Levels and Scales of Measurement in Statistics

Levels and Scales of Measurement in Statistics Level of measurement refers to the particular way that a variable is measured within scientific research, and  scale of measurement refers to the particular tool that a researcher uses to sort the data in an organized way, depending on the level of measurement that they have selected. Choosing the level and scale of measurement are  important parts of the research design process  because they are necessary for systematized measuring and categorizing of data, and thus for analyzing it and drawing conclusions from it as well that are considered valid. Within science, there are four commonly used levels and scales of measurement: nominal, ordinal, interval, and ratio. These were developed by  psychologist Stanley Smith Stevens, who wrote about them in a 1946 article in  Science, titled On the Theory of Scales of Measurement. Each level of measurement and its corresponding scale is able to measure one or more of the four properties of measurement, which include identity, magnitude, equal intervals, and a minimum value of zero. There is a hierarchy of these different levels of measurement. With the lower levels of measurement (nominal, ordinal), assumptions are typically less restrictive and data analyses are less sensitive. At each level of the hierarchy, the current level includes all the qualities of the one below it in addition to something new. In general, it is desirable to have higher levels of measurement (interval or ratio) rather than a lower one. Let’s examine each level of measurement and its corresponding scale in order from lowest to highest in the hierarchy. The Nominal Level and Scale A nominal scale is used to name the categories within the variables you use in your research. This kind of scale provides no ranking or ordering of values; it simply provides a name for each category within a variable so that you can track them among your data. Which is to say, it satisfies the measurement of identity, and identity alone. Common examples within sociology include the nominal tracking of  sex (male or female),  race  (white, Black, Hispanic, Asian, American Indian, etc.),  and class  (poor, working class, middle class, upper class). Of course, there are many other variables one can measure on a nominal scale. The nominal level of measurement is also known as a categorical measure  and is considered qualitative in nature. When doing statistical research and using this level of measurement, one would use the mode, or the most commonly occurring value, as a  measure of central tendency. The Ordinal Level and Scale Ordinal scales are used when a researcher wants to measure something that is not easily quantified, like feelings or opinions. Within such a scale the different values for a variable are progressively ordered, which is what makes the scale useful and informative. It satisfies both the properties of identity and of magnitude. However, it is important to note that as such a scale is not quantifiable- the precise differences between the variable categories are unknowable. Within sociology, ordinal scales are commonly used to measure peoples views and opinions on social issues,  like racism  and sexism, or how important certain issues are to them in the context of a political election. For example, if a researcher wants to measure the extent to which a population believes that racism is a problem, they could ask a question like How big a problem is racism in our society today? and provide the following response options: its a big problem, it is somewhat a problem, it is a small problem, and racism is not a problem. When using this level and scale of measurement, it is the median which denotes central tendency. The Interval Level and Scale Unlike nominal and ordinal scales, an interval scale is a numeric one that allows for ordering of variables  and provides a precise, quantifiable understanding of the differences between them (the intervals between them). This means that it satisfies the three properties of identity, magnitude,  and  equal intervals. Age is a common variable that sociologists track using an interval scale, like 1, 2, 3, 4, etc. One can also turn non-interval, ordered variable categories into an interval scale to aid  statistical analysis. For example,  it is common to measure income as a range, like $0-$9,999; $10,000-$19,999; $20,000-$29,000, and so on. These ranges can be turned into intervals that reflect the increasing level of income, by using 1 to signal the lowest category, 2 the next, then 3, etc. Interval scales are especially useful because they not only allow for measuring the frequency and percentage of variable categories within our data, they also allow us to calculate the  mean, in addition to the median, mode. Importantly, with the interval level of measurement, one can also calculate  the standard deviation. The Ratio Level and Scale The ratio scale of measurement is nearly the same as the interval scale, however, it differs in that it has an absolute value of zero, and so it is the only scale that satisfies all four properties of measurement. A sociologist would use a ratio scale to measure actual earned income in a given year, not divided into categorical ranges, but ranging from $0 upward. Anything that can be measured from absolute zero can be measured with a ratio scale, like for example the number of children a person has, the  number of elections a person has voted in, or the  number of friends who are of a race different from the respondent. One can run all the statistical operations as can be done with the interval scale, and even more with the ratio scale. In fact, it is so called because one can create ratios and fractions from the data when one uses a ratio level of measurement and scale. Updated  by Nicki Lisa Cole, Ph.D.

