Perform a t-test of the null hypothesis mean (x) == m for a sample x from a normal distribution with unknown mean and unknown standard deviation. Under the null, the test statistic t has a Student’s t distribution. The default value of m is 0.

If the second argument y is a vector, a paired-t test of the hypothesis mean (x) = mean (y) is performed. If x and y are vectors, they must have the same size and dimensions.

x (and y) can also be matrices. For matrices, ttest performs separate t-tests along each column, and returns a vector of results. x and y must have the same number of columns. The Type I error rate of the resulting vector of pval can be controlled by entering pval as input to the function multcompare.

ttest treats NaNs as missing values, and ignores them.

Name-Value pair arguments can be used to set various options. "alpha" can be used to specify the significance level of the test (the default value is 0.05). "tail", can be used to select the desired alternative hypotheses. If the value is "both" (default) the null is tested against the two-sided alternative mean (x) != m. If it is "right" the one-sided alternative mean (x) > m is considered. Similarly for "left", the one-sided alternative mean (x) < m is considered. When argument x is a matrix, "dim" can be used to select the dimension over which to perform the test. (The default is the first non-singleton dimension).

If h is 1 the null hypothesis is rejected, meaning that the tested sample does not come from a Student’s t distribution. If h is 0, then the null hypothesis cannot be rejected and it can be assumed that x follows a Student’s t distribution. The p-value of the test is returned in pval. A 100(1-alpha)% confidence interval is returned in ci.

stats is a structure containing the value of the test statistic (tstat), the degrees of freedom (df) and the sample’s standard deviation (sd).

See also: hotelling_ttest, ttest2, hotelling_ttest2

Source Code: ttest