code: def ttest_ind_no_p(a, b, equal_var=True, sigma=0.0):
      """Independent samples t-test without p calculation.
  
      This is a modified version of :func:`scipy.stats.ttest_ind`. It operates
      along the first axis. The ``sigma`` parameter provides an optional "hat"
      adjustment (see :func:`ttest_1samp_no_p` and :footcite:`RidgwayEtAl2012`).
  
      Parameters
      ----------
      a : array-like
          The first array.
      b : array-like
          The second array.
      equal_var : bool
          Assume equal variance. See :func:`scipy.stats.ttest_ind`.
      sigma : float
          The regularization. See :func:`ttest_1samp_no_p`.
  
      Returns
      -------
      t : array
          T values.
  
      References
      ----------
      .. footbibliography::
      """
      v1 = np.var(a, axis=0, ddof=1)
      v2 = np.var(b, axis=0, ddof=1)
      n1 = a.shape[0]
      n2 = b.shape[0]
      if equal_var:
          df = n1 + n2 - 2.0
          var = ((n1 - 1) * v1 + (n2 - 1) * v2) / df
          var = var * (1.0 / n1 + 1.0 / n2)
      else:
          vn1 = v1 / n1
          vn2 = v2 / n2
          with np.errstate(divide="ignore", invalid="ignore"):
              df = (vn1 + vn2) ** 2 / (
                  vn1**2 / (n1 - 1) + vn2**2 / (n2 - 1)
              )
  
          # If df is undefined, variances are zero (assumes n1 > 0 & n2 > 0).
          # Hence it doesn't matter what df is as long as it's not NaN.
          df = np.where(np.isnan(df), 1, df)
          var = vn1 + vn2
      if sigma > 0:
          var += sigma * np.max(var)
      denom = np.sqrt(var)
      d = np.mean(a, 0) - np.mean(b, 0)
      with np.errstate(divide="ignore", invalid="ignore"):
          t = np.divide(d, denom)
      return t
  
file_path: mne-python/mne/stats/parametric.py
imports: from functools import reduce
  from string import ascii_uppercase
  import numpy
  from scipy import stats
  from scipy.signal import detrend
  from ..utils import _check_option
label_desc: Use image node_id 2 for calling a global function with example usage: ttest_ind_no_p(a, b, equal_var, sigma) and returns: t