Question

Which of the following factors can possibly make the observed linear correlation from a sample larger than the true correlation in the population? Can be many answers.

1. Presence of a non-linear relationship

2. Outliers that deviate from the main cluster of data

3. Different correlations for different subgroups within the data

4. Range restriction on the predictor and/or criterion variables

5. Unreliable measures of the predictor and/or the criterion variables

6. Standardizing the scores on the predictor and/or the criterion

Answer 1

The factors that can possibly make the observed linear correlation from a sample larger than the true correlation in the population are:

1) Different correlations for different subgroups within the data : If this is the case, then we may not be able to capture the true correlations for different groups from the sample. Techniques like sampling can prove to be of great use here before the analysis.

2) Unreliable measurements of the predictor and/or criterion variables: If the measurements or observations in the sample are unreliable, then we may end up with a rogue estimate of sample correlation that is nowhere close to the true correlation coefficient.

Outliers and standardising do not have a significant effect on the correlation measure as the variance in both the numerator and the denominator get cancelled.

Since correlation measure is concerned only with the linear relationship between the variables, presence of non linear relationship does not really bother the question here.