Essential Statistical Concepts and Formulas Reference
Descriptive Measures: Center and Variability
Measures of Variation
- Standard Deviation (SD): The average measure of distance between data points and the mean (the square root of the variance). It indicates how far the data is, on average, from the mean.
- Calculation: Find the variance and take its square root.
- Coefficient of Variation (CV): Used to compare the standard deviation of two different data sets. Shown as a percentage, it measures variation relative to the mean.
- Formula: CV = (Standard Deviation
Key Concepts in Probability Distributions and Statistical Analysis
Continuous Probability Distributions
A continuous distribution is a type of probability distribution in which the random variable can take any value within a given range or interval. Unlike discrete distributions that deal with countable outcomes, continuous distributions describe data that can vary infinitely, such as height, weight, temperature, or time.
These distributions are represented using a Probability Density Function (PDF). Probabilities are calculated over intervals, since the probability
Read MoreEnsemble Methods Comparison: Bagging, Boosting, and Stacking Techniques
Bagging Classifier Implementation
Base Model Performance
base_model = DecisionTreeClassifier(random_state=42)
base_model.fit(X_train, y_train)
y_pred_base = base_model.predict(X_test)
base_recall = recall_score(y_test, y_pred_base)
print("Recall del modelo base: {:.4f}".format(base_recall))Hyperparameter Tuning (Grid Search)
param_grid = {
"n_estimators": [10, 50, 100],
"max_samples": [0.5, 0.8, 1.0],
"max_features": [0.5, 0.8, 1.0],
"bootstrap": [True]
}
bagging = BaggingClassifier(Fundamentals of Statistical Graphics and Data Analysis
Understanding Statistical Graphics
A statistical graphic is the representation of statistical data to obtain an overall visual impression of the material presented, which facilitates its rapid comprehension. Graphics are an alternative to tables for representing frequency distributions. Some recommended requirements for building a graph include: simplicity, avoiding exaggerated scale distortions, and the appropriate choice of chart type according to the objectives and the measurement level of the
Read MoreStatistical Foundations for Data Analysis
PPDAC Cycle: Data Problem-Solving
Problem: Clearly define your research question.
Plan: Choose a sampling method and variables.
Data: Collect and clean data (e.g., remove errors, handle missing values).
Analysis: Use EDA (plots & statistics) and model relationships (e.g., regression).
Conclusion: Answer your research question. Be cautious about generalizing!
Essential Sampling Methods
| Method | Description | Pros | Cons |
|---|---|---|---|
| Simple Random | Each unit has equal chance (like a lucky draw) | Unbiased | May need full list of population |
| Systematic | Pick |
Data Analysis & Measurement in Psychology: Scientific Method Foundations
Data Analysis and Measurement in Psychology: The Scientific Method
The objective of scientific method studies is to conduct procedures that are systematic (with established steps) and verifiable (with data that can be replicated or refuted by any researcher). However, the scientific method is just one component of the scientific research process, which consists of three levels (Arnaud):
Theoretical and Conceptual Level
1. Defining the problem and hypotheses
2. Deduction of testable predictionsTheoretical-