2.13.2.4 ttest2

1 Brief Information
2 Command Line Usage
3 X-Function Execution Options
4 Variables
5 Description
6 Algorithm
7 References
8 Related X-Functions

Brief Information

Two-Sample t-test

Command Line Usage

1. ttest2 irng:=(Col(a), Col(b));

2. ttest2 irng:=( Col(a), Col(b)) mdiff:=0.5;

3. ttest2 irng:=( Col(a), Col(b)) tail:=2 equal:=0;

4. ttest2 irng:=(Col(a), Col(b)) prob:=myprob;

X-Function Execution Options

Please refer to the page for additional option switches when accessing the x-function from script

Variables

Display Name	Variable Name	I/O and Type	Default Value	Description
Input	irng	Input Range	<active>	This variable specifies the input data ranges on which to perform a two-sample t-test. It should contain two columns.
Hypothetical means difference	mdiff	Input double	0	This variable specifies the hypothetical difference between the sample means
Tail	tail	Input int	two	This variable indicates whether an upper-, lower-, or 2- tailed t-test should be performed. (Suppose m1 and m2 are sample means and m is the mean difference) Option list two:Two Tailed This variable indicates the two-tailed t-test is performed. upper:Upper Tailed This variable indicates the upper-tailed t-test is performed. lower:Lower Tailed This variable indicates the lower-tailed t-test is performed.
Significance level	alpha	Input double	0.05	This variable specifies alpha value, or the significance level value. With this value, the associated confidence interval will be computed. It should be larger than 0 and less than 1.
Equal variances	equal	Input int	1	This variable indicates whether or not the sample variances are assumed to be equal
T-Statistic	stat	Output double	<unassigned>	Value of the t-test statistic
Degrees of freedom	df	Output double	<unassigned>	Degrees of freedom for the sample data
P-value	prob	Output double	<unassigned>	Associated p-value of the test. Users can compare it with their desirable significance level (commonly 0.05). If the p-value is greater than or equal to alpha, the null hypothesis will not be rejected.
Lower confidence limit	lcl	Output double	<unassigned>	Specifies the lower limit of confidence levels for which the confidence intervals will be computed. This option is only available when Confidence Interval(s) is chosen.
Upper confidence limit	ucl	Output double	<unassigned>	Specifies the upper limit of confidence levels for which the confidence intervals will be computed. This option is only available when Confidence Interval(s) is chosen.

Description

The independent two-sample t-test analysis tests whether or not the means of two independent samples from a normal distribution are equal or whether they differ by a given value, and creates a confidence interval for the difference of the sample means. The two-sample t-test also enables you to test whether or not the means of two samples differ by a specified amount. The two variables are assumed to be independent and variances between two variables can be equal or unequal. Note that if the two samples are not independent, the two-sample t-test is inappropriate and you should use the paired-sample t-test instead.

The test could be either one-tailed or two-tailed. Therefore, you can test if the sample mean difference is 1) greater than, 2) less than, or 3) different from the hypothetical value. The test statistic and p-value will be calculated so that you can decide whether or not to reject the null hypothesis. A small p-value, which less than a significance level $\alpha$ , indicates that you can reject the null hypothesis

To estimate the difference between two population means, the sample mean difference with confidence interval is also computed for each confidence levels.