code: def _std_diff_prop(p1, p2, ratio=1):
      return np.sqrt(p1 * (1 - p1) + p2 * (1 - p2) / ratio)
  
imports: from statsmodels.compat.python import lzip
  from typing import Callable
  import numpy
  import pandas
  from scipy import optimize, stats
  from statsmodels.stats.base import AllPairsResults, HolderTuple
  from statsmodels.stats.weightstats import _zstat_generic2
  from statsmodels.tools.sm_exceptions import HypothesisTestWarning
  from statsmodels.tools.testing import Holder
  from statsmodels.tools.validation import array_like
label_desc: Use image node_id 8 for calling a global function with example usage: _std_diff_prop(p1, p2, ratio) and returns: np