Alternative

An alternative is a set of mutually exclusive hypotheses that are used to explain the data.

The alternative hypothesis is typically the one being tested, while the null hypothesis is assumed to be true.

How to calculate

  1. State the null and alternative hypotheses: The null hypothesis (H0) states that the expected outcome did not occur, while the alternative hypothesis (H1) states that the expected outcome did occur.

  2. Select a significance level: The significance level is the probability of rejecting the null hypothesis when it is true. It is usually set at 0.05 or 5%.

  3. Calculate the test statistic: The test statistic is a measure of how different the observed data is from the expected data. It is calculated using the sample data and the parameters of the null hypothesis.

  4. Make a decision: The decision is based on the calculated test statistic and the chosen significance level. If the test statistic is greater than the critical value, then the null hypothesis is rejected and the alternative hypothesis is accepted.

  5. Interpret the results: The results of the test should be interpreted in terms of the null and alternative hypotheses. If the null hypothesis is rejected, then the alternative hypothesis is accepted. This means that the observed data is unlikely to have occurred by chance and is likely to be due to the expected outcome.

Examples

  1. Bootstrap sampling: Bootstrap sampling is an alternative to traditional sampling methods in which a sample of size n is drawn from a population. It is a non-parametric technique that can be used to estimate population parameters when the population size is large or the population is not well-defined.

  2. Bayesian statistics: Bayesian statistics is an alternative to traditional frequentist statistics that is based on the Bayesian interpretation of probability. It allows for the incorporation of prior knowledge in the form of prior distributions and can provide a more flexible approach to inference.

  3. Monte Carlo simulation: Monte Carlo simulation is an alternative to traditional analytical approaches for solving complex problems. It involves randomly sampling from a probability distribution to simulate a process and obtain estimates of the parameters of interest.

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