DQ 1.5b
Statistics

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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. Nonetheless, physical objects as well as abstract concepts can be measured.
MEASUREMENT SCALES
Scales of measurement can be considered in terms of their mathematical or nonmathematical 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 unordered
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 standarddeviationis 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 antilogarithm)
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
interviewerrespondent 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 rewording or by reordering
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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