Statistical techniques [Neurosurgery Wiki]

This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong.
====== Statistical techniques ======

{{rss>https://pubmed.ncbi.nlm.nih.gov/rss/search/1zWVHjJausiyg6iZzBwejYCR1qDaVYtzHECznkKWD8WWy-D9_7/?limit=15&utm_campaign=pubmed-2&fc=20240111065207}}

"Statistical methods" and "[[statistical analysis]]" are two different but related concepts in the field of statistics:

Statistical Methods:

Definition: Statistical methods refer to the specific techniques, tools, and procedures used to collect, process, analyze, and interpret data. These methods are the mathematical and computational approaches that statisticians and data analysts employ to draw meaningful conclusions from data.

Purpose: The primary purpose of statistical methods is to provide a structured and systematic way to work with data. These methods help researchers and analysts summarize data, test hypotheses, make predictions, and quantify uncertainty.

Examples: Statistical methods include t-tests, chi-squared tests, regression analysis, ANOVA (Analysis of Variance), hypothesis testing, bootstrapping, maximum likelihood estimation, and Bayesian inference. Each of these methods has a specific application in statistical analysis.

Statistical Analysis:

Definition: Statistical analysis is the broader process of applying statistical methods and techniques to data in order to gain insights, draw conclusions, and make informed decisions. It encompasses the entire workflow of working with data, from data collection and cleaning to exploratory data analysis and the application of statistical methods.

Purpose: The primary purpose of statistical analysis is to extract meaningful information and knowledge from data. It involves summarizing data, detecting patterns, testing hypotheses, building models, and making predictions based on statistical methods.

Steps: Statistical analysis involves several key steps, including data collection, data preparation, exploratory data analysis (EDA), choosing appropriate statistical methods, conducting the analysis, and interpreting and communicating the results.

In summary, statistical methods are the specific tools and techniques used within the broader context of statistical analysis. Statistical analysis is the comprehensive process of working with data, where statistical methods are applied at various stages to achieve specific objectives, such as hypothesis testing, modeling, or data exploration. Statistical analysis encompasses the entire workflow, while statistical methods are the individual procedures used within that workflow.

----

A [[statistical]] [[technique]] is a method or procedure applied to analyze and interpret data in order to make informed inferences or draw conclusions. These techniques are used in various fields, including science, social sciences, economics, finance, and many others. The choice of a statistical technique depends on the nature of the data, the research question, and the assumptions underlying the analysis.

Some common statistical techniques include:

Descriptive Statistics: Summarizing and describing the main features of a dataset, such as mean, median, mode, range, and standard deviation.

Inferential Statistics: Making predictions or inferences about a population based on a sample of data. This includes techniques such as hypothesis testing and confidence intervals.

Regression Analysis: Examining the relationship between one or more independent variables and a dependent variable. Linear regression is a common example.

Analysis of Variance (ANOVA): Comparing means across multiple groups to assess whether there are statistically significant differences.

Chi-Square Test: Assessing the association between categorical variables.

Cluster Analysis: Grouping similar observations into clusters based on certain criteria.

Factor Analysis: Identifying underlying factors that explain patterns of variation in observed variables.

Time Series Analysis: Examining patterns and trends in time-ordered data.

Machine Learning Techniques: Algorithms that enable computers to learn patterns and make predictions without being explicitly programmed. This includes methods like decision trees, support vector machines, and neural networks.

Bayesian Statistics: A statistical approach that incorporates prior knowledge and beliefs into the analysis.

These techniques help researchers and analysts make sense of data, test hypotheses, and make predictions in a rigorous and systematic manner. The choice of a specific technique depends on the research question, the nature of the data, and the assumptions underlying the analysis.

----

[[Statistic]]al [[technique]]s refer to various methods and tools used in [[statistics]] to analyze, interpret, and draw conclusions from data. These techniques are essential for making sense of data, identifying patterns, making predictions, and drawing meaningful insights. Here are some common statistical techniques:

Descriptive Statistics:

Measures of Central Tendency: These include the mean (average), median (middle value), and mode (most frequent value), which summarize the "center" of a dataset.
Measures of Dispersion: Techniques like standard deviation and variance quantify how spread out the data is.
Percentiles and Quartiles: These help understand the distribution of data by dividing it into equal parts.
Inferential Statistics:

Hypothesis Testing: This involves testing hypotheses about populations based on sample data. Common tests include t-tests, chi-squared tests, and analysis of variance (ANOVA).
Confidence Intervals: These provide a range of values within which a population parameter is likely to fall.
Regression Analysis: Techniques like linear regression help establish relationships between variables and make predictions.
Correlation Analysis: Measures the strength and direction of the relationship between two or more variables.
Probability Distributions:

Normal Distribution: Often used to describe naturally occurring phenomena and serves as a foundation for many statistical tests.
Binomial Distribution: Models the number of successes in a fixed number of trials with two possible outcomes (success and failure).
Poisson Distribution: Models the number of events occurring in a fixed interval of time or space.
Non-parametric Statistics:

Techniques like the Mann-Whitney U test and the Wilcoxon signed-rank test are used when data does not meet the assumptions of parametric tests.
Time Series Analysis:

Used for analyzing data collected over time, with techniques like autoregressive integrated moving average (ARIMA) modeling and exponential smoothing.
Multivariate Analysis:

Techniques such as principal component analysis (PCA) and factor analysis are used when dealing with multiple variables simultaneously.
Sampling Techniques:

