Error Bars

The option of error bars is available whenever replicate information is available for one or more data points. In TableCurve 2D, this can occur in one of two ways:

• In any Import option which offers Column Selection, a weights column is imported with the SD Wts box checked. Since the n for each entry is not imported, error bars associated with replicates are limited to multiples of the standard deviation and to intervals based on a normal distribution. Student-t distribution based confidence and prediction intervals will not be available.

• The Process Replicates option in the Data menu is used on a data table containing replicates. This option automatically searches a composite data table for replicate X values, and replaces the various instances with a single table entry where the Y value consists of the mean of the individual Y values, and the weight value consists of 1/variance (1/SD²). This option also stores the n for each processed replicate entry, enabling error bars to be expressed as a Student-t distribution based confidence or prediction interval.

This graph option opens the Error Bars dialog.

This graph option toggles the error bars on and off.

Student-t Based Confidence Interval

The As Conf Interval selections offer an interval for the mean of the n entries comprising a given data point. Since the mean converges to the true value as n goes to infinity, confidence intervals are often thought of as the limits about the true value.

Student-t Based Prediction Interval

The As Pred Interval selections offer an interval for the next observation based on the n entries comprising a given data point.

Simple Multiples of Standard Deviation

The As ± SD selections offer the simple SD multiples often used for error bars.

Normal Distribution Prediction Intervals

The As ± SD (%Pred n=Inf) selections also offer simple SD multiples. These are based upon the prediction intervals computed using a normal distribution (a Student-t distribution with n equal to infinity).

Just as the intervals about a fitted curve require normally distributed residuals, the error bar intervals require normally distributed errors within the replicates comprising each point in order to be fully valid. Since the n for each point representing a replicate is often small, and the confirmation of normality is seldom made, error bar intervals should generally be regarded as approximate. This is particularly true for 99% and higher levels where deviations from normality are more pronounced.