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t2val(x1,x2 [,df:T or pooled:F]), x1 and x2 REAL vectors or matrices
  with the same number of columns

Keywords: probabilities, descriptive statistics, comparisons
t2val(x1,x2) computes the two-sample Student's t statistic for testing
the null hypothesis that the data in REAL vectors x1 and x2 have the
same population means mu1 and mu2.  The usual pooled estimate of
variance is used in computing the standard error of the difference of
means.  This assumes that the two variances are equal.

t2val(x1,x2,df:T) computes a structure with two components, 't' and
'df', containing the t-statistic and its degrees of freedom,

t2val(x1,x2,pooled:F) computes a structure with components 't' and 'df'.
't' contains the t-statistic computed using the unpooled estimate
sqrt(s1^2/n1 + s2^2/n2) of the standard error of the difference of
means.  'df' contains Satterthwaite's approximate degrees of freedom.  A
test of H0: mu1 = mu2 based on t and df does not assume the two
populations have the same variance.

When there are missing values, they are omitted from the computation and
an informative message is printed.

When the null hypothesis is that mu1 - mu2 is some specific value other
than zero, say delta, then t2val(x1-delta,x2) will produce the correct t
value for that null hypothesis.  For example, if delta is -3, use
t2val(x1-(-3),x2 [,df:T or pooled:T]).

When x1 and x2 are REAL matrices with ncols(x1) = ncols(x2) = M, t2val()
computes two-sample t-statistics for each column separately.
t2val(x1,x2) returns a vector of length M.  t2val(x1,x2,df:T) and
t2val(x1,x2,pooled:F) return a structure with components 't' and 'df',
with each component a REAL vector of length M.

P values may be computed using the function cumstu() or the macro
twotailt(), for example, by
  Cmd> result <- t2val(x1,x2,df:T);twotailt(result$t,result$df)
  Cmd> result <- t2val(x1,x2,pooled:F);twotailt(result$t,result$df)

See also topics tval(), tint(), t2int(), cumstu(), and twotailt().

Gary Oehlert 2003-01-15