The statistical power of a research design is the probability that the study will reject the null hypothesis, given a specific sample size and an expected relationship strength. For instance, if a design has a power of 0.80, there is an 80% chance of correctly rejecting the null hypothesis when the expected relationship exists in the population. It is the complement of the probability of making a Type II error (represented as $$ \beta $$), which is calculated as $$ 1 - \beta $$. Therefore, researchers strive for high statistical power to avoid missing a real effect.

Statistical Power

A quantitative measure, such as Cohen's $$d$$ or Pearson's $$r$$, used to estimate the strength of a statistical relationship within a population. In response to criticisms of null hypothesis testing, researchers are encouraged to report effect sizes alongside their tests. This practice is crucial because a $$p$$-value alone only indicates whether a relationship is statistically significant—which is heavily influenced by sample size—but fails to convey the actual magnitude or importance of that relationship.

Effect Size

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Statistics is the process of gathering, analyzing, and interpreting information in order to help people make decisions when faced with uncertainty.

Statistics

The list of helpful broad references about Statistics is categorized as follows:
- Statistics books
- Statistical Software 
- Statistics online courses
- Statistics research papers

Statistics References

The marriage of Statistics, Computer Science, and Domin knowledge built Data Science.

Data science is interdisciplinary

A few of the common statistical paradoxes are:"

- Monty Hall's paradox 
- Berkson's paradox
- Simpson's paradox

Common statistical paradoxes

Probability is the branch of math concerned with the likelihood of an event occuring, or the likelihood that an event is true. 

Probability Theory

Bayesian statistics is an approach to inferential statistics where a researcher specifies the prior probability that the null hypothesis and alternative hypotheses are true before conducting a study. Once the study is conducted, the probabilities are updated based on the newly collected data. This approach offers a potential alternative to traditional null hypothesis testing by providing a logical framework for quantifying uncertainty using probability distributions.

Bayesian Statistics

Descriptive statistics are a set of quantitative techniques used to summarize, organize, and visually display the data collected from a research sample. Important examples include measures of central tendency (such as the mean, median, and mode), which describe average scores, and measures of dispersion (such as the range, standard deviation, and variance), which indicate how spread apart the scores are.

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