# Hypothesis Testing (T Test » Paired Samples) (G Dataflow)

Version:

Tests hypotheses about the mean of the differences between two dependent populations. The distributions of the differences are at least approximately normal but the variances of the differences are unknown.

## sample set x

Sampled data from population x.

## sample set y

Sampled data from population y.

## delta

Hypothetical mean of the differences between sample set x and sample set y.

Default: 0

## 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 mean.

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

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

Default: mean(x) - mean(y) != delta

## 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 difference between the means of two populations. confidence interval indicates the uncertainty in the estimate of the true difference of means.

### low

Lower limit of the estimate of the difference between the means of two populations.

### high

Upper limit of the estimate of the difference between the means of two populations.

## t test information

Sample statistics of the Student's t test.

### sample mean of the differences

Mean of the differences between sample set x and sample set y.

### sample standard deviation of the differences

Standard deviation of the differences between sample set x and sample set y.

### sample standard error of the differences

Standard error of the differences between sample set x and sample set y.

### degree of freedom

Degree of freedom of the Student's t distribution that the test statistic follows.

### sample t value

Sample test statistic used in the Student's t test.

sample t value is equal to $\frac{\left(\mathrm{sample mean of the differences}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}\mathrm{delta}\right)}{\mathrm{sample standard error of the differences}}$.

### t critical value

Student's t value that corresponds to significance level and alternative hypothesis.

Algorithm for Calculating t critical value

Let Tn represent a student's t distributed variate with n degrees of freedom. t critical value satisfies the following equations based on the value of alternative hypothesis.

alternative hypothesis t critical value
mean(x - y) != delta Prob{Tn > t critical value} = significance level / 2
mean(x - y) > delta Prob{Tn > t critical value} = significance level
mean(x - y) < delta Prob{Tn > t critical value} = significance level

## 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