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7.4.A ONEâ€“TAILED CONFIDENCE INTERVALS

95% Confidence Interval

A 95 % Confidence Interval contains all but 5% of the extreme values on

oneâ€“tail of the Density Function (Probability Density Function (PDF)) or

is the value that corresponds to 0.05 or 0.95 on the Cumulative Density

Function (CDF) (the former for the left tail of 5% and the latter for a right

tail of 5%).

The 95% Confidence Interval for a Tâ€“distributed series is defined by the

results of the two inverse functions at this probability:

Left tail: Negative infinity to TINV (0.05, degrees of freedom).

Right tail: TINV(0.95, degrees of freedom) to positive infinity.

Note:

TINV(0.05, degrees of freedom) = â€“TINV(0.95, degrees of freedom)

90% Confidence Interval

A 90 % Confidence Interval contains all but 10% of the extreme values on

oneâ€“tail of the Density Function (Probability Density Function (PDF)) or

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Chapter 7: Probabiity Density Functions & Confidence Intervals

is the value that corresponds to 0.1 or 0.9 on the Cumulative Density

Function (CDF) (the former for the left tail of 10% and the latter for a

right tail of 10%).

The 90% Confidence Interval for a Tâ€“distributed series is defined by the

results of the two inverse functions at this probability:

â€¢ Left tail: Negative infinity to TINV (0.1, degrees of freedom).

â€¢ Right tail: TINV (0.9, degrees of freedom) to positive infinity.

Note:

TINV(0.1, degrees of freedom) = â€“TINV(0.9, degrees of freedom)

Table 19: T Density Functionâ€” Formulae for 90%, 95%, and 99% Confidence limits (right tail

only).

Confidence Formula for lower left-tail Confidence upper limit (the lower

level limit equals negative infinity)

90% TINV (0.9, degrees of freedom)

95% TINV (0.95, degrees of freedom)

99% TINV (0.99, degrees of freedom)

Table 20: T Density Functionâ€” Formulae for 90%, 95%, and 99% Confidence limits (left tail

only)

Confidence Formula for right-tail Confidence lower limit (the upper limit

level equals positive infinity)

90% â€“TINV (0.1, degrees of freedom)

95% â€“TINV (0.05, degrees of freedom)

99% â€“TINV (0.01, degrees of freedom)

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Statistical Analysis with Excel

Fâ€“DENSITY FUNCTION

7.5

The F test is used for testing model significance and other joint hypothesis

in ANOVA, Regression Analysis, etc.

CDF:

FDIST (x, numerator degrees of freedom, denominator degrees of freedom)

Menu path to function: INSERT / FUNCTION / STATISTICAL / FDIST.

Figure 114: Fâ€“Distribution

Data requirements: The data series should follow the assumed Density

Function type (F).

Inverse function

FINV (probability below the X, numerator degrees of freedom, denominator

degrees of freedom) X

Menu path to function: INSERT / FUNCTION / STATISTICAL /FINV.

Data requirements: The data series should follow the F Density Function.

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Chapter 7: Probabiity Density Functions & Confidence Intervals

Figure 115: The inverse function for an Fâ€“Density Function

Oneâ€“tailed Confidence Intervals

Table 21: F Density Functionâ€” Formulae for 90%, 95%, and 99% Confidence Intervals (right

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