Methods like simple random sampling, stratified sampling, and cluster sampling are used to select representative samples from larger populations.
Statistical Software:

Tools like R, Python with libraries such as NumPy and SciPy, and commercial software like SPSS and SAS are used for performing various statistical analyses.
Experimental Design:

Techniques for designing experiments that allow for valid statistical conclusions, including randomization, control groups, and factorial designs.
Bayesian Statistics:

This approach uses Bayes' theorem to update probabilities as more data becomes available, making it particularly useful in situations with limited data.
These statistical techniques are used across various fields, including science, business, social sciences, healthcare, finance, and engineering, to gain insights from data, test hypotheses, and make informed decisions. The choice of technique depends on the specific research question or problem being addressed and the nature of the data available.
----
"Statistical methods" and "statistical analysis" are two different but related concepts in the field of statistics:

Statistical Methods:

Definition: Statistical methods refer to the specific techniques, tools, and procedures used to collect, process, analyze, and interpret data. These methods are the mathematical and computational approaches that statisticians and data analysts employ to draw meaningful conclusions from data.

Purpose: The primary purpose of statistical methods is to provide a structured and systematic way to work with data. These methods help researchers and analysts summarize data, test hypotheses, make predictions, and quantify uncertainty.

Examples: Statistical methods include t-tests, chi-squared tests, regression analysis, ANOVA (Analysis of Variance), hypothesis testing, bootstrapping, maximum likelihood estimation, and Bayesian inference. Each of these methods has a specific application in statistical analysis.

Statistical Analysis:

Definition: Statistical analysis is the broader process of applying statistical methods and techniques to data in order to gain insights, draw conclusions, and make informed decisions. It encompasses the entire workflow of working with data, from data collection and cleaning to exploratory data analysis and the application of statistical methods.

Purpose: The primary purpose of statistical analysis is to extract meaningful information and knowledge from data. It involves summarizing data, detecting patterns, testing hypotheses, building models, and making predictions based on statistical methods.

Steps: Statistical analysis involves several key steps, including data collection, data preparation, exploratory data analysis (EDA), choosing appropriate statistical methods, conducting the analysis, and interpreting and communicating the results.

In summary, statistical methods are the specific tools and techniques used within the broader context of statistical analysis. Statistical analysis is the comprehensive process of working with data, where statistical methods are applied at various stages to achieve specific objectives, such as hypothesis testing, modeling, or data exploration. Statistical analysis encompasses the entire workflow, while statistical methods are the individual procedures used within that workflow.
----


Statistical [[test]]s are a way of mathematically determining whether two sets of data are significantly different from each other. To do this, statistical tests use several statistical measures, such as the mean, standard deviation, and coefficient of variation.

[[Statistic]]al [[method]]s are mathematical formulas, [[model]]s, and [[technique]]s that are used in [[statistical analysis]] of raw research data. The application of statistical methods extracts information from research data and provides different ways to assess the robustness of research outputs.

Statistical [[analysis]] has usually been used to determine the quality of an individual [[metrics]]. Using metrics individually, as practiced so far, to differentiate [[performance]] in a unidimensional feature space may not provide adequate distinction.
----
Examples: [[t-test]]/[[ANOVA]] and [[Kruskal-Wallis test]]/[[Mann-Whitney U test]].
----





Is fundamental to all [[experiment]]s that use [[statistics]] as a [[research]] [[methodology]]. Most experiments in social sciences and many important experiments in natural science and engineering need statistical analysis.

Statistical analysis is also a very useful tool to get approximate solutions when the actual process is highly complex or unknown in its true form.

Example: The study of turbulence relies heavily on statistical analysis derived from experiments. Turbulence is highly complex and almost impossible to study at a purely theoretical level. Scientists therefore need to rely on a statistical analysis of turbulence through experiments to confirm theories they propound.

In social sciences, statistical analysis is at the heart of most experiments. It is very hard to obtain general theories in these areas that are universally valid. In addition, it is through experiments and surveys that a social scientist is able to confirm his theory.

What is the link between money and happiness? Does having more money make you happier? This is an age-old question that scientists are now trying to answer. Such experiments are highly complex in nature. After various studies, it turns out that there is a direct relationship between money and happiness till you reach a certain income level that corresponds to minimum basic requirements of food, shelter and clothing and after this level (it is about $60,000/year in the US), money and happiness seem independent of each other.

Beware the Pitfalls

Students of science need to know statistical analysis as so many areas use it. There are also many pitfalls to avoid. Statistics can be used, intentionally or unintentionally, to reach faulty conclusions. Misleading information is unfortunately the norm in advertising. The drug companies, for example, are well known to indulge in misleading information.

Knowledge of statistics therefore will help you look behind the numbers and know the truth instead of being misled to believe something that is not true. Data dredging is another huge problem especially in this internet era where numbers and data are so easy to come by. Only by knowing the robust elements of statistical analysis can one really harness the potential of this incredible tool.

Survey questions are another favorite area that can very easily be manipulated. This happens all the time, right from presidential election surveys to market surveys by corporations. It can always happen unintentionally, which means you need to be even more careful. Such bias is hard to detect because it doesn’t come out easily in the statistical analysis and there is no mathematical technique that will determine whether this question is biased.

It is therefore important that you understand not just the numbers but the meaning behind the numbers. Statistics is a tool, not a substitute for in-depth reasoning and analysis. It should supplement your knowledge of the area that you are studying.


===== ComBat harmonization =====

[[ComBat harmonization]]


===== Statistical software =====
see [[Statistical software]].