Scales of measurements
Normally, scales of measurement are used to denote the manner in which numbers or variables are categorized, quantified and defined. Each measurement scale has particular properties that sequentially define the relevance of its usage under statistical analysis.
For instance, in statistical analysis, the commonly used scales of measurements are the ordinal, ratio, nominal and interval scales (Gravetter & Forzano, 2011). All measurement scales must however satisfy either one or more of the subsequent measurement properties.
Equal intervals: When using measurement scale, the scale divisions must be equal to each other along the scale. This would imply that the variance amid one and two should be equivalent to the variance between nineteen and twenty.
Identity: Every value found on the scale of measurement possesses a distinctive meaning.
Absolute zero: When using measurement scales, the employed scale must have a real zero point under which there must be no values.
Magnitude: Every value on the scale of measurement has ordered correlation to the others. That is to say, some of the used values are smaller while others are larger.
Nominal Scale of Measurement
Nominal measurement scale entails categorical numbers and data which are basically utilized as names or identifiers. From the above named properties, this type of scale just fulfills the identity measurement property. In fact, values that are assigned to statistical variables signify descriptive categories (Gravetter & Forzano, 2011).
Thus, they do not possess the inherent numerical values with regard to magnitude. It is sometimes crude when assigning numbers to concepts that are being studied especially in situations where numbers are used to reflect people’s genders. For example, asserting that Female = 0 and Male = 1. Such kind of statistical measurement is dubbed as nominal scale of measurement.
This scale is applied in studies where the variables denoting the observations or participants ought to be placed in a particular mutually exhaustive and exclusive category. For instance, when study participants are categorized as female and male, the categories show that gender is gauged under the nominal scale.
Therefore, each study observation made belong to only nominal category and there are no relative category orderings (Gravetter & Forzano, 2011). The numeric scores assignment to every category (Female, Male) are simply arbitrary.
Gender is thus a clear and simple illustration of a statistical variable gauged under the nominal measurement scale. People might be categorized as either female or male, yet neither of these values symbolizes less or more gender when compared to the other.
Normal distribution
In statistics, normal distribution refers to a distributional pattern of a given set of data that depicts bell shaped curve. The curve under normal distribution tends to decrease on either sides but is concentrated at the center.
This implies that statistical data have minimal tendencies of producing abnormally extreme values in comparison to any other distribution. Further, the bell-shaped curve which has a single peak is always symmetrical signifying that the mean (µ) deviations are equal in both directions (Sapsford & Jupp, 2006).
The relevance of studying normal distribution
Apparently, the study of normal distribution is very important given that it assists in picturing various natural phenomena in which the general notion connotes that the distribution of probabilities are equal around the mean. Thus, the relevancy of studying normal distribution in most cases ensues from the fact that it assist in approximating statistical functions.
Philosophically, normal distribution in this sense symbolizes an empirically certified elemental truth concerning the reality depicted by the general nature (Sapsford & Jupp, 2006). The status of normal distribution is hence comparable to some of the fundamental natural sciences laws.
References
Gravetter, F. J. & Forzano, L. B. (2011). Research Methods for the Behavioral Sciences. Florence, KY: Cengage Learning.
Sapsford, R. & Jupp, V. (2006). Data collection and analysis. Thousands Oak, CA: Sage Publications.