Technical Brief
Correlation
Correlation
Researchers find it convenient to have a single number to measure the strength of the
relationship between two variables and to have that number be independent of the units
used to make the measurement. The correlation between two measurement variables is an
indicator of how closely their values fall to a straight line. Sometimes this measure is
called the "Pearson product moment correlation" or the "correlation
coefficient"; sometimes it is simply represented by the letter "r." A
correlation of zero could indicate that there is no linear relationship between the two
variables. It could also indicate that the best straight line through the data on a
scatter plot is exactly horizontal. A positive correlation indicates that the variables
increase together. A correlation of +1 (or 100%) indicates that there is a perfect linear
relationship between the two variables. As one increases so does the other,
proportionally. A negative correlation indicates that as one variable increases the other
decreases. A correlation of -1 indicates that there is a perfect linear relationship
between the two variables, but as one increases the other decreases.
Correlations of +1 or -1 would be extremely strong relationships. They are rarely observed
when exploring relationships between different variables. Even when a perfect correlation
is observed, things may not be as simple as they seem. Correlations can be affected by a
number of factors. For example, data points that sit significantly outside the rest of the
points in a data sample (outliers) will inflate the correlation when it is consistent with
the trend (direction) of the data set as a whole. An outlier that is not consistent with
the rest of the sample will likewise substantially decrease the correlation. For example,
if one or more very low-income students in a class submit perfect writing samples on a
state assessment, their high scores will substantially suppress the overall correlation
between SES and achievement seen in the data set as a whole.
Sometimes outliers occur simply because the data were erroneously recorded. The URI
research team used a variety of methods to detect such errors in the data sets that make
up the statistical model. They also used these methods to check (or "clean") the
other data sets that make up this year's school and district reports. Changing the units
of measurement does not affect correlations. For example, the correlation between weight
and height remains the same regardless of whether height is expressed in inches, feet, or
millimeters. Similarly, the kinds of correlations seen in the RI model hold true whether
we are expressing the results as actual numerical test results (raw scores) or as
percentage of items correct.
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