"Neyman-Pearson lemma" meaning in All languages combined

{
  "etymology_text": "Named after Jerzy Neyman and Egon Pearson.",
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  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
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          "name": "English entries with incorrect language header",
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      "glosses": [
        "A lemma stating that when performing a hypothesis test between two point hypotheses H₀: θ = θ₀ and H₁: θ = θ₁, then the likelihood-ratio test which rejects H₀ in favour of H₁ when Λ(x)=(L(θ₀∣x))/(L(θ₁∣x))≤η where P(Λ(X)≤η∣H_0)=α is the most powerful test of size α for a threshold η."
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      "raw_glosses": [
        "(statistics) A lemma stating that when performing a hypothesis test between two point hypotheses H₀: θ = θ₀ and H₁: θ = θ₁, then the likelihood-ratio test which rejects H₀ in favour of H₁ when Λ(x)=(L(θ₀∣x))/(L(θ₁∣x))≤η where P(Λ(X)≤η∣H_0)=α is the most powerful test of size α for a threshold η."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "statistics"
      ],
      "wikipedia": [
        "Neyman–Pearson lemma"
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  "word": "Neyman-Pearson lemma"
}

{
  "etymology_text": "Named after Jerzy Neyman and Egon Pearson.",
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  "lang_code": "en",
  "pos": "name",
  "senses": [
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      "glosses": [
        "A lemma stating that when performing a hypothesis test between two point hypotheses H₀: θ = θ₀ and H₁: θ = θ₁, then the likelihood-ratio test which rejects H₀ in favour of H₁ when Λ(x)=(L(θ₀∣x))/(L(θ₁∣x))≤η where P(Λ(X)≤η∣H_0)=α is the most powerful test of size α for a threshold η."
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      "raw_glosses": [
        "(statistics) A lemma stating that when performing a hypothesis test between two point hypotheses H₀: θ = θ₀ and H₁: θ = θ₁, then the likelihood-ratio test which rejects H₀ in favour of H₁ when Λ(x)=(L(θ₀∣x))/(L(θ₁∣x))≤η where P(Λ(X)≤η∣H_0)=α is the most powerful test of size α for a threshold η."
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        "sciences",
        "statistics"
      ],
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}