Interval scale data

Now think about the differences in weights as we step from one object to the next. These steps, each of one unit along the scale, have the following characteristics  

The steps are of an exactly defined size. If you told somebody that you had a series of objects like those described above, he or she would know exactly how large the weight differences were as we progressed along the series. 

All the steps are of exactly the same size. The weight difference between the 1 and 2 g objects is the same as the step from 2 to 3 g or from 6 to 7 g, and so on. 

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Where data are reasonably normally distributed, non-parametric methods are a little less powerful than their parametric equivalents, but where the data are severely nonnormal, the non-parametric test may be much more powerful. With non-normally distributed interval scale data, the best solution is transformation to normality, but failing that, non-parametric methods can be used with only modest loss of power. 

Although interval scale data (e.g. ages) will probably be reported in bands, there is a good case for collecting it as actual values. Outcome data are commonly classified as factual , opinion seeking or knowledge testing . 

The student collected one data pair for each business day for the past nine-months. Each data pair consisted of (1) the amount of money issued by her department in computer-generated checks on that day, and (2) the amount of money in checks that cleared the banks on that day. Table 10.1 is a four-column list of the 177 pairs of data she collected. Each entry gives (1) the sequence, or acquisition number ( Seq ), starting with Thursday, August 8, and increasing by one each business day, five business days a week (2) a nominal scale (that can also be used as an ordinal or interval scale) for the day of the week ( D ), where 1 = Monday, 2 = Tuesday, 3 = Wednesday, 4 = Thursday, and 5 = Friday (3) the amount of money issued in checks ( Iss ) and (4) the amount of money in checks that cleared ( Clr ). 

There are two main types of quantitative data discrete and continuous. Discrete quantitative data usually come about by the counting of numbers of events. Examples of this form of data are the number of asthma attacks, the numbers of rescue tablets taken, the number of relapse events, etc. There are two types of continuous quantitative data defined by, whether there is a true zero point of the scale or not. If there is such a zero point the scale is a ratio scale, otherwise it is an interval scale. Examples of the former are height, weight or volume, etc, while a typical example of the latter is temperature in which the origin is essentially arbitrary - 0°F is... 

The first two types of data that we will consider are both concerned with the measurement of some characteristic. Interval scale , or what is commonly called Continuous measurement , data include most of the information that would be generated in a laboratory. These include weights, lengths, timings, concentrations, pressures, etc. Imagine we had a series of objects weighing 1, 2, 3 up to 7 g as in Figure 1.1. 

Because these measurements have constant sized steps (intervals), the measurement scale is described as a constant interval scale and the data as interval scale . Although the weights quoted in Figure 1.1 are exact integers, weights of 1.5 or 3.175 g are perfectly possible, so the measurement scale is said to be continuous . 

Since we have no idea how large the steps are between scores, we obviously cannot claim that all steps are of equal size. In fact, it is not even necessarily the case that the difference between scores of —2 and 0 is greater than that between +1 and +2. So, neither of the special characteristics of an constant interval scale apply to this data. 

Interval scale - measurements on a scale with defined and constant intervals. Data are continuous. 

With interval scale (continuous measurement) data, there are two aspects to the figures that we should be trying to describe ... 

With an unpaired design and measurements on an interval scale, we would have used a two-sample t-test to check for any difference. However, this data are ordinal and not remotely normally distributed, so we will have to move to its non-parametric equivalent - the Mann-Whitney test. 

As explained in Appendix M, you can estimate the values of the coefficients in Eq. (3.32) by the method of least squares. We look at another way, a graphical method. Over very wide temperature intervals experimental data will not prove to be exactly linear as indicated by Eq. (3.31), but have a slight tendency to curve. This curvature can be straightened out by using a special plot known as a Cox chart. The In or logic of the vapor pressure of a compound is plotted against a special nonlinear temperature scale constructed from the vapor-pressure data for water (called a reference substance). 

Table 5A.—Stem Correction Data for Pensky-Martin Flash-point Apparatus Thermometer used up to 150 C., range 40 to 160°C. in 1 intervals, scale length 9.5 cm. Thermometer used from 200 to 300°, range 200 to 360° in 1° intervals, scale length 12 cm.

The nonparametric one-way ANOVA can be quite useful in a number of settings. The most obvious is when reasonable judgment does not allow you to conclude that the distributional assumptions for the one-way parametric ANOVA will hold. Another instance is when the data available for analysis are only ordinal (for example, like a rank) such that the difference between two values does not hold the same meaning as an interval scaled random variable. 

The scales are hierarchically arranged from least information provided (nominal) to most information provided (ratio). Any scale can be degraded to a lower scale, eg, interval data can be treated as ordinal. For the USMLE, concentrate on identifying nominal and interval scales. 

The quantity of work to be done must be defined by the appropriate time period, which could be by as little as a 15-minute interval for cashiers and as long as a day for paper mills. For continuous process industries, such as chemical plants and some mining processes, the definition of what is needed is relatively easy to determine. Even so, the work must be defined by the hour and day of the year to allow for maintenance and shutdowns for holidays. There are many other industries that also have a well-known stable demand for work profile—for example, prisons, long-term health care facilities, and many manufacturing systems, such as assembly lines. At the other end of the scale are situations such as retad outlets and telephone operators, that have a demand that varies constantly during the day, and from day to day, and from season to season. Many of the organizations with such a fluctuating demand pattern have a detailed data bank of historic data, usually by the 15-minute interval. These data can be used to predict the work requirements for future time periods. 

By conducting a Rasch analysis of basic test (or survey) data, researchers can quickly convert possibly non-equal interval raw data to interval data. To best understand this issue, consider the following Sarah completes a test and earns 95/100, while Pam emis 90/100. The difference between Sarah and Pam may not necessarily be the same as the difference between Tom who earns 50/100 and Henry who scores 55/100. Although the differences (5 points in each case) between the raw scores are the same, the raw score at different parts of the scale may not have die same substantive meaning. Rasch analysis software can be easily used to convert the possibly non-interval raw score data of tests and surveys to an interval scale, and it is that data which is used for statistical analyses. 

Ratio data This method is an estimation of magnitude by comparison with a reference stimulus. Data are collected on a magnitude estimation scale. Panelists receive a reference sample to which any number that seems appropriate (unspecified modulus) or a prescribed value (fixed modulus) is assigned. All the other samples are scaled in comparison with the reference sample. And this scale can be open or limited by the highest and lowest standards provided. A ratio scale has the same properties as an interval scale and, in addition, the ratio between the value allocated to two stimuli is equal to the ratio between the perceived intensities of these stimuli. 

We claim that non-metric MDS is better suited to analyzing free sorting data than metric MDS (Faye et al., 2004 Lawless et al., 1995). Our claim is backed up by the fact that the dissimilarities in matrix A are computed by counting the number of subjects who did not set the products in the same groups and, therefore, do not stem from interval or ratio scale data. 

An interval scale is characterized by three basic properties, including those of nominal and ordinal data. 

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