##### DQ 1.5b

*label*Statistics

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*schedule*1 Day

*account_balance_wallet*$5

There are four data measurement scales. Please give the class one and then explain it with examples.

__MEASUREMENT IN RESEARCH__

Measurement is the **procedure of
applying a standard scale** (e.g. numbers) to a variable (e.g. objects
or observations) or to a set of values.

It is easy to assign numbers in respect of some properties of some objects, but relatively difficult in respect of others e.g. measuring such things as social conformity, intelligence or marital adjustment. Properties like weight, height, e.t.c. can be measured directly with some standard unit of measurement, unlike properties like motivation to succeed, ability to withstand stress, e.t.c. None-the-less, physical objects as well as abstract concepts can be measured.

**MEASUREMENT SCALES**

Scales of measurement can be considered in terms of their mathematical or non-mathematical properties and are classified as follows:

**a) ****Nominal
scale**

**b) ****Ordinal
scale**

**c) ****Interval
scale**

**d) ****Ratio
scale and**

e)
**Dichotomous scale** (scale that arranges items in either of two
mutually

exclusive categories → male/female, e.t.c.).

**a)
****Nominal Scale**

** **A nominal scale is a system of **assigning number symbols to events**

in order to label them. Classification is done into un-ordered

qualitative categories e.g. race, religion, birth, e.t.c. It is the least

powerful level of measurement, which indicates no order or

distance relationship and has no arithmetic origin. It describes

differences between things by assigning them to categories.

Nominal data are thus counted data.

__Example:__

Assigning numbers to basketball players in order to
identify them. Such numbers cannot be considered to be associated with an
ordered scale for their order is of no consequence:- the numbers are just **convenient
labels** for the particular class of events and as such have no
quantitative value. Nominal scales provide convenient ways of keeping track of
people, objects and events. One cannot do much with the numbers involved, e.g.
one cannot usefully average the numbers on the back of a group of football
players and come up with a meaningful value. Neither can one usefully compare
the numbers assigned to one group with the numbers assigned to another. The
counting of members in each group is the only possible arithmetic operation
when a nominal scale is used, thus restricting us to use __mode__( mode is one of the measures of
central tendency which refers to the __most frequently occurring __value in
a set of observations) as the measure of central tendency. Measures of central
tendency ( statistical averages) tell us the point about which items have a
tendency to cluster.

**b)
****Ordinal scale:**

Here classification is into ordered qualitative categories e.g. social

classes ( I, II, III) where the values have a distinct order, but their

categories are qualitative in that there is no natural (numerical)

distance between their possible values. This is the lowest level of

ordered scale that places events in order with no attempt to make the

intervals of scale equal in terms of some rule. Ordinal scales only

permit **ranking** of items from highest to lowest.
Ordinal measures

have no absolute values, and the real differences between adjacent

ranks may not be equal. All that can be said is that one person is

higher or lower on the scale than another, but more precise

comparison cannot be made.

** **

** Example:**

A student’s rank in the graduation class, e.g. if John’s position in this class is 10 and that of Robert’s position is 40, it cannot be said that John’s position is four times as good as that of Robert. The statement cannot make sense at all.

The
use of ordinal scale implies a statement of “greater than” or “less than”
without stating how much greater or less. Since the numbers of this scale have
only a rank meaning, the appropriate measure of central tendency is the __median__( median is the value of middle item of
series when it is arranged in ascending or descending order of magnitude. It
divides the series into halves; in one half all items are less than median,
whereas in the other half all items have values higher than median).

**c)
****Interval scale:**

** **This involves assignment of values with natural
distance between

them, so that a particular distance (
**interval**)
between two values in

one region of the scale meaningfully represents the same distance

between two values in another region of the scale, e.g. Celsius and

Fahrenheit temperatures, date of birth, e.t.c.

Interval scales provide more powerful measurement than ordinal

scale since interval scale also incorporates the concept of equality of

interval. As such more powerful statistical measures can be used

with interval scales.

