Multivariate inductive statistics

Multivariate inductive statistics explores relationships between dependent or criterion variable(s) Y and several independent or predictor variables X. Independent variables are those that are manipulated whereas dependent variables are only measured or registered. The terms dependent and independent variable apply mostly to experimental research where some variables are manipulated, and in this sense they are "independent" from the initial reaction patterns, features, intentions, etc. of the subjects. Some other variables are expected to be "dependent" on the manipulation or experimental conditions. Somewhat contrary to the nature of this distinction, these terms are also used in studies where we do not literally manipulate independent variables, but only assign subjects to "experimental groups" based on some pre-existing properties of the subjects.

Select the appropriate combination of measurement scales:

a) Interval Y's : Interval X's

b) Interval Y's : Interval + Nominal X's

c) Interval Y : Interval + Nominal X's

d) Interval Y : Interval X's

e) Interval Y : Nominal X's

f) Nominal Y : Interval X's

g) Nominal Y : Interval + Nominal X's

h) Binary Y : Interval + Nominal X's

i) Nominal variables

Measurement scales

Interval
Scale with a fixed and defined interval. In general, an interval should keep the same importance throughout the scale. For example, the length of time between 1905 and 1925 is the same as the length of time between 1995 and 2015. More examples: height, weight, income, costs, turnover.

Ordinal
Ordinal variables allow us to rank order the items we measure in terms of which has less and which has more of the quality represented by the variable, but still they do not allow us to say "how much more." A typical example of an ordinal variable is the socioeconomic status of families. For example, we know that upper-middle is higher than middle but we cannot say that it is, for example, 18% higher.

Nominal
Nominal variables allow for only qualitative classification. That is, they can be measured only in terms of whether the individual items belong to some distinctively different categories, but we cannot quantify or even rank order those categories. Typical examples of nominal variables are race, color, city, blood group.

Binary (Dichotomous)
As for nominal but two categories only e.g. gender, time moment (before / after action), improvement (yes / no).