Statistical Analysis

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Hire developers in descriptive statistics for simple hypothesis tests with experience in statistical software (SAS, R or Stata); macro vs function programming. Find Statistical Analysis WFH freelancers on January 21, 2025 who work remotely. Read less

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From college-level to SAT, ACT, AP, find statisticians to teach

Math / Statistics

MATLAB

Mathcad

Build simulation models to solve real-world problem using Discrete Event

Simulation Modeling

Regression test planning; writing of test cases and test scripts;

Regression Testing

Interpret data from disparate sources, analyze results using stats, AI

Machine Learning

Design, build and delivery of analytics and reporting products and

Business Intelligence / Analysis

Digital Signal Processing

Graduates

Verified

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Wikipedia Statistical Analysis Courses

Top Frequently Asked Questions

What to Know

What should a good freelancer doing statistical analysis absolutely know?

Here are the 20 key principles of statistical analysis that any freelancer who you hire should be qualified in doing:

1. Data Collection
Representative Sampling: Ensure your sample represents the population you're studying to make valid inferences.

2. Data Quality
Accuracy and Precision: Data must be both accurate (close to the true value) and precise (consistent with repeated measures).

3. Objectivity
Avoid Bias: Consciously minimize selection bias, measurement bias, and other forms of bias that can skew results.

4. Replicability
Reproducibility: The same methods should yield similar results when repeated by different analysts or in different settings.

5. Variability
Understand Variation: Recognize that data has natural variability, and statistical methods help quantify this variation.

6. Central Tendency
Mean, Median, Mode: Use these measures to summarize data, understanding when each is appropriate.

7. Dispersion
Variance and Standard Deviation: Measure how data is spread around the central tendency.

8. Normality Assumption
Normal Distribution: Many statistical tests assume normal distribution of data, so understanding and checking for normality is crucial.

9. Hypothesis Testing
Null and Alternative Hypotheses: Clearly define what you're testing to avoid misinterpretation of results.

10. Significance Levels
P-Value and Alpha: Decide on significance thresholds to determine if your results are due to chance.

11. Confidence Intervals
Estimation: Use confidence intervals to estimate population parameters with a known level of confidence.

12. Effect Size
Measure Practical Significance: Beyond statistical significance, understand the practical impact of your findings.

13. Correlation vs. Causation
Avoid Causal Misinterpretation: Correlation does not imply causation; be cautious in drawing causal conclusions.

14. Regression Analysis
Modeling Relationships: Use regression to understand relationships between variables, but be aware of assumptions like linearity and independence of errors.

15. Multivariate Analysis
Multiple Variables: Consider the impact of multiple variables simultaneously to understand complex relationships.

16. Outlier Detection
Identify Anomalies: Outliers can skew results; decide whether to include or exclude them based on context.

17. Data Transformation
Normalizing Data: Sometimes data needs to be transformed (e.g., log transformation) to meet assumptions of statistical tests.

18. Non-parametric Methods
When Assumptions Fail: Use non-parametric tests when data does not meet the assumptions for parametric tests.

19. Statistical Power
Power Analysis: Ensure your study has enough power to detect an effect if one exists.

20. Ethical Considerations
Data Privacy and Integrity: Handle data with respect to privacy laws, ethical guidelines, and maintain integrity in reporting.

These principles guide the practice of statistical analysis, ensuring that conclusions drawn are valid, reliable, and ethically sound. They cover the spectrum from data collection to interpretation, emphasizing both the technical and ethical aspects of statistics.

What is that math underneath statistical analysis?

Statistical analysis is built upon a foundation of mathematical concepts, primarily from several branches of mathematics:

1. Probability Theory
Basic Concepts: Probability measures the likelihood of events, which is fundamental to understanding data variability, sampling, and making inferences. Key concepts include probability distributions (e.g., normal, binomial, Poisson), conditional probability, Bayes' Theorem, and the Law of Large Numbers.
Random Variables: These are variables that can take on different values according to an underlying probability distribution, crucial for modeling data.

2. Calculus
Integration: Used for calculating probabilities over continuous distributions, determining expected values, and computing areas under curves for cumulative distribution functions.
Differentiation: Essential for optimization problems in statistical estimation (like maximum likelihood estimation), and for understanding how changes in parameters affect probability distributions.

3. Linear Algebra
Matrices and Vectors: Used in multivariate statistics for data representation, in regression analysis for solving systems of equations, and in principal component analysis for dimensionality reduction. Operations like matrix inversion, eigenvalues, and eigenvectors are important in various statistical methods.
Eigenvalues and Eigenvectors: These are critical for understanding covariance matrices in multivariate analysis.

4. Algebra
Equations and Inequalities: Solving for unknowns in statistical models, manipulating expressions for hypothesis testing, and understanding relationships between variables.

5. Discrete Mathematics
Combinatorics: Useful for calculating permutations and combinations, which are crucial in counting probabilities in discrete distributions or in sample spaces.
Set Theory: Fundamental for probability, where sets represent outcomes or events.

6. Numerical Methods
Approximation Techniques: Since many statistical computations involve complex calculations that aren't always solvable analytically, numerical methods like Monte Carlo simulations for integration or optimization algorithms for parameter estimation are essential.

7. Optimization
Optimization Techniques: Statistical methods often involve finding the best parameters (e.g., in regression or maximum likelihood estimation) which requires knowledge of optimization, including gradient descent or least squares methods.

8. Geometry
Geometric Interpretation: Especially in multivariate statistics, geometric concepts help visualize data in higher dimensions or understand concepts like distances in clustering algorithms.

9. Measure Theory (Advanced)
For Rigorous Probability: While not always necessary for practical statistics, measure theory provides a rigorous foundation for probability, particularly useful in advanced statistical research or when dealing with complex probability spaces.

10. Functional Analysis (For Some Areas)
Infinite Dimensional Spaces: In areas like functional data analysis or when dealing with stochastic processes, concepts from functional analysis become relevant.

Application in Statistics:
Descriptive Statistics: Uses basic algebra for measures like mean, median, mode, variance.
Inferential Statistics: Relies heavily on probability theory for hypothesis testing, confidence intervals, and p-values.
Regression Analysis: Combines algebra, calculus, and linear algebra for model fitting and parameter estimation.
Time Series Analysis: Utilizes calculus for understanding trends, seasonal effects, and forecasting.
Machine Learning: While not strictly a subset of statistics, many machine learning techniques are rooted in statistical principles, using probability, calculus, and linear algebra.

This mathematical foundation allows statisticians to develop, apply, and interpret methods for organizing, analyzing, and interpreting data, making predictions, and testing hypotheses.

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