Stats Anjal

Explain the Scales of Measurements

Why we need the scale of measurements?

Observation and measurement are the fundamentals of empirical research. One basic technique for studying any phenomenon involves carefully observing it as it occurs. Such observation is not the kind of informal inquiry that all of us practice from childhood on; rather, in scientific research, it is observation accompanied by careful, accurate measurements (Baron & Kalsher 2001). Uniform and replicable measurement scales make observation objective and comparable with those of other investigators both contemporaries and those of subsequent generations. However full of insight an investigator’s “considerings” might be, if they are not supported by observations objectively recorded in quantitative terms, they are unlikely to form a basis for the considerings of successive generations of investigators (MacMahon & Trichopoulos, 1996).

Same lacunae has been pointed out by Greenwood (1935), in Hippocrates’ paper titled On Airs, Waters, and Places, which states: “Whoever wishes to investigate medicine properly should proceed thus: in the first place to consider the seasons of the year, and what effects each of them produces. Then the winds, the hot and the cold, especially such as are common to all countries, and then such as are peculiar to each locality…one should consider most attentively the waters which the inhabitants use, whether they be marshy and soft, or hard and running from elevated and rocky situations, and then if saltish and unfit for cooking; and the ground, whether it be naked and deficient in water, or wooded and well watered, and whether it lies in a hollow, confined situation, or is elevated and cold; and one should consider the mode in which the inhabitants live, and what are their pursuits, whether they are fond of drinking and eating to excess, and given to indolence, or are fond of exercise and labor.”

In light of such clear instructions from this influential teacher, it is remarkable that virtually nothing was discovered about the cause-effect relationships of unhealthy environments during the subsequent 2000 years. Greenwood (1935), attributes this to the fact that the operative word in Hippocrates’ statement is consider, not count or measure.

Counting and Measurement

One of the first “counters” of health events was John Graunt. In 1662, John Graunt published his Natural and Political Observations Made upon the Bills of Mortality (Graunt 1662, re-published 1939). He is widely regarded as a founder of the science of biostatistics. In using quantitative methods, he led the way to epidemiology. Since the methods he used saw no further development for almost 200 years, Graunt might be more appropriately regarded as forerunner, rather than a founder of epidemiology.

The roots of today’s epidemiology are more clearly detectable in the work of William Farr, a physician who was given responsibility for medical statistics in the office of the Registrar General for England and Wales in 1839. The annual reports of the Registrar General during the subsequent 40 years established a tradition of the careful application of vital data to problems of public health. In considering the population at risk, the need to take into account differences in characteristics of compared groups, the biases involved in the selection of persons exposed to a suspected cause, and the ways of measuring risk, Farr identified some of the major concerns of researchers today [MacMahon & Trichopoulos 1996].

Types of measurement scale (Abramson & Abramson 1999)

As part of the process of clarifying each of the variables to be studied, its scale of measurement should be specified. The scale of measurement may be categorical (consisting of two or more mutually exclusive categories) or metric (noncategorical: interval and ratio scales).

Types of Scale of Measurements

Nominal :

A categorical scale consists of mutually exclusive categories (classes). If these do not fall into a natural order, the scale is nominal. Numbers may be used to identify the categories, but these are ‘code numbers’ with no quantitative significance. Examples are:

(a)        Marital status: single, married, widowed, divorced.

(b)        Religion: Hindu, Muslim, Buddhist, Christian, Sikh, others.

(c)        Types of Anemia: (i) iron deficiency, (ii) other deficiency anemia, (iii) hereditary hemolytic anemia, (iv) acquired hemolytic anemia, (v) aplastic anemia, (vi) other anemias.

If the categories fall into what is regarded as a natural order, the scale is ordinal. The scale shows ranks, or positions on a ladder; each class shows the same situational relationship to the class that follows it. If numbers are used, they indicate the positions of the categories in the series. Examples are:

(a) Social Class: I, II, III, IV

(b) Years of education: 0, 1 – 5, 6 – 9, 10 – 12, > 12.

(c)Limitations of activity: 0, none; 1, limited activity but not home-bound; 2, home-bound but not bed-bound; 3, bed-bound.

(d)Severity of disease: mild, moderate, severe.

(e)Pain score: 0, no pain; 1, mild pain; 2, moderate pain; 3, severe pain; 4, unbearable pain.

