3.For variables measured at the nominal level, what values can the measures of association take on? What about variables at the ordinal and interval/ratio levels?
A variable can have four kinds of levels of measurement:
Nominal, Ordinal, Interval, or Ratio. It is on the basis of how the research question is phrased, dictate what statistical analysis is appropriate.
1.Nominal: This is the first level of measurement .In this level of measurement, the numbers in the variable are used only to classify the data. In this level of measurement, words, letters, and alpha-numeric symbols can be used. Example: In this case, the female gender could be classified as F, male gender by M transgender as T.
2.Ordinal:This is the second level of measurement.In this level of measurement variable’s of the observations are ordered. Example: highest grade of 100 in the class would be assigned the first rank;second highest grade of an 92; she would be assigned the second rank.
3.Interval: This is the third level of measurement. In this interval level of measurement orders the measurements and the distances between each interval on the scale are equivalent along the scale from low interval to high interval is measured. e.g.12 and 13 interval is same as 40 and 41.Another example is temperature in centigrade, where, for example, the interval between 920 C and 940 C is the same as the distance between 1080 C and 1100 C.
4.Ratio:This is the fourth level of measurement .In this level of measurement, the observations, in addition to having equal intervals,value of zero is also considered. The zero in the scale makes this type of measurement unlike the other types of measurement.This is similar to the interval measurement .In the ratio level of measurement, the divisions between the points on the scale have an equivalent distance between them.