# Hypothesis Testing (F Test) (G Dataflow)

Tests hypotheses about the variance of two independent populations whose distributions are at least approximately normal.

## sample set x

Sampled data from population x.

## sample set y

Sampled data from population y.

## ratio

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

Default: 1

## significance level

Probability that this node incorrectly rejects a true null hypothesis.

Default: 0.05

## error in

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

## alternative hypothesis

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.

Name Value Description
variance(x) / variance(y) != ratio 0 The quotient between the variance of population x and population y is not equal to ratio.
variance(x) / variance(y) > ratio 1 The quotient between the variance of population x and population y is greater than ratio.
variance(x) / variance(y) < ratio -1 The quotient between the variance of population x and population y is less than ratio.

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

## null hypothesis rejected?

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

 True p value is less than or equal to significance level. This node rejects the null hypothesis and accepts the alternative hypothesis. False p value is greater than significance level. This node accepts the null hypothesis and rejects the alternative hypothesis.

## p value

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

## confidence interval

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.

## F test information

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 out

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.

Where This Node Can Run:

Desktop OS: Windows

FPGA: This product does not support FPGA devices

Web Server: Not supported in VIs that run in a web application