An ordinal scale of measurement is ‘stronger’ than a nominal one, in the sense that it provides more information. When there is a choice, use of an ordinal scale is preferable.


With ordinal scales, the order of the values is what’s important and significant, but the differences between each one is not really known.  Take a look at the example below.  In each case, we know that a #4 is better than a #3 or #2, but we don’t know–and cannot quantify–how much better it is.  For example, is the difference between “OK” and “Unhappy” the same as the difference between “Very Happy” and “Happy?”  We can’t say.Ordinal scales are typically measures of non-numeric concepts like satisfaction, happiness, discomfort, etc.“Ordinal” is easy to remember because is sounds like “order” and that’s the key to remember with “ordinal scales”–it is the order that matters, but that’s all you really get from these.

A scale with only two categories is a dichotomy (or binary scale). Many statistical procedures are applicable to dichotomies but not to scales with three or more categories (polychotomous). Numbers may be used as code numbers, or to indicate the presence or absence of an attribute (1 & 0) respectively.

Examples of dichotomous or binary scales are:

  • Agreement with a statement: agree, disagree.
  • Sex: 1, male; 2, female.
  • Presence of mental illness: 0, absent; 1, present.
  • Occurrence of headaches: 0, no; 1, yes.
Example of Ordinal Scales
Ordinal Scale Example

Interval and ratio scales(noncategorical, metric, or dimensional scales)

It use numbers that indicate the quantity of what is being measured. They have two features: firstly, equal differences in the attribute between any pairs of numbers in the scale mean equal differences in the attribute being measured, i.e. the difference between any two values reflects the magnitude of the difference in the attribute – the difference in temperature between 22 and 26º C is the same as that between 32 and 36° C; this makes the scale an interval scale. Secondly, in some of these scales, zero indicates absence of the attribute, as a consequence of which the ratio between any two values indicates the ratio between the amounts of the attribute for e.g. an income of Rs 1000 is twice as high as an income of Rs 500; this additional feature makes the scale a ratio scale. Most noncategorical scales have both these features; exceptional ones, like the Centigrade scale for temperature, are interval but not ratio scales – 0° C does not mean ‘absence of heat’, and 20° C is therefore not ‘twice as hot’ as 10° C. Examples of ratio scales are:

  • Weight: measured in kgs.
  • Height: measured in cm.
  • Blood pressure: measured in mm of Hg.

Interval or ratio scale provides more information than an ordinal one, and is to be preferred when there is a choice. Interval or ratio scale may be continuous or discrete. The scale is said to be continuous if an infinite number of values is possible along a continuum, e.g. when measuring or cholesterol level. It is discrete if only certain values along the scale are possible – a woman’s parity, for e.g. cannot be 3.44

example of interval scale
Interval Scale of Measurement

An interval or ratio scale may be ‘collapsed’ into broader categories by grouping values together, as under:

Income (in rupees); 500 – 999, 1000 – 1499, 1500 – 1999 and so on.If equal class intervals are used, as in the above example, the scale can still be treated as an interval one, taking the midpoints, ( 725, 1225, 1725, etc) as the values of the successive classes. However, it would be better to consider it an ordinal scale now, as the individual values may not be uniformly spread within the classes, and the intervals, between the average incomes of people in adjacent classes may hence not be equal. The scale is immediately degraded to an ordinal scale if an ‘open-ended’ category such as income > Rs 2000 is used. Also, if the class intervals vary, e.g. 500 – 999, 1000 – 2000, 2000 – 4000, etc, the scale is definitely an ordinal one.

Interval scales are numeric scales in which we know both the order and the exact differences between the values.  The classic example of an interval scale is Celsius temperature because the difference between each value is the same.  For example, the difference between 60 and 50 degrees is a measurable 10 degrees, as is the difference between 80 and 70 degrees.

Interval scales are nice because the realm of statistical analysis on these datasets opens up.  For example, central tendency can be measured by mode, median, or mean; standard deviation can also be calculated.

Like the others, you can remember the key points of an “interval scale” pretty easily. “Interval” itself means “space in between,” which is the important thing to remember–interval scales not only tell us about order, but also about the value between each item.

