إطار المعاينة والاختيار والأوزان

from itertools import combinations

frame = ("a", "b", "c", "d")
possible_samples = list(combinations(frame, 2))
inclusions = [sum(unit in sample for sample in possible_samples) for unit in frame]
probabilities = [count / len(possible_samples) for count in inclusions]
print("samples", len(possible_samples))
print("inclusions", inclusions)
print("probabilities", probabilities)

samples 6
inclusions [3, 3, 3, 3]
probabilities [0.5, 0.5, 0.5, 0.5]

توجد ست مجموعات ثنائية متساوية الاحتمال وفق التصميم وتظهر كل وحدة في ثلاث فيكون احتمالها0.5.

strata = [
    {"population": 200, "sample": 40, "mean": 10.0},
    {"population": 800, "sample": 10, "mean": 30.0},
]
weights = [s["population"] / s["sample"] for s in strata]
unweighted = sum(s["sample"] * s["mean"] for s in strata) / sum(s["sample"] for s in strata)
weighted = sum(s["sample"] * w * s["mean"] for s, w in zip(strata, weights)) / sum(
    s["sample"] * w for s, w in zip(strata, weights)
)
print("weights", weights)
print(f"unweighted {unweighted:.1f}")
print(f"weighted {weighted:.1f}")

weights [5.0, 80.0]
unweighted 14.0
weighted 26.0

تعطي حصص العينة80% و20% المتوسط14، وتعطي حصص المجتمع20% و80% القيمة26. يغير الوزن الهدف الممثل بافتراضات معلنة.