Trifles A One-act Play by Susan Glaspell

Trifles A One-act Play by Susan Glaspell Farmer John Wright has been murdered. While he was asleep in the middle of the night, someone strung a rope around his neck. Shockingly, that someone might have been his wife, the quiet and forlorn Minnie Wright.   Playwright Susan Glaspells one-act play, written in 1916,  is loosely based on true events. As a young reporter, Glaspell covered a murder case in a small town in Iowa. Years later, she crafted a short play, Trifles,  inspired by her experiences and observations. The Meaning of the Name Trifles for This Psychological Play The play was first performed in Provincetown, Massachusetts, and Glaspell herself played the character, Mrs. Hale. Considered an early illustration of feminist drama, the themes of the play focus on men and women and their psychological states along with their social roles. The word trifles typically refer to objects of little to no value. It makes sense in the context of the play due to the items that the female characters come across. The interpretation may also be that men do not understand the value of women, and consider them trifles. The Plot Summary of a Family Murder-drama The sheriff, his wife, the county attorney, and the neighbors (Mr. and Mrs. Hale) enter the kitchen of the Wright household. Mr. Hale explains how he paid a visit to the house on the previous day. Once there, Mrs. Wright greeted him but behaved strangely. She eventually stated in a dull voice that her husband was upstairs, dead.  (Though Mrs. Wright is the central figure in the play, she never appears onstage. She is only referred to by the on-stage characters.) The audience learns of John Wright’s murder through Mr. Hale’s exposition. He is the first, aside from Mrs. Wright, to discover the body. Mrs. Wright claimed that she was sound asleep while someone strangled her husband. It seems obvious to the male characters that she killed her husband, and she is been taken into custody as the prime suspect. The Continued Mystery With Added Feminist Critique The attorney and sheriff decide that there is nothing important in the room: â€Å"Nothing here but kitchen things.† This line is the first of many disparaging comments said to minimize the importance of women in society, as noticed by several Feminist critics.  The men criticize Mrs. Wright’s housekeeping skills, irking Mrs. Hale and the sheriff’s wife, Mrs. Peters. The men exit, heading upstairs to investigate the crime scene. The women remain in the kitchen. Chatting to pass the time, Mrs. Hale and Mrs. Peters notice vital details that the men would not care about: Ruined fruit preservesBread that has been left out of its boxAn unfinished quiltA half clean, half messy table topAn empty birdcage Unlike the men, who are looking for forensic evidence to solve the crime, the women in Susan Glaspells Trifles observe clues that reveal the bleakness of Mrs. Wright’s emotional life. They theorize that Mr. Wright’s cold, oppressive nature must have been dreary to live with. Mrs. Hale comments about Mrs. Wright being childless: â€Å"Not having children makes less work- but it makes a quiet house.† The  women are simply trying to pass the awkward moments with civil conversation. But to the audience, Mrs. Hale and Mrs. Peters unveil a psychological profile of a desperate housewife. The Symbol of Freedom and Happiness in the Story When gathering up the quilting material, the two women  discover a fancy little box. Inside, wrapped in silk, is a dead canary. Its neck has been wrung. The implication is that Minnie’s husband did not like the canarys beautiful song (a symbol of his wife’s desire for freedom and happiness). So, Mr. Wright busted the cage door and strangled the bird. Mrs. Hale and Mrs. Peters do not tell the men about their discovery. Instead, Mrs. Hale puts the box with the deceased bird into her coat pocket, resolving not to tell the men about this little â€Å"trifle† they have uncovered. The play ends with the characters exiting the kitchen and the women announcing that they have determined Mrs. Wright’s quilt making style. She â€Å"knots it† instead of â€Å"quilts it†- a play on words denoting the way in which she killed her husband. The Theme of the Play Is That Men Do Not Appreciate Women The men within this play betray a sense of self-importance. They present themselves as tough, serious-minded detectives  when in truth, they are not nearly as observant as the female characters. Their pompous attitude  causes the women to feel defensive and form ranks. Not only do Mrs. Hale and Mrs. Peters bond, but they also  choose to hide evidence as an act of compassion for Mrs. Wright. Stealing the box with the dead bird is an act of loyalty to their gender and an act of defiance against a callous patriarchal society. Key Character Roles in the Play Trifles Mrs. Hale: She had not visited the Wright household for over a year because of its bleak, cheerless atmosphere. She believes that Mr. Wright is responsible for crushing the merriment out of Mrs. Wright. Now, Mrs. Hale feels guilty for not visiting more often. She believes she could have improved Mrs. Wright’s outlook on life.Mrs. Peter: She has tagged along to bring back clothes for the imprisoned Mrs. Wright. She can relate to the suspect because they both know about â€Å"stillness.† Mrs. Peters reveals that her first child died at the age of two. Because of this tragic experience, Mrs. Peters understands what it is like to lose a loved one (in Mrs. Wright’s case- her songbird).Mrs. Wright: Before she was married to John Wright, she was Minnie Foster, and she was more cheerful in her youth. Her clothes were more colorful, and she loved to sing. Those attributes diminished after her wedding day. Mrs. Hale describes Mrs. Wright’s personality: She was kind of like a bird herself–real sweet and pretty, but kind of timid and- fluttery. How- she- did- change.