# tTest

Syntax

tTest(X, [Y], [mu=0.0], [confLevel=0.95], [equalVar=false])

Arguments

X is a numeric vector indicating the sample for the t-test.

Y is a numeric vector indicating the second sample for a paired-sample t-test. It is optional.

mu is a floating number. If Y is not specified, mu is the mean value of X in the null hypothesis; if Y is specified, mu is the difference in the mean values of X and Y in the null hypothesis. It is optional and the default value is 0.

confLevel is a floating number between 0 and 1 indicating the confidence level of the test. It is optional and the default value is 0.95.

equalVar is a Boolean value indicating whether the variance of X and Y are the same in the null hypothesis. It is optional and the default value is false.

Details

If Y is not specified, conduct a one-sample t-test on X. If Y is specified, conduct a paired-sample t-test on X and Y.

Return a dictionary with the following keys:

• stat: a table with p-value and confidence interval under 3 alternative hypotheses.

• df: degree of freedom

• confLevel: confidence level

• method: type of t-test used

• tValue: t-stat

Examples

One-sample t-test:

```\$ x = norm(10.0, 1.0, 20)
\$ tTest(x, , 10.0);

stat->
alternativeHypothesis        pValue   lowerBound upperBound
---------------------------- -------- ---------- ----------
true mean is not equal to 10 0.499649 9.68582    10.621998
true mean is less than 10    0.750176 -Infinity  10.540616
true mean is greater than 10 0.249824 9.767202   Infinity

df->19
confLevel->0.95
method->One sample t-test
tValue->0.688192
```

Paired-sample t-test with equal sample variance:

```\$ x = norm(10.0, 1.0, 20)
\$ y = norm(4.0, 1.0, 10)
\$ tTest(x, y, 6.0, , true);

stat->
alternativeHypothesis                pValue   lowerBound upperBound
------------------------------------ -------- ---------- ----------
difference of mean is not equal to 6 0.438767 5.539812   7.03262
difference of mean is less than 6    0.780616 -Infinity  6.906078
difference of mean is greater than 6 0.219384 5.666354   Infinity

df->28
confLevel->0.95
method->Two sample t-test
tValue->0.785483
```

Paired-sample t-test with no restriction on sample variance:

```\$ x = norm(10.0, 1.0, 20)
\$ y = norm(1.0, 2.0, 10)
\$ tTest(x, y, 9.0);

stat->
alternativeHypothesis          pValue   lowerBound upperBound
------------------------------ ----------------- ---------- ----------
true difference of mean is n...0.983376 7.752967   10.271656
true difference of mean is l...0.508312 -Infinity  10.04285
true difference of mean is g...0.491688 7.981773   Infinity

df->12.164434
confLevel->0.95
method->Welch two sample t-test
tValue->0.021269
```