Scale interval

Interval data allow in addition, means, standard deviations (although not all common statistics computed with standard deviations), and product moment 

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Skalen-ablesung, /. scale reading, -araometer, n. graduated hydrometer, -einteilung, /. scale graduation, -intervall, n, scale interval, scale division. 

The interval scale makes use of both the order and the distance characteristics of numbers but does not use the origin property. The origin of an interval scale is arbitrary. For instance, the zero point on the scale of elevation is arbitrarily set at sea level. Other interval scales are Celsius and Fahrenheit temperature, date, latitude, and exam scores. The origin of latitude, for example, is the equator. Because this... 

When two interval scales are used to measure the amount of change in the same property, the proportionality of differences is preserved from one scale to the other. For example. Table 1.4 shows reduction potentials of three electrochemical half-cell reactions measured in volts with reference to the standard hydrogen electrode (SHE, E°) and in millivolts with reference to the standard silver-silver chloride electrode (Ag/AgCl, ). For the SHE potentials the proportion of differences between the intervals +0.54 to +0.80 and +0.34 to +0.80 is... 

Degrees Kelvin is an obvious example of a ratio scale its use gives accuracy of prediction to the gas law PV = nRT. Using the interval scale of Celsius degrees for T will not work. 

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 two methods only differ in the third step. Simple scoring uses a standardized interval scale (e.g., 0 - 100) for evaluation of all objectives. Decision makers directly rate the performance of each alternative with respect to each objective on this scale (cf. Fig. 25 for an example). Simple... 

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 with defined and constant intervals between successive values. Values are continuous. 

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

Describe the use of the two-sample t-test to determine whether there is a real difference in a measured (interval scale) end-point between two sets of observations... 

The end point is a measured value (generally on an interval scale). 

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. 

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 most common graphic displays of interval and ratio information are X-Y plots, where distance in the display corresponds to distance on the relevant property or properties. Musical notation is a specialized interval scale that makes use of a limited visual alphabet corresponding to modes of execution of notes as well as a spatial scale corresponding to pitch. Finally, for displaying ratio information, pie charts can be useful,... 

Ratio - similar to the interval scale, except that the zero point represents an absence of that character, i.e. it is an absolute zero. 

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.

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