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Have
you ever been curious to know if one event affects another
event?
For example, if I study longer, will I get a better grade on my
Regents examination? |
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Statisticians and quality control
technicians gather data to determine correlations
(relationships) between such events. Scatter plots will often show
at a glance whether a relationship exists between two sets of data.
Let's decide if studying longer will affect Regents
grades based upon a specific set of data. Given the data below, a
scatter plot has been prepared to represent the data.
Remember when making a scatter plot, do NOT
connect the dots.
| Study
Hours |
Regents
Score |
| 3 |
80 |
| 5 |
90 |
| 2 |
75 |
| 6 |
80 |
| 7 |
90 |
| 1 |
50 |
| 2 |
65 |
| 7 |
85 |
| 1 |
40 |
| 7 |
100 |
|
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Notice: Certain
values may have more than one result,
such as (7,90) and (7,85) and (7,100).
The data displayed on the graph
resembles a line rising from left to right. Since the slope of the
line is positive, there is a positive
correlation between the two sets of data. This means
that according to this set of data, the longer I study, the better grade
I will get on my Regents examination.
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Note:
Just because this set of data showed a
positive correlation does not mean that the relationship is
positive for all sets of data concerning study time and
Regents scores. There may be sets of data
that show that there is NOT a positive correlation between hours
studying and better Regents scores.
It all depends on the
data being examined. |
If the slope of the
line had been negative (falling from left to right), a negative
correlation would exist since
the slope of the line would have been negative.
Under a negative correlation, the longer I study, the worse grade I
would get on my Regents examination. YEEK!!
If the plot on the
graph is scattered in such a way that it does not approximate a line (it
does not appear to rise or fall),
there is no correlation
between the sets of data. No correlation means that the data just
doesn't show if studying longer has any affect on Regents examination scores.
Check out these graphs for visual
interpretations of types of correlations:
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The points are clustered as to resemble a rising straight
line with a positive slope.
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While the points "tend" to be rising, it is not a clearly
positive relationship since points are not clustered as to
show a clear straight line. |
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The points are clustered as to resemble a falling straight
line with a negative slope.
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While the points "tend" to be falling, it is not a clearly
negative relationship since points are not clustered as to
show a clear straight line. |
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There is no way of determining from these points, if the
pattern is rising or falling. There is no evidence of
a straight line. |
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See how to use
your
TI-83+/TI-84+ graphing calculator with
scatter plots.
Click calculator. |
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Warning!! |
Correlation does not necessarily mean Causation.
Just because there is a strong correlation between data, does not
necessarily mean that one set of data is causing the affect
that is occurring in the other set of data. |
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During the months of February and March,
the weekly number of jars of strawberry jam sold at a local
market in New York was recorded. For the same time frame,
the number of copies of a popular classical music CD sold in
Florida was recorded. The data was examined and was plotted
From looking at the graph, it can be seen that there is a
high positive correlation between these two sets of data.
So, this must mean that the number of jars of strawberry jam
sold in New York was causing an increase in the number of
classical music CDs sold in Florida. Of course this is not true!
Always be
careful what you infer from your statistical analyses. Be
sure the relationship makes sense. Also keep in mind that
other factors may be involved in a cause-effect
relationship.
|
|
Weekly Data
Collection |
|
The jars of strawberry jam
sold in New York |
The number of CDs sold in
Florida |
| 5 jars |
25 CDs |
| 7 |
30 |
| 9 |
35 |
| 10 |
42 |
| 11 |
48 |
| 11 |
52 |
| 12 |
56 |
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