mathematically. For instance, you could not calculate the difference between a brunette and a blonde if assigned the numbers 1 and 2 respectively. Both provide general description of data, but neither provides information about relative difference between data points. Levels of Measurement part 2 2 Different Statistics Because the data types are different, different statistics are possible. For nominal data, you can only calculate the mode (most of), which is counting the number of times each data point occurs. (how many blondes and brunettes). For Ordinal Data, you can calculate the mode and the median, but not the mean. The median is the middle number in the data set, so you have information on the central tendency of the order or the rank. Interval Data uses central tendencies of mode, median and arithmetic mean, as well as range and standard deviation, which are important especially in money matters and sports statistics. Ratio data uses mode, median, arithmetic mean, geometric mean, range, standard deviation and coefficients of variations. With the Olympics there is a lot of good data sets. By Country: Nominal Finishing Place: Ordinal Time: Interval and Ratio Ok to compute… Frequency Distribution (MODE) Median and percentiles Add or Subtract Mean, Standard Deviation, Standard Error of the mean Ratio, or coefficient of variation Nominal Yes Ordinal Yes Interval Yes Ratio Yes No Yes Yes Yes No No No No Yes Yes Yes Yes No NO NO Yes Levels of Measurement part 2 3 Does it matter for data analysis? The concepts are mostly pretty obvious, but putting names on different kinds of variables can help prevent mistakes like taking the average of a group of zip codes, or taking the ratio of two pH values. Beyond that, there is not much to putting labels on the different kinds of variables, but it really helps you plan your anlyses to interpret the results. . Note that the categories are not as clear cut as they sound. What kind of variable is color? In a psychological study of perception, different colors would be regarded as nominal. In a physics study, color is quantified by wavelength, color could be a ratio variable as well as nominal. What about counts? If your dependent variable is the number of cells in a certain volume, what kind of variable is that. It has all the properties of a ratio variable, except it must be an integer. Is this a ratio variable or not? These questions just point out that the classification scheme appears to be more complicated and comprehensive than it appears. So the more in depth statistics becomes the more knowledge about what kind of data is important and how to collect so it is reliable to what is being researched. Levels of Measurement part 2 4