140
Uncertainties and Graphs: Error Bars
(a) Error Bars
Data
that you plot on a graph
will have experimental uncertainties
. These are shown on a graph with
error bars
, and used to find uncertainties in the slope and intercept. In this discussion we will describe
simple means for finding uncertainties in slope and intercept; a full statistical discussion would begin
with "Least Squares Fitting."
Consider a point with coordinates X ±
Δ
X and Y ±
Δ
Y.
(a) Plot a point, circled, at the point (X,Y).
(b) Draw lines from the circle to X +
Δ
X, X 
Δ
X, Y +
Δ
Y, and Y 
Δ
Y and put bars on the lines, as
shown in Figure 6(a). These are called
error bars
.
(c) The true value of the point is likely to lie somewhere in the oval whose dimension is two
deviations,
i.e. twice the size of the error bars.
The oval shown in Figure 6(c) shows the uncertainty region (at 95% confidencethis is statistics speak).
It is not usually drawn on graphs. Often the error bars may be visible only for the ordinate (vertical), as
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 Fall '09
 LIND

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