# Hypothesis Testing (Chi-Squared Test) (G Dataflow)

Tests hypotheses about the variance of a population whose distribution is at least approximately normal.

## sample set

Randomly sampled data from the population.

## variance

Hypothesized variance of the population.

The null hypothesis is that the population variance is equal to variance.

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 population variance is equal to variance.

Name Value Description
variance(pop) != variance 0 The population variance is not equal to variance.
variance(pop) > variance 1 The population variance is greater than variance.
variance(pop) < variance -1 The population variance is less than variance.

Default: variance(pop) != variance

## 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 population variance. confidence interval indicates the uncertainty in the estimate of the true population variance.

### low

Lower limit of the estimate of the population variance.

### high

Upper limit of the estimate of the population variance.

## chi-squared test information

Sample statistics of the chi-squared test.

### sample variance

Variance of sample set.

### degree of freedom

Degree of freedom of the chi-squared distribution that the test statistic follows.

### sample chi-squared value

Sample test statistic used in the chi-squared test.

sample chi-squared value is equal to $\frac{\left(n-1\right)\text{\hspace{0.17em}}*\text{\hspace{0.17em}}\mathrm{sample variance}}{\mathrm{variance}}$.

### chi-squared critical value (lower)

Lower chi-squared value that corresponds to significance level and alternative hypothesis.

Algorithm for Calculating chi-squared critical value (lower)

Let Xn represent a chi-squared distributed variate with n degrees of freedom. chi-squared critical value (lower) satisfies the following equations based on the value of alternative hypothesis.

alternative hypothesis chi-squared critical value (lower)
variance(pop) != variance Prob{Xn < chi-squared critical value (lower)} = significance level / 2
variance(pop) > variance chi-squared critical value (lower) = NaN
variance(pop) < variance Prob{Xn < chi-squared critical value (lower)} = significance level

### chi-squared critical value (upper)

Upper chi-squared value that corresponds to significance level and alternative hypothesis.

Algorithm for Calculating chi-squared critical value (upper)

Let Xn represent a chi-squared distributed variate with n degrees of freedom. chi-squared critical value (upper) satisfies the following equations based on the value of alternative hypothesis.

alternative hypothesis chi-squared critical value (upper)
variance(pop) != variance Prob{Xn > chi-squared critical value (upper)} = significance level / 2
variance(pop) > variance Prob{Xn > chi-squared critical value (upper)} = significance level.
variance(pop) < variance chi-squared critical value (upper) = 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: Not supported

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