a) Assume you have collected data from your experiments, how would you perform arigorous statistical analysis of the results.

To perform a rigorous statistical analysis of the results, follow these steps:

1. Data Preparation: Start by organizing and cleaning the collected data. Remove any outliers or errors, and ensure that the data is in the appropriate format for analysis.

2. Descriptive Statistics: Calculate descriptive statistics such as mean, median, standard deviation, and range to summarize the main characteristics of the data. This will provide an initial understanding of the data distribution.

3. Hypothesis Testing: Formulate a null hypothesis and an alternative hypothesis based on the research question. Choose an appropriate statistical test, such as t-test, chi-square test, or ANOVA, depending on the nature of the data and the research question.

4. Statistical Test: Apply the chosen statistical test to the data. Calculate the test statistic and determine the p-value. The p-value represents the probability of obtaining the observed results if the null hypothesis is true.

5. Interpretation: Evaluate the p-value against a predetermined significance level (usually 0.05). If the p-value is less than the significance level, reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis. If the p-value is greater than the significance level, fail to reject the null hypothesis.

6. Effect Size: Assess the effect size, which measures the magnitude of the observed effect. This helps determine the practical significance of the results.

7. Confidence Intervals: Calculate confidence intervals to estimate the range within which the true population parameter lies. This provides a measure of uncertainty around the point estimate.

8. Conclusion: Summarize the findings of the statistical analysis, including the results of hypothesis testing, effect size, and confidence intervals. Discuss the implications of the results in relation to the research question.

9. Limitations and Future Directions: Acknowledge any limitations of the study and suggest areas for future research.

10. Reporting: Present the results in a clear and concise manner, using appropriate tables, graphs, and statistical language. Ensure that the analysis is reproducible by providing all necessary details and code.

By following these steps, you can perform a rigorous statistical analysis of your experimental results.