An educational psychologist finds a fairly strong correlation
between the scores on a reading test and on a math test. The psychologist
is curious about whether the relationship holds for both students who are above the median and for students who are below the median on the reading test.
Therefore, the psychologist computes the correlation
between reading and math for both these subgroups. How do you think these correlations
will compare to the correlation with all students?

true
false
If there are no extreme scores the correlations should be about the same as the original correlation.
Using the simulation, move the left bar to the the right to choose roughly the lower half of the data. See how that affects the correlation. Then select the data outside the bars to see the correlation for the lower half.
false
Since the sample sizes are smaller, the correlations should be higher in the lower and upper halfs than in the whole class.
Using the simulation, move the left bar to the the right to choose roughly the lower half of the data. See how that affects the correlation. Then select the data outside the bars to see the correlation for the lower half.
true
The correlations would be expected to be smaller in the lower and upper halfs than in the whole class.
false
It depends on whether the students are better at math or better at reading.
Using the simulation, move the left bar to the the right to choose roughly the lower half of the data. See how that affects the correlation. Then select the data outside the bars to see the correlation for the upper half.
false
The correlation would be higher in the upper half and lower in the lower half.
Using the simulation, move the left bar to the the right to choose roughly the lower half of the data. See how that affects the correlation. Then select the data outside the bars to see the correlation for the upper half.
The range of reading and math scores will be restricted when only the lower (or upper) half of the students are considered. This leads to a smaller
correlation.
If only scores from students below the 10th percentile and above the 90th percentile are considered, the correlation between reading and math would be expected to be

false
false
Smaller than the correlaton for all students.
Move the left bar a little toward the right and the right bar a little toward the left. Then click on the Outside the Bars option.
false
The same as the correlaton for all students.
Move the left bar a little toward the right and the right bar a little toward the left. Then click on the Outside the Bars option.
true
Greater than the correlaton for all students.
Selecting the extreme values at both ends of a distribution generally increases the correlation.
You wish to demonstrate that there is a relationship between self esteem and grades. Assuming the relationship between these variables is linear, you would find the highest
correlaton if you:

true
false
Choose a sample so that everyone had about the same level of self esteem.
This will give you the smallest relationship.
false
Include a wide range of levels of self esteem.
The wider the range, the higher the correlation. But, there is an alternative that will give an even higher correlation.
true
Choose subjects so that half are very low and half are very high on self esteem.
Selecting the extreme values at both ends of a distribution generally gives you the highest correlation.