5. Suppose the standard error of measurement (SEM) for the CM scale was 1.70. Would the scores of the youth who scored 21 be considered different from one another? Why or Why not?
To determine if the scores of the youth who scored 21 are considered different from one another, we need to compare their scores within the context of the standard error of measurement (SEM).
The standard error of measurement provides an estimate of the amount of error present in a particular measurement. It quantifies the variability or uncertainty in the scores obtained from a test or measurement tool.
In this case, if the SEM for the CM scale is 1.70, it implies that the scores of the youth can be expected to vary around their true scores by approximately 1.70 units.
To determine if scores are statistically different from one another, we need to consider the range within which the scores are likely to fall. Two scores are considered different if their difference is greater than the range of measurement error.
So, if two youth both scored 21 on the CM scale, and the SEM is 1.70, their scores would not be considered different from one another. This is because the range of measurement error (1.70) is larger than the difference between their scores (which is 0).
In conclusion, based on the given SEM, the scores of the youth who scored 21 would not be considered different from one another because the difference of 0 falls within the range of measurement error.