It would be useful for you to not only understand the terms ‘construct’ and ‘variable’ but should first have an improved understanding of the term “concept”. A concept is a verbal abstraction drawn from observation of a number of specific cases. For example, we can observe people paying money for occupying a place and can call it the concept of ‘rent’. In similar lines, we observe individuals and find some of them heavily build while some others are seen to be thin, and from these observations we generate the concept “weight”. It is important to understand that concepts are “observed”, because it means that there is a direct link between the concept (the abstraction) and its referents (the reality).
Constructs are theoretical creations that are based on observations but which cannot be seen either directly or indirectly. Examples of constructs are satisfaction, happiness, norms, IQ, values, etc. construct serves the same function as a concept, but it is more abstract. Importantly, constructs are not characterized by a direct link between the abstraction and its observed manifestations. Thus, even though we can use the term satisfaction in the same way as a concept, but we should recognize that we cannot directly observe different levels of satisfaction directly. Constructs are built from the logical combination of a number of more observable concepts. For example, if we talk about the construct source credibility, then we could define the construct as the combination of the concepts of expertise, objectivity, and status. Each of these concepts can be more directly observed in an individual.
Both, concepts as well as constructs, could be variables if they are free to vary else they are constants.
It would be useful for you to not only understand the terms ‘construct’ and ‘variable’ but should first have an improved understanding of the term “concept”. A concept is a verbal abstraction drawn from observation of a number of specific cases. For example, we can observe people paying money for occupying a place and can call it the concept of ‘rent’. In similar lines, we observe individuals and find some of them heavily build while some others are seen to be thin, and from these observations we generate the concept “weight”. It is important to understand that concepts are “observed”, because it means that there is a direct link between the concept (the abstraction) and its referents (the reality).
Constructs are theoretical creations that are based on observations but which cannot be seen either directly or indirectly. Examples of constructs are satisfaction, happiness, norms, IQ, values, etc. construct serves the same function as a concept, but it is more abstract. Importantly, constructs are not characterized by a direct link between the abstraction and its observed manifestations. Thus, even though we can use the term satisfaction in the same way as a concept, but we should recognize that we cannot directly observe different levels of satisfaction directly. Constructs are built from the logical combination of a number of more observable concepts. For example, if we talk about the construct source credibility, then we could define the construct as the combination of the concepts of expertise, objectivity, and status. Each of these concepts can be more directly observed in an individual.
Both, concepts as well as constructs, could be variables if they are free to vary else they are constants.
The variable is the measurable expression of the construct. The construct typically is thus more general and it is not guaranteed that your variable is actually related to your construct in the desired way. For example, trust is a construct, the answer to "How often do you follow your mother's advise?" could be the variable and the specific definition of the question / answer (categories) the variable's operational definition. Or, unemployment is a construct and the ILO unemployment definition a variable (and its operational definition at the same time).
These research-jargons can seem confusing. If you know what 'construction' means a 'construct' is an assembly of related issues which may add to, say, one "brick". To become a thing that looks like a wall it requires more than one brick, except perhaps to a dazed ant. Variables in the ideas or tests lead to a variety of concepts which can become that wall, or construct. Constructs are so often represented as emotions but I think some practicality can be invoked. Constructs are referred-to as the 'building blocks of theory' and useful if ultimately measurable.
For example, I have a concept 'temperature'. If I buy a 'temperature-thing' and measure temperature inside my beachfront house in Tasmania, it would be invalid to claim that single intangible as the temperature in sub-Sahara. I have constructed nothing. A construct is not a single impression nor must it be ultimately abstract. It may lead to an operational utility.
If I measure outside the house under the trees, in the fields, where wind is blowing and where it is still, when cloudy and when not and tabulate the impressions I am receiving from the thermometer, I am starting to form a higher level of 'abstract', a construct.
The effect of the sun has been presumed and sought. It is not something which can be verifiably 'observed' other than through measuring devices, generally of limited accuracy, giving a concept which may change on the instant but summed construct a theory. Enough measuring devices and points of measure can give an instantaneous construct.
The concept "temperature" using a variety of attributes has grown to perhaps a 'local temperature experience' , another brick in the wall.
Constructs in the theme of 'totally abstract perception' still require variables from changes in framing or 'viewpoint' to create a mental image of any arguable validity...or 'operational definition'.