ConfidenceInterval (FPScript)

07.02.2018
 Analyzing Data Mathematically > Reference > FPScript Functions > Statistics > ConfidenceInterval

ConfidenceInterval (FPScript)

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ConfidenceInterval (FPScript)

Calculates a confidence interval for the mean or the variance of the normal distribution to which the specified sample belongs.

Syntax

ConfidenceInterval(Sample, ConfidenceLevel, Parameter [ , Mode = PROCESS_ROWS ])

 

The syntax of the ConfidenceInterval function consists of the following parts:

Teil

Beschreibung

Sample

The sample to be examined.

All data structures are allowed. All numeric data types are permitted.

For complex data types the absolute value is formed.

If the argument is a list, then the function is executed for each element of the list and the result is also a list.

ConfidenceLevel

Specifies the confidence level, on which the calculation is to be based, as a percentage.

Permitted data structures are scalar value. All numeric data types are permitted. The argument is transformed to the unit %.

The value must be greater or equal to 0 % and less or equal to 100 %.

If the argument is a list, then the first element in the list is taken. If this is also a list, then the process is repeated.

Parameter

Selects the parameter for which a confidence interval is to be calculated.

The argument Parameter can have the following values:

Constant

Meaning

PARAMETER_MEAN

Calculates the confidence interval to the mean value.

PARAMETER_VARIANCE

Calculates the confidence interval to the variance.

PARAMETER_DISTFROMMEAN

Calculates the absolute distance of the confidence interval limits to the mean value (equal to half the width of the confidence interval).

If the argument is a list, then the first element in the list is taken. If this is also a list, then the process is repeated.

Mode

Specifies how data matrices and signal series are to be processed.

The argument Mode can have the following values:

Constant

Meaning

PROCESS_COLUMNS

Processing takes place column by column. The result contains one value per column.

PROCESS_ROWS

Processing takes place row by row. The result contains one value per row.

If this argument is omitted, it will be set to the default value PROCESS_ROWS.

Remarks

As the result the function returns a data series of data type 64-bit floating point.

The sample must originate from a normally distributed population. The function returns a data series with two floating point values as the result, which contains the upper and lower interval limits. If DataSet is a data series or signal, the result is a data series containing the upper and lower limits of the interval. If DataSet is two-dimensional, then the result is a data matrix or a signal series with two columns containing the upper and lower limits of the intervals for each column or row of the DataSet. If Parameter has the value PARAMETER_DISTFROMMEAN, then half the width of the interval is returned instead of the interval limits. This result is ideal for situations such as displaying the confidence intervals of a signal series as error indicators in a diagram. The rank of the result then decreases by one for each, so that in the event that DataSet is two-dimensional, for instance, a data series is returned instead of a data matrix with two columns.

Available in

Option Enhanced Statistics

Examples

ConfidenceInterval({87, 112, 110, 87, 96, 118, 108, 114, 87, 90, 85, 84, 113, 90, 90, 104 }, 95, PARAMETER_MEAN)

Results in {91.05, 105.08}.For example, the data series involves the quantity of a product sold over 15 days. You can assume that the count is distributed evenly. In 95% of the cases, distribution is between 91 and 105 pieces.

See Also

Confidence Interval Analysis Object

Statistics Option

References

 [1] "Hartung, Joachim": "Statistik (Statistics), 9th Edition", page 160 f. "Oldenbourg Verlag GmbH, Munich", 1993. ISBN 3-486-22055-1.

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