statistics hypothesis testing cheat sheet

Guri Bee

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21-10-2024

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Hypothesis Testing Cheat Sheet: Demystifying Statistical Significance

Hypothesis testing is a fundamental tool in statistics that helps us draw meaningful conclusions from data. It's a powerful technique used to determine if a claim about a population is supported by evidence. This cheat sheet will guide you through the essential steps of hypothesis testing, providing insights and examples to clarify the process.

Understanding the Basics:

• Null Hypothesis (H0): This is the statement we are trying to disprove. It often represents the status quo or the absence of an effect. For example, "There is no difference in the average height of men and women."
• Alternative Hypothesis (Ha): This is the statement we are trying to prove. It contradicts the null hypothesis. For example, "There is a difference in the average height of men and women."
• Significance Level (α): This is the threshold for rejecting the null hypothesis. It's typically set at 0.05 (5%), meaning we are willing to accept a 5% chance of rejecting the null hypothesis when it's actually true (Type I error).

Key Steps in Hypothesis Testing:

1. Formulate Hypotheses: Clearly state your null and alternative hypotheses.
2. Choose a Test: Select the appropriate statistical test based on the type of data and research question. Common tests include t-tests, z-tests, ANOVA, and chi-square tests.
3. Set the Significance Level: Determine the significance level (α) for your test.
4. Collect Data: Obtain a sample of data relevant to your research question.
5. Calculate Test Statistic: Perform the chosen statistical test to calculate the test statistic. This value reflects how much the sample data deviates from the null hypothesis.
6. Determine p-value: The p-value represents the probability of observing the obtained results if the null hypothesis is true. A low p-value (typically less than α) suggests that the observed results are unlikely under the null hypothesis.
7. Make a Decision:
   • Reject H0: If the p-value is less than α, reject the null hypothesis. This suggests evidence supporting the alternative hypothesis.
   • Fail to Reject H0: If the p-value is greater than α, fail to reject the null hypothesis. This indicates that there is not enough evidence to reject the null hypothesis.

Practical Example:

Imagine you want to test if a new fertilizer increases plant growth.

• H0: The fertilizer has no effect on plant growth.
• Ha: The fertilizer increases plant growth.
• Test: You could use a t-test to compare the average growth of plants treated with the fertilizer to a control group.
• Data: You measure the height of plants in both groups after a certain period.
• Test Statistic and p-value: The t-test will calculate a test statistic and a p-value based on the data.
• Decision: If the p-value is less than 0.05, you would reject the null hypothesis and conclude that the fertilizer does increase plant growth. Otherwise, you would fail to reject the null hypothesis.

Additional Insights:

• Type I Error (False Positive): Rejecting the null hypothesis when it's actually true.
• Type II Error (False Negative): Failing to reject the null hypothesis when it's false.
• Power of a Test: The probability of correctly rejecting a false null hypothesis.
• Confidence Interval: A range of values that is likely to contain the true population parameter.

Where to Learn More:

• GitHub Repository: https://github.com/rstudio/cheatsheets/tree/master/stats
  • Key Author: RStudio (https://www.rstudio.com/)
  • Contribution: This repository provides comprehensive cheat sheets on various statistical concepts, including hypothesis testing.
• Online Resources:
  • https://www.statisticshowto.com/probability-and-statistics/hypothesis-testing/
  • https://www.khanacademy.org/math/statistics-probability/statistical-inference/hypothesis-testing/a/hypothesis-testing-overview

Conclusion:

Hypothesis testing is a powerful tool for analyzing data and drawing meaningful conclusions. Understanding the key steps and concepts outlined in this cheat sheet will empower you to effectively conduct and interpret hypothesis tests. Remember that while hypothesis testing can provide valuable insights, it's essential to consider the context of your research and draw conclusions based on the full body of evidence.