Bayes vs. NHST

Attribute	Bayes	NHST
Philosophy	Subjective interpretation of probability	Objective interpretation of probability
Use of prior knowledge	Requires specification of prior beliefs	Does not incorporate prior beliefs
Interpretation of results	Posterior probability distribution	P-value and significance testing
Flexibility	Can update beliefs with new evidence	Fixed decision criteria

Introduction

Bayesian statistics and null hypothesis significance testing (NHST) are two widely used approaches in statistical analysis. While both methods aim to draw conclusions from data, they have distinct differences in their underlying principles and interpretations. In this article, we will compare the attributes of Bayes and NHST to provide a better understanding of their strengths and limitations.

Bayesian Statistics

Bayesian statistics is a framework for statistical inference that involves updating beliefs about the parameters of a model based on observed data. In Bayesian analysis, prior beliefs about the parameters are combined with the likelihood of the data to obtain a posterior distribution. This posterior distribution represents the updated beliefs about the parameters after observing the data. One of the key advantages of Bayesian statistics is its ability to incorporate prior knowledge into the analysis, which can lead to more accurate and informative results.

• Bayesian statistics involves updating beliefs about parameters based on data.
• Prior beliefs are combined with data likelihood to obtain a posterior distribution.
• It allows for the incorporation of prior knowledge into the analysis.
• Results are often more accurate and informative.
• Bayesian analysis provides a full probability distribution for the parameters.

Null Hypothesis Significance Testing (NHST)

Null hypothesis significance testing (NHST) is a frequentist approach to statistical inference that involves testing hypotheses about the parameters of a model. In NHST, a null hypothesis is specified, and the data are used to determine the likelihood of observing the data under the null hypothesis. The p-value is then calculated, which represents the probability of obtaining the observed data or more extreme data if the null hypothesis is true. NHST is widely used in scientific research but has been criticized for its reliance on arbitrary thresholds and dichotomous decision-making.

• NHST involves testing hypotheses about model parameters.
• A null hypothesis is specified, and the likelihood of the data under the null hypothesis is determined.
• The p-value is calculated to assess the evidence against the null hypothesis.
• NHST is commonly used in scientific research.
• It has been criticized for its reliance on arbitrary thresholds and dichotomous decision-making.

Interpretation of Results

One of the key differences between Bayesian statistics and NHST lies in the interpretation of results. In Bayesian analysis, the focus is on the posterior distribution, which provides a full range of plausible values for the parameters along with their associated probabilities. This allows researchers to make probabilistic statements about the parameters and quantify uncertainty in the estimates. On the other hand, NHST typically involves comparing the p-value to a predetermined threshold (e.g., 0.05) to make a binary decision about the null hypothesis, leading to a more categorical interpretation of results.

Handling of Uncertainty

Bayesian statistics offers a more flexible and intuitive way to handle uncertainty compared to NHST. By providing a full probability distribution for the parameters, Bayesian analysis allows researchers to quantify uncertainty and make informed decisions based on the entire range of plausible values. This can be particularly useful in situations where decision-making requires a nuanced understanding of uncertainty. In contrast, NHST often leads to a dichotomous interpretation of results, where decisions are based on a single p-value threshold without considering the full range of possible outcomes.

Incorporation of Prior Knowledge

Another important distinction between Bayesian statistics and NHST is the incorporation of prior knowledge into the analysis. Bayesian analysis explicitly allows researchers to incorporate existing knowledge or beliefs about the parameters through the specification of prior distributions. This can be especially valuable in situations where prior information is available or when researchers want to update their beliefs based on new data. In contrast, NHST does not provide a formal mechanism for incorporating prior knowledge, which can limit the ability to leverage existing information in the analysis.

Robustness to Sample Size

Bayesian statistics and NHST also differ in their robustness to sample size. Bayesian analysis tends to be more robust to small sample sizes because it can incorporate prior information to supplement the limited data. This can help improve the precision of estimates and reduce the impact of sampling variability. On the other hand, NHST may be more sensitive to sample size, as small samples can lead to unstable results and unreliable conclusions based on p-values alone.

Conclusion

In conclusion, Bayesian statistics and NHST are two distinct approaches to statistical inference with their own strengths and limitations. Bayesian analysis offers a more flexible and informative way to handle uncertainty, incorporate prior knowledge, and interpret results probabilistically. On the other hand, NHST is commonly used in scientific research but has been criticized for its reliance on arbitrary thresholds and dichotomous decision-making. Researchers should carefully consider the goals of their analysis and the nature of their data when choosing between Bayesian statistics and NHST to ensure that the chosen approach aligns with the research objectives and provides meaningful insights.