Rasch Model Implementation

Rasch modeli asosida o'quvchilarni baholash tizimi. Bu loyiha o'quvchilarning imtihon natijalarini Rasch modeli yordamida tahlil qilish va baholash uchun mo'ljallangan.

Xususiyatlar

• Rasch modeli asosida baholash: O'quvchilarning skill level (θ) ni hisoblash
• Z-score va scaled score: Standartlashtirilgan ballni hisoblash (0-100 oralig'ida)
• Daraja belgilash: A+, A, B+, B, C+, C, NC darajalarini avtomatik belgilash
• Excel fayl bilan ishlash: Excel fayllardan ma'lumotlarni o'qish va natijalarni eksport qilish
• Statistik tahlil: Natijalar bo'yicha batafsil statistika
• Moslashuvchan konfiguratsiya: Daraja chegaralarini o'zgartirish imkoniyati

O'rnatish

PyPI dan o'rnatish (tavsiya etiladi)

pip install rasch-pkg

Repository dan o'rnatish

1. Repository ni klonlash:

git clone <repository-url>
cd rasch

2. Virtual muhit yaratish:

python3 -m venv .venv
source .venv/bin/activate  # Windows: .venv\Scripts\activate

3. Bog'liqliklarni o'rnatish:

pip install -r requirements.txt

Foydalanish

1. Asosiy misol (fayllar bilan)

from rasch_pkg import RaschModel

# Rasch modeli obyektini yaratish
rasch = RaschModel()

# O'quvchi javoblari (1 - to'g'ri, 0 - noto'g'ri)
answers = [1, 1, 0, 1, 0, 1, 1, 0, 1, 1]  # 10 ta savol

# O'quvchini baholash
result = rasch.process_student_answers(
    student_id="001",
    name="Ahmadov Ahmad",
    answers=answers
)

print(f"Ball: {result.scaled_score:.2f}")
print(f"Daraja: {result.grade.value}")

2. PostgreSQL ma'lumotlar bazasi bilan ishlash

from rasch_pkg import RaschEvaluator

# Database konfiguratsiyasi
db_config = DatabaseConfig(
    host="localhost",
    port=5432,
    database="postgres",
    username="postgres",
    password="password"
)

# Context manager bilan ishlash
with DatabaseRaschProcessor(db_config) as processor:
    # Barcha foydalanuvchilarni qayta ishlash
    results = processor.process_all_users()

    # Excel fayliga eksport qilish
    excel_path = processor.export_to_excel(
        results,
        "matematika_test_natijalari.xlsx"
    )

    print(f"Natijalar {excel_path} fayliga saqlandi")

Excel fayl bilan ishlash

import pandas as pd
from src.rasch_model import RaschModel

# Excel faylni o'qish
df = pd.read_excel('exam_results.xlsx')

# Rasch modeli
rasch = RaschModel()

# Barcha o'quvchilarni baholash
results = rasch.process_multiple_students(df)

# Natijalarni eksport qilish
rasch.export_results(results, 'output_results.xlsx')

Ko'p o'quvchilarni baholash

# O'quvchilar ma'lumotlari
students_data = [
    {
        'id': '001',
        'name': 'O\'quvchi 1',
        'answers': [1, 1, 0, 1, 0, 1, 1, 0, 1, 1]
    },
    {
        'id': '002', 
        'name': 'O\'quvchi 2',
        'answers': [1, 0, 1, 1, 0, 0, 1, 1, 0, 1]
    }
]

results = rasch.process_multiple_students(students_data)

# Statistika
stats = rasch.get_statistics(results)
print(f"O'rtacha ball: {stats['score_statistics']['mean']}")

Daraja tizimi

Daraja	Ball oralig'i	Tavsif
A+	70.0 - 100.0	A'lo
A	65.0 - 69.99	A'lo
B+	60.0 - 64.99	Yaxshi
B	55.0 - 59.99	Yaxshi
C+	50.0 - 54.99	Qoniqarli
C	46.0 - 49.99	Qoniqarli
NC	0.0 - 45.99	Qoniqarsiz

Rasch modeli formulalari

1. Theta (θ) hisoblash:

   θ = ln(p / (1-p))
   