Here’s the problem with interval scales: they don’t have a “true zero.”  For example, there is no such thing as “no temperature,” at least not with celsius.  In the case of interval scales, zero doesn’t mean the absence of value, but is actually another number used on the scale, like 0 degrees celsius.  Negative numbers alsohave meaning.  Without a true zero, it is impossible to compute ratios.  With interval data, we can add and subtract, but cannot multiply or divide.


Confused?  Ok, consider this: 10 degrees C + 10 degrees C = 20 degrees C.  No problem there.  20 degrees C is not twice as hot as 10 degrees C, however, because there is no such thing as “no temperature” when it comes to the Celsius scale.  When converted to Fahrenheit, it’s clear: 10C=50F and 20C=68F, which is clearly not twice as hot.


Ratio scales are the ultimate nirvana when it comes to data measurement scales because they tell us about the order, they tell us the exact value between units, AND they also have an absolute zero–which allows for a wide range of both descriptive and inferential statistics to be applied.  At the risk of repeating myself, everything above about interval data applies to ratio scales, plus ratio scales have a clear definition of zero.  Good examples of ratio variables include height, weight, and duration.

Ratio scales provide a wealth of possibilities when it comes to statistical analysis. These variables can be meaningfully added, subtracted, multiplied, divided (ratios). Central tendency can be measured by mode, median, or mean; measures of dispersion, such as standard deviation and coefficient of variation can also be calculated from ratio scales.

Example of Ratio Scales

  1. Height of person
  2. Weight of person
  3. Pulse per min
  4. Volume in units


General Information:

Visual analogue scale (VAS)

A frequently used tool in measuring a diverse range of subjective phenomenon (rather frequent in psychological research), is the 0 – 100 visual analogue scale [Revill et al 1976]. This may be used to measure pain, anxiety, patient satisfaction, etc. Because there are infinite possible values that can occur throughout the range 0 – 100, describing a continuum of for e.g. pain intensity, most researchers treat the resulting data as continuous [ Mantha S et al 1993, Dexter and Chestnut 1995]. However, if there is doubt about the sample distribution, then the data should

be considered ordinal. VAS should also be treated as ordinal scale when small number of observations are being analyzed [sample size < 30].

A Visual Analogue Scale (VAS) is a measurement instrument that tries to measure a characteristic or attitude that is believed to range across a continuum of values and cannot easily be directly measured.[1] It is often used in epidemiologic and clinical research to measure the intensity or frequency of various symptoms.[2] 

For example, the amount of pain that a patient feels ranges across a continuum from none to an extreme amount of pain.[1] From the patient’s perspective, this spectrum appears continuous ± their pain does not take discrete jumps, as a categorization of none, mild, moderate and severe would suggest. It was to capture this idea of an underlying continuum that the VAS was devised

A common problem in anesthesia is to assess the effect of some intervention on levels of pain. For example, one may want to know whether patients who have a wound infiltrated with local anesthetic have less pain postoperatively. Visual analog scale (VAS) measurements are frequently used for pain assessment. Subjects mark the position along a 10-cm line, which denotes the severity of their pain. The distance from the marked point to the bottom of the scale is used as a measure of pain. For guidance, the phrases “no pain” and “worst imaginable pain” are placed at the bottom and top of the line, respectively.

The choice of a statistical test to analyze VAS data is controversial. [1] Procedures based on the rank order of data (nonparametric procedures) have an advantage. They do not incorrectly suggest that a difference exists among groups more often than specified by the nominal false-positive or type 1 error rate, regardless of whether the statistical distribution of VAS measurements is normal or not. Scott and Huskisson [2] have recommended that nonparametric methods be used to analyze VAS measurements. Procedures that assume that the VAS measurements follow a normal distribution (parametric procedures) also have an advantage. If the distribution of the data were normal, the tests would have the highest power (i.e., ability) to detect differences among groups. However, even if the distribution were not normal, parametric tests usually give false-positive rates that are close to the nominal value. [3] Therefore, Philip [4] recommended that parametric statistics be used to analyze VAS data. A recent literature review of papers that analyzed VAS measurements showed that 54% of the studies used a nonparametric test (Mann-Whitney or Kruskal-Wallis), and 34% used a parametric test (t test or analysis of variance [ANOVA]). [1] It appears no consensus has emerged in the scientific literature.

