Hypothesis Testing (F Test) (G Dataflow)

Sampled data from population x.

Sampled data from population y.

Hypothetical quotient between the variances of sample set x and sample set y.

Default: 1

Probability that this node incorrectly rejects a true null hypothesis.

Default: 0.05

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error	error in contains an error
If no error occurred before the node runs, the node begins execution normally. If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.	If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error

Hypothesis to accept if this node rejects the null hypothesis that the two populations have a common variance.

If the null hypothesis is true, the variance of the quotient between sample set x and sample set y is zero.

Default: variance(x) - variance(y) != ratio

A Boolean that indicates whether this node rejects the null hypothesis.

Smallest significance level that leads to rejection of the null hypothesis based on the sample sets.

Lower and upper limits for the ratio. confidence interval indicates the uncertainty in the estimate of the true ratio.

low

Lower limit of the estimate of the ratio.

high

Upper limit of the estimate of the ratio.

Sample statistics used in the F test.

sample x variance

Variance of sample set x.

sample y variance

Variance of sample set y.

sample variance ratio

Quotient of sample x variance and sample y variance.

degree of freedom 1

Degree of freedom of the first chi-squared variate in the F distribution that the test statistic follows.

degree of freedom 2

Degree of freedom of the second chi-squared variate in the F distribution that the test statistic follows.

sample F value

Sample test statistic used in the F test.

sample F value is equal to $\frac{\mathrm{sample\; variance\; ratio}}{\mathrm{ratio}}$.

F critical value (lower)

Lower F value that corresponds to significance level and alternative hypothesis.

Algorithm for Calculating F critical value (lower)

Let F_{(n1, n2)} represent an F distributed variate with n1 and n2 degrees of freedom. F critical value (lower) satisfies the following equations based on the value of alternative hypothesis.

alternative hypothesis	F critical value (lower)
variance(x) / variance(y) != ratio	Prob{F(n1, n2) < F critical value (lower)} = significance level / 2
variance(x) / variance(y) > ratio	F critical value (lower) = NaN
variance(x) / variance(y) < ratio	Prob{F(n1, n2) < F critical value (lower)} = significance level

F critical value (upper)

Upper F value that corresponds to significance level and alternative hypothesis.

Algorithm for Calculating F critical value (upper)

Let F_{(n1, n2)} represent an F distributed variate with n1 and n2 degrees of freedom. F critical value (upper) satisfies the following equations based on the value of alternative hypothesis.

alternative hypothesis	F critical value (upper)
variance(x) / variance(y) != ratio	Prob{F(n1, n2) > F critical value (upper)} = significance level / 2
variance(x) / variance(y) > ratio	Prob{F(n1, n2) > F critical value (upper)} = significance level
variance(x) / variance(y) < ratio	F critical value (lower) = NaN

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error	error in contains an error
If no error occurred before the node runs, the node begins execution normally. If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.	If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.