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Scales of Measurement

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The way the numbers are assigned to observations determines the scale of measurement being used. Recall that measurement is based on assigning numbers according to rules. The rule chosen for the assignment process determines the measurement scale being used.

This classification system, called the Stevens system, is used a lot in statistics, which is a useful set of rules for determining which statistical test should be applied in some research situations.

The following are four different types of measurement scales:

Nominal Scale: Categorical Data
Nominal scaling, which uses numbers to label categories, is the lowest order of measurement. Out of all the scales, it contains the least amount of information about the data.

A nominal scale is created by assigning observations into different, independent categories, then counting the frequency of occurrence within those categories, such as observing how many people in a given voting district are registered as Republicans, Independents, or Democrats.

The only mathematics involved in nominal scaling is the rule of equality versus nonequality, where the same number must be assigned to the observations that are identical, with a different number for each category that differs from each other. These categories are independent from each other, or mutually exclusive. If a given observation is placed in category number 1, it cannot be placed in category number 2. Therefore, in nominal scaling, it determines how many observations have something in common.

The concept of quantity cannot be expressed, only identity versus nonidentity. If observations of people were to be measured according to their gender by assigning, for example, “1” to females and “0” to males, it is not saying that females have more gender than males, or that the average gender in a group is 0.75. Nominal scaling is a rule that arbitrarily substitutes a numerical value for a verbal label.

Ordinal Scale: Ranked Data
It is not always enough to just know that some categories are present in observations. It is also important to know how much in each category. The ordinal scale is used for this by using ranks to order observations in a given category.

Mathematically, an ordinal scale must satisfy two rules: the equality versus nonequality rule and the greater-than-or-less-than rule. If two observations have the same amount of a given trait, then they must be assigned the same number (equality versus nonequality rule). If one of the two observations in the same category has more or less than the given trait compared to the other observation, then they must be assigned different numbers (greater-than-or-less-than rule). However, although ordinal scaling provides information regarding greater than or less than, it does not provide now much greater than or how much less than. The distance between the points/values on an ordinal scale are unknown.

Ordinal data is therefore ranked data, where it defines only the order of the numbers and not the degree of difference between them, such as A is greater than B (A > B) or A is less than B (A < B). Therefore, if a certain item costs “more than a dollar,” in ordinal scaling, the item could cost anywhere from $1.01 to infinity.

Interval Scale: Measurement Data
In an interval scale, the assigning of numbers is done so that the intervals between the points on the scale are meaningful. From this kind of scale, not only is the greater-than-or-less-than status given, but also how much greater than or how much less than. Theoreticially, the distances between sucessive points on an interval scale are equal. Therefore, inferences made from each interval data can be more meaningful and useful than inferences made from nominal or ordinal data.

For example, the Fahrenheit temperature scale provides interval data. The difference between 80°F and 79°F is the same as the difference between 35°F and 34°F. Therefore, the thermometer measures temperature in degrees that are of the same distance at any point on the scale.

Ratio Scale
When a scale has an absolute zero, which is not an arbitrary zero such as 0°F temperature measure, then ratio comparsions among the data can be made, such as someone who is 6 feet tall is twice as tall as someone who is 3 feet tall. This scale is then called the ratio scale.

Like interval data, data from a ratio scale have equal interval differences between sucessive scale points. However, ratio scale has the added feature of an absolute, nonarbitrary zero point.

The social sciences do not often use ratio scaling, because not many categories can be defined to have an absolute zero data point, such as I.Q., prejudice, interest in politics, etc.

Distinguishing Between the Scales
The following list helps distinguish among the various scales of measurement:

1. If it only shows that one observation is different from another observation, then it is nominal data.
2. If it only shows that one observation is greater (bigger, better, more) than another observation, then it is ordinal data.
3. If it only shows that one observation is many units greater than another observation, where the units could be I.Q. points, degrees, test scores, etc., then it is interval data.
4. It only shows that one observation is many times larger, or heavier, or colder, etc. than another observation, then it is ratio data.