VAS can be presented in a number of ways, including:

  • scales with a middle point,graduations or numbers (numerical rating scales),
  • meter-shaped scales (curvilinear analogue scales),
  • “box-scales” consisting of circles equidistant from each other (one of which the subject has to mark), and
  • scales with descriptive terms at intervals along a line (graphic rating scales or Likert scales)

The most simple VAS is a straight horizontal line of fixed length, usually 100 mm. The ends are defined as the extreme limits of the parameter to be measured (symptom,pain,health) orientated from the left (worst) to the right (best). In some studies,horizontal scales are orientated from right to left ,and many investigators use vertical VAS.

Scoring and Interpretation

Using a ruler, the score is determined by mea-suring the distance (mm) on the 10-cm line between the “no pain” anchor and the patient’s mark, providing a range of scores from 0–100. A higher score indicates greater pain intensity. Based on the distribution of pain VAS scores in post- surgical patients (knee replacement, hyster-ectomy, or laparoscopic myomectomy) who described their postoperative pain intensity as none, mild, moderate, or severe, the following cut points on the pain VAS have been recommended: no pain (0–4 mm), mild pain(5-44 mm), moderate pain (45–74 mm), and severe pain (75–100 mm) (11). Normative values are not available. The scale has to be shown to the patient otherwise it is an auditory scale not a visual one.

Sadface vas.jpg
Perceptioons Of VAS Scale

Merits and Demerits Vas Scale

  • The VAS is widely used due to its simplicity and adaptability to a broad range of populations and set-tings.
  • VAS is more sensitive to small changes than are simple descriptive ordinal scales in which symptoms are rated,for example, as mild or slight,moderate,or severe to agonizing.
  • These scales are of most value when looking at change within individuals
  • The VAS takes < 1 minute to complete
  • No training is required other than the ability to use a ruler to measure distance to determine a score
  • Minimal translation difficul-ties have led to an unknown number of cross-cultural adaptations
  • However, assessment is clearly highly subjective
  • Are of less value for comparing across a group of individuals at one time point.
  • It could be argued that a VAS is trying to produce interval/ratio data out of subjective values that are at best ordinal.
  • The VAS is administered as a paper and pencil measure. As a result, it cannot be admin-istered verbally or by phone.
  • Caution is required when photo-copying the scale as this may change the length of the 10-cm line and also, the same alignment of scale should be used consistently within the same

Decisions regarding scale of measurements

This has to be undertaken in the planning stage of the study as these effects the mode of data collection and designing of study instruments. Moreover, choice of scales will also dictate the choice of statistical procedures. As a rule of thumb, interval or ratio scales facilitate most robust statistical tests (parametric tests such as t-test, ANOVA), categorical scales the least rigorous (chi- square), with ordinal scale in between the two (non-parametric tests such as Kruskal Wallis and Mann-Whitney). Choice of measurement scale also has a bearing on the sample size. If outcome of interest is measured on the interval or ratio scale a smaller sample size may suffice than if measured in categorical scale.

During planning it is often helpful to construct skeleton or dummy tables, i.e. tables without figures, or containing fictional figures respectively, incorporating variables under consideration. If there are categories, they should be specified in the column or row headings. At this stage it is not essential to decide exactly how the finer categories will be ‘collapsed’ into broader categories for the purpose of analysis. It is often desirable to defer such decisions, since they may be difficult to make without knowing the actual distribution of the values. If doubt exists about the way a variable will be treated in the analysis, care should be taken to collect data in such a way as to leave the options open.

Criteria of a satisfactory scale [Abramson & Abramson 1999].

A satisfactory scale of measurement is one that meets the following seven requirements.

1.Appropriate (keeping in view the conceptual definition of the variable and the study question)

2.Practicable (to the methods that will be used in data collection, e.g. record study may limit the choice of scales as data is pre-recorded)

3.Sufficiently powerful (to satisfy the objectives of the study. If there is a choice, on ordinal scale is preferred over a categorical one, and interval scale over ordinal)

4.Clearly defined components (operational definitions should be formulated not only for the variables but also for the categories)

5.Sufficient categories (the compression of data into too few categories may lead to loss of essential information)

6.Comprehensive (the scale should be collectively exhaustive providing niche for the

classification of every subject)

7.Mutually exclusive (each item of information should fit into only one place along the scale)

That’s it!  I hope this explanation is clear and that you know understand the four types of data measurement scales: nominal, ordinal, interval, and ratio!  

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