QUESTION
Course: Educational Assessment and Evaluation
Course code 8602
Level: B.Ed Solved Assignment
Course code 8602
Level: B.Ed Solved Assignment
ANSWER
Interpreting Test Scores by ordering and ranking
Organizing and reporting students’ scores starts with placing the scores in ascending or descending
order. Teachers can find the smallest, largest, range, and some other facts like the variability of scores associated with scores from ranked scores. Teacher may
use ranked scores to see the relative position of each student within the class
but ranked scores does not yield any significant numerical value for result
interpretation or reporting.
Measurement Scales
Measurement is the assignment of numbers to
objects or events in a systematic fashion. Measurement scales are critical
because they relate to the types of statistics you can use to analyze your
data. An easy way to have a paper rejected is to have used either an incorrect
scale/statistic combination or to have used a low-powered statistic on a high-powered set of data. The following four levels of measurement scales are commonly
distinguished so that the proper analysis can be used on the data a number can
be used merely to label or categorize a response.
Nominal Scale.
Nominal scales are the lowest
scales of measurement. A nominal scale, as the name implies, is simply some
placing of data into categories, without any order or structure. You are only
allowed to examine if a nominal scale datum is equal to some particular value
or to count the number of occurrences of each value. For example, the categorization of blood groups of classmates into A, B AB, O, etc. The only
mathematical operation we can perform with nominal data is to count. Variables
assessed on a nominal scale are called categorical variables; Categorical data
are measured on nominal scales which merely assign labels to distinguish
categories. For example, gender is a nominal scale variable. Classifying people
according to gender is a common application of a nominal scale.
Nominal Data
• classification or categorization of data,
e.g. male or female
• no ordering, e.g. it makes no
sense to state that male is greater than female (M > F), etc
• arbitrary labels, e.g., pass=1
and fail=2, etc
Ordinal Scale.
Something measured on an "ordinal"
scale does have an evaluative connotation. You are also allowed to examine if
an ordinal scale datum is less than or greater than another value. For example
rating of job satisfaction on a scale from 1 to 10, with 10 representing
complete satisfaction. With ordinal scales, we only know that 2 is better than
1 or 10 is better than 9; we do not know by how much. It may vary. Hence, you
can 'rank' ordinal data, but you cannot 'quantify' differences between two
ordinal values. Nominal scale properties are included in the ordinal scale.
Ordinal Data
• ordered but differences between
values are not important. Differences between values may or may not same or
equal.
• e.g., political parties on left to right
spectrum given labels 0, 1, 2
• e.g., Likert scales, rank on a
scale of 1..5 your degree of satisfaction
• e.g., restaurant ratings
Interval Scale
An ordinal scale has quantifiable
differences between values and becomes an interval scale. You are allowed to quantify
the difference between two interval scale values but there is no natural zero.
A variable measured on an interval scale gives information about more or better
than ordinal scales do, but interval variables have an equal distance between
each value. The distance between 1 and 2 is equal to the distance between 9 and
10. For example, temperature scales are interval data with 25C warmer than 20C
and a 5C difference has some physical meaning. Note that 0C is arbitrary so it does not make sense to say that 20C is twice as hot as 10C but there is
the exact same difference between 100C and 90C as there is between 42C and 32C.
Students’ achievement scores are measured on an interval scale
Interval Data
• ordered, constant scale, but no
natural zero
• differences make sense, but
ratios do not (e.g., 30°-20°=20°-10°, but 20°/10° is not twice as hot!
• e.g., temperature (C, F), dates
Ratio Scale
Something measured on a ratio
scale has the same properties that an interval scale has except, with a ratio
scaling, there is an absolute zero point. Temperature measured in Kelvin is an
example. There is no value possible below 0 degrees Kelvin, it is absolute
zero. Physical measurements of height, weight, and length are typically ratio
variables. Weight is another example, 0 lbs. is a meaningful absence of weight.
This ratio holds true regardless of which scale the object is being measured in
(e.g. meters or yards). This is because there is a natural zero.
Ratio Data
• ordered, constant scale,
natural zero
• e.g., height, weight, age, length One can
think of nominal, ordinal, interval, and ratio as being ranked in their
relation to one another. Ratio is more sophisticated than interval, interval is
more sophisticated than ordinal, and ordinal is more sophisticated than
nominal.
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