The intervals are adjusted in terms of some rule that has been

established as a basis for making the units equal. The units are equal

only in so far as one accepts the assumptions on which the rule is

based.
Interval scales can have an arbitrary zero, but is __not possible__

__to determine
an absolute zero__ for the unique origin. Thus the primary

limitation of the interval scale is the lack of absolute zero, since it

does not have the capacity to measure the complete absence of a trait

or a characteristic.

__Example:__

__The Fahrenheit scale__:- This is an interval scale which shows similarities
in what one can and cannot do with it. One can say that an increase in
temperature from 30 degrees to 40 degrees involves the same increase in
temperature as an increase from 60 degrees to 70 degrees, but cannot say that
the temperature of 60 degrees is twice as warm as the temperature of 30 degrees
because both numbers are dependent on the fact that the zero on the scale is
set arbitrarily as the temperature of the freezing point of water. The ratio of
the two temperatures, 30 degrees and 60 degrees means nothing because zero is
an arbitrary point.

In this case __mean__ is
the appropriate measure of central tendency, while __standard____deviation__is the most widely used measure of __dispersion.__

**d)
****Ratio scale:**

** **A ratio is an **interval scale with a true zero point**, so that
the ratios

between values are meaningfully defined.

** Examples:** Absolute temperature,
weight, height, blood count, and

income. In each case , it is meaningful to speak of one

value as being so many times greater or less than another

value.

A ratio scale is the most precise type of measurement scale. Ratio

scales have an absolute or true zero of measurement and represent the

actual amounts of variables. Measures of physical dimensions include:

weight, height, distance, e.t.c. Generally, all statistical techniques are

usable with ratio scales and all manipulations that one can carry out

with real numbers can also be carried out with ratio scale values.

Multiplication and division can be used with this scale but not with

other scales mentioned above. ** Geometric**
( Geometric mean is a

measure of central tendency calculated only for positive values and

calculated by taking the logarithms of the values, calculating their

arithmetic mean, then converting back by taking the anti-logarithm)

**and harmonic** ( Harmonic mean is a
measure of central tendency

computed by summing the reciprocals of all the individual values and

dividing the resulting sum into the number of
values) **means**
( An

arithmetic mean is a measure of central tendency computed by adding

all the individual values together and dividing by the number in the

group)
**can be used**
as measures of central tendency and coefficients of

variation may also be calculated.

**e)
****Dichotomous scale:**

This is a
scale that arranges items into either of **two mutually**

** exclusive categories** e.g. male or female, alive or dead, e.t.c.

__SOURCES OF ERROR IN MEASUREMENT __

Measurement should be precise and unambiguous in an ideal research study. However, since this is rarely met, the researcher should be aware of possible sources of error in measurement which can be avoided. Possible sources of error could result from:

a) Respondent

b) Situation

c) Measurer

d) Instrument

**a) ****Respondent
:**

At times the respondent may be reluctant to express strong negative feelings

or may have very little knowledge but may not admit his ignorance. Resultant

reluctance is likely to result in an interview of “guesses”. Transient factors

like fatigue, boredom, anxiety, e.t.c. may limit the ability of the respondent to

respond accurately and fully.

**b) ****Situation:**

Situational factors may come in the way of correct measurement. Any

Condition which places a strain on interview can have serious effects on the

interviewer-respondent rapport e.g. if someone else is present, he can distort

responses by joining in or merely by being present. If the respondent feels

that anonymity is not assured; he may be reluctant to express certain feelings.

**c) ****Measurer:**

The interviewer can distort responses by re-wording or by re-ordering

questions. His behaviour, style and looks may encourage or discourage

certain replies from respondents. Careless mechanical processing may distort

the findings. Errors may also creep in because of incorrect coding, faulty

tabulation and/ or statistical calculations, particularly in the data analysis

stage.

**d) ****Instrument:**

Error may also arise because of the defective measuring instruments. Use of

complex words beyond the comprehension of the respondent, ambiguous

meanings, poor printing, inadequate space for replies, response choice

omissions, e.t.c. are some things that make measuring instrument defective

and may result in measurement errors. Another type of instrument deficiency

is poor sampling of the universe of items of concern.

Thus with respect to sources of error, the researcher must as much as possible try to eliminate, neutralize or otherwise deal with all the possible sources of error, so that the final results may not be contaminated.

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