Explain four (4) levels of measurement and give one (1) example each

A. Nominal Scale: Nominal data are counted data. Each individual can only be a member of mutually exclusive category and not the other. All members of each category include notionally, gender, socioeconomic status, occupation, role, religious affiliation etc. Numbers are often used at the nominal level, but only in order to identify the categories. The numbers arbitrarily assigned to the categories serve mainly as labels or names. The numbers do not represent absolute or relative amounts of any characterization. For instance, the numbers given to football players do not represent their degree of skillfulness but just for recognition and positions.

B. Ordinal Scale: Nominal scales show that things are different but ordinal scale shows the direction of differences. It shows relative position of one thing to another but can not specify the magnitude of the interval between two measures. Ordinal scales, thus only permit the ranking of items or individuals from highest to lowest. The criterion for highest to lowest ordering is expressed as relative position or rank in a group: 1st, 2nd, 3rd …..nth. This is why ordinal scale is also called rank order. Ordinal measures have no absolute values and real differences between adjacent ranks may not be equal. Neither difference between the number nor their ratio has meaning. When numbers 1, 2, 3 and so on are used there is implication that rank 1 is as much higher than rank 2 as 2 is than 3, and so on.

C. Interval Scale: This is an arbitrary scale based on equal units of measurement which indicates how much of a given characteristic is present. It provides equa intervals from an arbitrary origin. An interval scale not only orders objects events according to the amount of the attribute they represent but also establish equal intervals between the units of measure.

Equal differences in the numbers represent equal differences in the amount the attributes being measured. The difference in the amount of the characteristi possessed by person with scores of 60 and 65 is assumed to be equivalent to th between persons with scores of 70 and 75. The limitation here is the lack o true zero. The zero point is arbitrary. Interval scale lacks ability to measure complete absence of the trait and a measure of 30 does not mean that the person has twice as much of the trait as someone who scored 15

D. Ratio Scale: The fourth and final type of scale is the ratio scale. It provides a true zero point as well as equal intervals. The numerals of the ratio scale have the qualities of real numbers and can be added, subtracted, multiplied divided and expressed in ratio relationship e.g. 10g is one half of 20g. 30cm is three times 10cm etc Examples of ratio data are usually found in the physical sciences and seldom if ever obtained in education and behavioural sciences. In education, these are limited to educational performance and other physiological measurements. All types of statistical procedures are appropriate with a ratio scale

In summary,

A. Nominal Scale: Nominal data involves categorizing individuals into mutually exclusive categories where each individual belongs to one specific category. The categories have no inherent order, and numbers are assigned merely for identification. Example: Categorizing people by their gender (Male or Female).

B. Ordinal Scale: In ordinal data, items are ranked or ordered according to some characteristic or attribute. While there’s a sense of order, the intervals between ranks are not uniform. Example: Ranking students’ performance as “Excellent,” “Good,” or “Average.”

C. Interval Scale: Interval data have equal intervals between values, but the scale lacks a true zero point. This means that while differences are meaningful, ratios are not. Example: Temperature measured in Celsius or Fahrenheit.

D. Ratio Scale: Ratio data have all the characteristics of nominal, ordinal, and interval scales, including a true zero point. Ratios between values are meaningful. Example: Height, weight, and age in years.

These different levels of measurement impact the types of statistical analyses that can be applied to the data. Nominal data often lead to frequency counts, ordinal data can be subjected to non-parametric tests, interval data allow for parametric tests, and ratio data provide the most robust level of measurement for performing various statistical operations.

[mediator_tech]

What is Scale of Measurement

Evaluation

Absolutely, here are 15 fill-in-the-blank questions on the topic “Four Levels of Measurement with Examples,” along with options (a), (b), and (c):

1. ____________ data involves categorizing individuals into mutually exclusive categories with no inherent order.

(a) Ordinal
(b) Ratio
(c) Nominal

2. Ranking items or individuals according to a characteristic without uniform intervals describes the ____________ scale.

(a) Interval
(b) Nominal
(c) Ordinal

3. An example of ____________ data is classifying people by their religious affiliations.

(a) Interval
(b) Ordinal
(c) Nominal

4. Temperature measured in Celsius or Fahrenheit is an example of ____________ data.

(a) Ordinal
(b) Interval
(c) Ratio

5. The ____________ scale has all the characteristics of nominal, ordinal, and interval scales.

(a) Nominal
(b) Ratio
(c) Interval

6. When intervals between values are meaningful, but there is no true zero point, it’s an ____________ scale.

(a) Ratio
(b) Interval
(c) Ordinal

7. ____________ data are counted and involve assigning individuals to specific categories.

(a) Interval
(b) Nominal
(c) Ratio

8. Ranking students’ performance as “Excellent,” “Good,” or “Average” is an example of ____________ data.

(a) Nominal
(b) Ratio
(c) Ordinal

9. A ____________ scale allows for ratios and has a true zero point.

(a) Ordinal
(b) Ratio
(c) Interval

10. Height and weight measurements are examples of ____________ data.

(a) Nominal
(b) Interval
(c) Ratio

11. In ____________ data, numbers are assigned as labels without any inherent numerical value.

(a) Interval
(b) Nominal
(c) Ratio

12. An example of ____________ data is ranking people by their socioeconomic status.

(a) Ratio
(b) Ordinal
(c) Nominal

13. The ____________ scale involves meaningful ratios, equal intervals, and a true zero point.

(a) Interval
(b) Ordinal
(c) Ratio

14. ____________ data has equal intervals but lacks a true zero point.

(a) Nominal
(b) Ratio
(c) Interval

15. ____________ data allows for ratios, has a true zero point, and includes all characteristics of the other scales.

(a) Nominal
(b) Ratio
(c) Interval

[mediator_tech]

A set of 30 people were asked how many coins they had in thier pockets and the following results were obtained : No. Of Coins = 0-4, 5-7, 8-10, 11-12. No. Of people = 6, 8, 8, 8. Find the mean of the coins.