Implications of Scaling
The choice of which statistical test can legitimately be used for data analysis is determined from which scale of measurement was used.

Antibiotic restores cell communication in brain areas damaged by Alzheimer’s disease

New research from the Djavad Mowafaghian Centre for Brain Health at UBC has found a way to partially restore brain cell communication around areas damaged by plaques associated with Alzheimer’s disease.

The findings, published this week in Nature Communications, demonstrate a possible target and a potential drug treatment to reduce damage to the brain that occurs in the early stages of Alzheimer’s disease. Using Ceftriaxone, an FDA-approved antibiotic used to treat bacterial infections, researchers were able to reduce synaptic disruption and clear the lines of neuronal communication in mice.

Amyloid plaques of -amyloid deposits develop in brain regions of patients with Alzheimer’s disease, These plaques are linked to the damage found in Alzheimer’s disease because they prevent cell communication and are toxic to nerve cells. The researchers found that the brain areas around these plaques show high levels of glutamate, a signaling molecule essential to communication between brain cells, accompanying high levels of hyperactivity in glia, the brain’s support cells. It’s in this glutamate-rich environment that communication between neurons is changed or disrupted, causing neurons to die in the later stages of the disease.

“By imaging the glial cells and glutamate itself around the plaques, we were able to see that the cells were not able to ‘remove’ the glutamate accumulating in these brain areas. By using Ceftriaxone, we were able to up-regulate glutamate transport,” explains Dr. MacVicar, principal investigator and professor of psychiatry. “By restoring glutamate levels, we were able to mostly restore neuronal activity.”

The team’s findings have implications for treatment of early symptoms of Alzheimer’s disease.

J. K. Hefendehl et al, Mapping synaptic glutamate transporter dysfunction in vivo to regions surrounding Aβ plaques by iGluSnFR two-photon imaging, Nature Communications (2016). DOI: 10.1038/ncomms13441

Ancient brain area controls eye movements

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An ancient area of the midbrain of all vertebrates called the corpora quadrigemina can independently contol and reorientate the eyes, researchers from Karolinska Institutet report in a study published in the journal eLIFE.

There is much going on around us all the time, phenomena that we perceive with our different senses, which send information to the brain. When we walk along the street, for example, we encounter other people that we have to avoid bumping into, or might find our attention drawn to an unexpected object. The brain then has the very difficult task of determining which of these multifarious events we need to respond to.
This problem is solved by an ancient part of the midbrain called the corpora quadrigemina, or tectum. This area is found in all vertebrates and contains a complex network of neurons that control the movements of the head and eyes. Information from different parts of the retina project onto different parts of the tectum creating a retina-based map that reflects the information sent by the retina.

“You could say there’s a spatial sensory map in the tectum, where images from the eye are projected to create signals about where things happen,” says Professor Sten Grillner at Karolinska Institutet’s Department of Neuroscience.
Different parts of the retinal map can then activate nerve cells that control motor centres for eye and head movements in the brain stem. When a movement is triggered, other parts of the tectum network are disabled and thus other movements of the eyes and head.
The study also shows that if an event is registered by two senses (e.g. vision and hearing) from the same point the signals will be merged. If two senses thus supply the tectum with contradictory information, the neurons will become less active, thus reducing the likelihood of a triggered physical event such as eye-movement.

The study was conducted on the lamprey, a small, eel-like fish that represents the earliest form of vertebrate, by Sten Grillner along with visiting researchers Andreas Kardamakis and Juan Pérez-Fernández.

“It’s more primitive than normal fish, but important parts of its nerve system share all their basic features with the more advanced nerve systems of mammals,” says Professor Grillner.
Although the study was basic research, it can help scientists understand certain clinical phenomena, such as the morbid impairment of ocular movements caused by Parkinson’s disease.

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Scales of Measurement

Antibiotic restores cell communication in brain areas damaged by Alzheimer’s disease

Ancient brain area controls eye movements