# t-tests and F-tests for rows or columns of a matrix

### Description

t-tests and F-tests for rows or columns of a matrix, intended to be speed efficient.

### Usage

1 2 3 4 5 6 |

### Arguments

`x` |
Numeric matrix. The matrix must not contain |

`fac` |
Factor which codes the grouping to be tested.
There must be 1 or 2 groups for the t-tests (corresponding to one-
and two-sample t-test), and 2 or more for the F-tests. If If |

`tstatOnly` |
A logical variable indicating whether to calculate
p-values from the t-distribution with appropriate degrees of
freedom. If |

`ig1` |
The indices of the columns of |

`ig2` |
The indices of the columns of |

`var.equal` |
A logical variable indicating whether to treat the variances in the samples as equal. If 'TRUE', a simple F test for the equality of means in a one-way analysis of variance is performed. If 'FALSE', an approximate method of Welch (1951) is used, which generalizes the commonly known 2-sample Welch test to the case of arbitrarily many samples. |

### Details

If `fac`

is specified, `rowttests`

performs for each
row of `x`

a two-sided, two-class t-test with equal variances.
`fac`

must be a factor of length `ncol(x)`

with two levels,
corresponding to the two groups. The sign of the resulting t-statistic
corresponds to "group 1 minus group 2".
If `fac`

is missing, `rowttests`

performs for each row of
`x`

a two-sided one-class t-test against the null hypothesis 'mean=0'.

`rowttests`

and `colttests`

are implemented in C and
should be reasonably fast and memory-efficient.
`fastT`

is an alternative implementation, in Fortran, possibly useful
for certain legacy code.
`rowFtests`

and `colFtests`

are currently implemented using
matrix algebra in R. Compared to the `rowttests`

and
`colttests`

functions,
they are slower and use more memory.

### Value

A `data.frame`

with columns `statistic`

,
`p.value`

(optional in the case of the t-test functions) and
`dm`

, the difference of the group means (only in the
case of the t-test functions).
The `row.names`

of the data.frame are taken from the
corresponding dimension names of `x`

.

The degrees of freedom are provided in the attribute `df`

.
For the F-tests, if `var.equal`

is 'FALSE', `nrow(x)+1`

degree of freedoms
are given, the first one is the first degree of freedom (it is the
same for each row) and the other ones are the second degree of freedom
(one for each row).

### Author(s)

Wolfgang Huber <whuber@embl.de>

### References

B. L. Welch (1951), On the comparison of several mean values: an alternative approach. Biometrika, *38*, 330-336

### See Also

`mt.teststat`

### Examples

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##
## example data
##
x = matrix(runif(40), nrow=4, ncol=10)
f2 = factor(floor(runif(ncol(x))*2))
f4 = factor(floor(runif(ncol(x))*4))
##
## one- and two group row t-test; 4-group F-test
##
r1 = rowttests(x)
r2 = rowttests(x, f2)
r4 = rowFtests(x, f4)
## approximate equality
about.equal = function(x,y,tol=1e-10)
stopifnot(is.numeric(x), is.numeric(y), length(x)==length(y), all(abs(x-y) < tol))
##
## compare with the implementation in t.test
##
for (j in 1:nrow(x)) {
s1 = t.test(x[j,])
about.equal(s1$statistic, r1$statistic[j])
about.equal(s1$p.value, r1$p.value[j])
s2 = t.test(x[j,] ~ f2, var.equal=TRUE)
about.equal(s2$statistic, r2$statistic[j])
about.equal(s2$p.value, r2$p.value[j])
dm = -diff(tapply(x[j,], f2, mean))
about.equal(dm, r2$dm[j])
s4 = summary(lm(x[j,] ~ f4))
about.equal(s4$fstatistic["value"], r4$statistic[j])
}
##
## colttests
##
c2 = colttests(t(x), f2)
stopifnot(identical(r2, c2))
##
## missing values
##
f2n = f2
f2n[sample(length(f2n), 3)] = NA
r2n = rowttests(x, f2n)
for(j in 1:nrow(x)) {
s2n = t.test(x[j,] ~ f2n, var.equal=TRUE)
about.equal(s2n$statistic, r2n$statistic[j])
about.equal(s2n$p.value, r2n$p.value[j])
}
##
## larger sample size
##
x = matrix(runif(1000000), nrow=4, ncol=250000)
f2 = factor(floor(runif(ncol(x))*2))
r2 = rowttests(x, f2)
for (j in 1:nrow(x)) {
s2 = t.test(x[j,] ~ f2, var.equal=TRUE)
about.equal(s2$statistic, r2$statistic[j])
about.equal(s2$p.value, r2$p.value[j])
}
## single row matrix
rowFtests(matrix(runif(10),1,10),as.factor(c(rep(1,5),rep(2,5))))
rowttests(matrix(runif(10),1,10),as.factor(c(rep(1,5),rep(2,5))))
``` |