## Convert Experiments supports mean and proportion testing by providing Frequentist, Bayesian, and Sequential statistical models, each offering unique methodologies and insights for comprehensive and reliable data analysis.

Convert Experiments is a powerful tool for A/B testing and optimization, enabling businesses to make data-driven decisions. A crucial aspect of this process involves mean and proportion testing, which Convert Experiments supports through three major statistical models: Frequentist, Bayesian, and Sequential. Here’s how these models relate to mean and proportion testing and how Convert Experiments leverages them to provide robust analytical capabilities.

#### Mean and Proportion Testing: The Basics

Before delving into the models, it’s essential to understand mean and proportion testing:

**Mean Testing** involves comparing sample means to determine if there is a significant difference from a hypothesized population mean or between two sample means. This can be achieved through:

**One-sample t-test**: Tests if the sample mean differs from a known population mean.**Two-sample t-test**: Compares the means of two independent samples.**Paired sample t-test**: Compares means from the same group at different times or under different conditions.

**Proportion Testing** involves comparing sample proportions to a hypothesized population proportion or between two sample proportions. This can be achieved through:

**One-sample proportion test**: Tests if the sample proportion differs from a known population proportion.**Two-sample proportion test**: Compares the proportions of two independent samples.

### Convert Experiments and Statistical Models

Convert Experiments supports mean and proportion testing by providing three statistical models: Frequentist, Bayesian, and Sequential. Each model offers unique methodologies and insights, allowing users to choose the most appropriate approach for their testing needs.

#### Frequentist Approach

**Frequentist statistics** is the traditional method used in hypothesis testing and inference, based on long-run frequencies and the concept of repeated sampling.

**Key Features**:

**Hypothesis Testing**: Involves formulating a null hypothesis (H0H_0H0) and an alternative hypothesis (H1H_1H1).**Significance Levels**: Uses a threshold (α\alphaα), commonly set at 0.05, to decide whether to reject H0H_0H0.**P-Value**: Calculates the probability of obtaining the observed results under H0H_0H0.

**Application in Convert Experiments**:

**Mean Testing**: Uses t-tests to compare sample means, helping to determine if observed differences are statistically significant.**Proportion Testing**: Uses z-tests for sample proportions to identify significant differences in conversion rates or other proportions.

Convert Experiments leverages Frequentist methods to provide clear decision rules and robust analysis for users without incorporating prior information, ensuring straightforward and widely understood results.

#### Bayesian Approach

**Bayesian statistics** incorporates prior knowledge or beliefs into the analysis through a prior distribution, updating it with observed data to form a posterior distribution.

**Key Features**:

**Prior Distribution**: Represents initial beliefs about the parameters.**Likelihood**: Based on observed data.**Posterior Distribution**: Updated belief about the parameters after considering the data.**Credible Intervals**: Probabilistic intervals indicating where the parameter likely lies.**Bayes Factor**: Used for hypothesis testing, comparing the likelihood of the data under different hypotheses.

**Application in Convert Experiments**:

**Mean Testing**: Bayesian t-tests incorporate prior distributions on means and variances, providing a comprehensive view of the data.**Proportion Testing**: Bayesian methods update the probability of success based on observed data and prior beliefs, offering a nuanced analysis.

Convert Experiments’ Bayesian methods allow users to integrate prior knowledge and obtain probabilistic interpretations of results, making it particularly useful for complex decision-making processes.

#### Sequential Approach

**Sequential analysis** involves evaluating data as it is collected and making decisions at interim points, rather than waiting until all data is collected. This approach is highly efficient and ethical, especially in fields like clinical trials.

**Key Features**:

**Interim Analysis**: Conducting hypothesis tests at multiple stages during data collection.**Stopping Rules**: Pre-defined criteria for early stopping if results are conclusive.**Error Rates**: Adjustments to control the overall error rate due to multiple testing points.

**Application in Convert Experiments**:

**Mean Testing**: Sequential methods test hypotheses about means, allowing for early stopping if results are convincing.**Proportion Testing**: Sequential methods test hypotheses about proportions, monitoring data at interim points.

Convert Experiments’ sequential methods provide the flexibility to make timely decisions, saving resources and time by potentially concluding tests early when sufficient evidence is gathered.

### Conclusion

Convert Experiments supports mean and proportion testing through the use of Frequentist, Bayesian, and Sequential statistical models. Each of these approaches offers distinct advantages:

**Frequentist methods**provide straightforward hypothesis testing and decision rules, ideal for clear and robust analysis without prior information.**Bayesian methods**offer a flexible framework for incorporating prior knowledge and making probabilistic inferences, suitable for more complex analyses.**Sequential methods**enable efficient, flexible testing with the ability to make timely decisions and conserve resources.

By integrating these diverse statistical models, Convert Experiments ensures comprehensive and reliable analysis, empowering users to make informed, data-driven decisions.