   Bu yerda p = to'g'ri javoblar nisbati

2. Z-score hisoblash:

   Z = (θ - μ) / σ
   

3. Scaled score hisoblash:

   Ball = 50 + 10 * Z
   

Loyiha tuzilishi

rasch/
├── src/
│   ├── __init__.py
│   ├── rasch_model.py          # Asosiy Rasch modeli klassi
│   └── database_rasch.py       # PostgreSQL bilan ishlash klassi
├── tests/
│   ├── __init__.py
│   ├── test_rasch_model.py     # Rasch modeli unit testlar
│   └── test_database_rasch.py  # Database unit testlar
├── examples/
│   ├── rasch_example.py        # Asosiy foydalanish misollari
│   ├── advanced_example.py     # Qo'shimcha misollar
│   └── database_example.py     # Database misollari
├── docs/
│   ├── rules.pdf               # Rasch modeli qoidalari
│   └── exam_answers_example_*.xlsx  # Misol Excel fayllari
├── output/                     # Natijalar papkasi
├── requirements.txt            # Python bog'liqliklar
├── README.md                   # Ushbu fayl
└── USAGE_GUIDE.md             # Foydalanish qo'llanmasi

Testlarni ishga tushirish

# Barcha testlar
python -m pytest tests/ -v

# Coverage bilan
python -m pytest tests/ --cov=src --cov-report=html

# Bitta test fayl
python -m unittest tests.test_rasch_model -v

Misollarni ishga tushirish

# Asosiy misollar
python examples/rasch_example.py

# Qo'shimcha misollar
python examples/advanced_example.py

# Database misollari
python examples/database_example.py

# Alohida misollar
python -c "from examples.rasch_example import example_1_single_student; example_1_single_student()"

API Hujjatlari

RaschModel klassi

Konstruktor

RaschModel(grade_thresholds=None, max_iterations=100, convergence_threshold=1e-6)

Asosiy metodlar

• process_student_answers(student_id, name, answers) - Bitta o'quvchini baholash
• process_multiple_students(data) - Ko'p o'quvchilarni baholash
• get_statistics(results) - Statistika hisoblash
• export_results(results, filename) - Natijalarni eksport qilish

Yordamchi metodlar

• calculate_theta(correct_answers, total_questions) - Theta hisoblash
• calculate_z_score(theta, mu, sigma) - Z-score hisoblash
• calculate_scaled_score(z_score) - Scaled score hisoblash
• determine_grade(scaled_score) - Daraja belgilash

StudentResult dataclass

O'quvchi natijasi uchun ma'lumotlar strukturasi:

@dataclass
class StudentResult:
    student_id: str
    name: str
    answers: List[Union[int, float]]
    correct_count: int
    total_questions: int
    raw_score: float
    theta: float
    mu: float
    sigma: float
    z_score: float
    scaled_score: float
    grade: GradeLevel

Konfiguratsiya

Maxsus daraja chegaralari

custom_thresholds = {
    'NC': (0.0, 39.99),
    'C': (40.0, 49.99),
    'C+': (50.0, 59.99),
    'B': (60.0, 69.99),
    'B+': (70.0, 79.99),
    'A': (80.0, 89.99),
    'A+': (90.0, 100.0)
}

rasch = RaschModel(grade_thresholds=custom_thresholds)

Xatoliklar va yechimlar

Keng uchraydigan xatoliklar

1. Excel fayl topilmadi

   • Fayl yo'lini tekshiring
   • Fayl mavjudligini tasdiqlang

2. Noto'g'ri javob formati

   • Javoblar 0 yoki 1 bo'lishi kerak
   • Boshqa qiymatlar avtomatik 0 ga aylantiriladi

3. Bo'sh ma'lumotlar

   • Kamida bitta javob bo'lishi kerak
   • Bo'sh ro'yxatlar xatolikka olib keladi

Hissa qo'shish

1. Fork qiling
2. Feature branch yarating (git checkout -b feature/yangi-xususiyat)
3. O'zgarishlarni commit qiling (git commit -am 'Yangi xususiyat qo'shildi')
4. Branch ni push qiling (git push origin feature/yangi-xususiyat)
5. Pull Request yarating

Litsenziya

MIT License

Muallif

Rasch modeli implementatsiyasi - O'zbekiston Milliy Universiteti