Final answer:
To determine the relationship between two measurements, the correlation coefficient is calculated. A coefficient not significantly different from zero indicates no significant relationship, whereas one significantly different from zero indicates a significant linear relationship.
Step-by-step explanation:
The demonstration that there is little or no relationship between the measurements of two different constructs typically involves statistical analysis, specifically calculating the correlation coefficient. When examining the association between two variables, x and y, researchers will calculate this coefficient to determine the strength and direction of the linear relationship.
If the test concludes the correlation coefficient is not significantly different from zero (it is close to zero), we say the correlation coefficient is not significant. In such cases, the conclusion drawn is that there is insufficient evidence to support a significant linear relationship between x and y. This means it would be inappropriate to use a regression line to model a linear relationship between these variables in the population.
Conversely, if the correlation coefficient is significantly different from zero, this would indicate a significant linear relationship between x and y. In conditions where there is no correlation, as with age structures and levels of economic development, the variation in one construct does not predict or affect the variation in the other.