Applying Bonferoni correction

After identifying significant differences between therapy groups with Tukey's HSD, we want to confirm our findings with the Bonferroni correction. The Bonferroni correction is a conservative statistical adjustment used to counteract the problem of multiple comparisons. It reduces the chance of obtaining false-positive results by adjusting the significance level. In the context of your study on the effectiveness of CBT, DBT, and ACT, applying the Bonferroni correction will help ensure that the significant differences you observe between therapy groups are not due to chance.

The therapy_outcomes DataFrame has again been loaded along with pandas as pd, from scipy.stats import ttest_ind, and from statsmodels.sandbox.stats.multicomp import multipletests.

This exercise is part of the course

Experimental Design in Python

Exercise instructions

Conduct independent t-tests between all pairs of therapy groups in therapy_pairs and append the p-values (p_val) to the p_values list.
Apply the Bonferroni correction to adjust the p-values from the multiple tests and print them.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

p_values = []

therapy_pairs = [('CBT', 'DBT'), ('CBT', 'ACT'), ('DBT', 'ACT')]

# Conduct t-tests and collect P-values
for pair in ____:
    group1 = therapy_outcomes[therapy_outcomes['Therapy_Type'] == ____]['Anxiety_Reduction']
    group2 = therapy_outcomes[therapy_outcomes['Therapy_Type'] == ____]['Anxiety_Reduction']
    t_stat, p_val = ____(group1, group2)
    p_values.____(p_val)

# Apply Bonferroni correction
print(____(____, alpha=0.05, method='____')[1])

Edit and Run Code

This exercise is part of the course

Experimental Design in Python

IntermediateSkill Level

4.8+

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Building knowledge in experimental design allows you to test hypotheses with best-practice analytical tools and quantify the risk of your work. You’ll begin your journey by setting the foundations of what experimental design is and different experimental design setups such as blocking and stratification. You’ll then learn and apply visual and analytical tests for normality in experimental data.

Exercise 1: Setting up experiments Exercise 2: Non-random assignment of subjects Exercise 3: Random assignment of subjects Exercise 4: Experimental data setup Exercise 5: Blocking experimental data Exercise 6: Stratifying an experiment Exercise 7: Which was stratified?Exercise 8: Normal data Exercise 9: Visual normality in an agricultural experiment Exercise 10: Analytical normality in an agricultural experiment

You'll delve into sophisticated experimental design techniques, focusing on factorial designs, randomized block designs, and covariate adjustments. These methodologies are instrumental in enhancing the accuracy, efficiency, and interpretability of experimental results. Through a combination of theoretical insights and practical applications, you'll acquire the skills needed to design, implement, and analyze complex experiments in various fields of research.

Exercise 1: Factorial designs: principles and applications Exercise 2: Understanding marketing campaign effectiveness Exercise 3: Heatmap of campaign interactions Exercise 4: Factorial designs and randomized block designs Exercise 5: Randomized block design: controlling variance Exercise 6: Implementing a randomized block design Exercise 7: Visualizing productivity within blocks by incentive Exercise 8: ANOVA within blocks of employees Exercise 9: Covariate adjustment in experimental design Exercise 10: Importance of covariates Exercise 11: Covariate adjustment with chick growth

Master statistical tests like t-tests, ANOVA, and Chi-Square, and dive deep into post-hoc analyses and power analysis essentials. Learn to select the right test, interpret p-values and errors, and skillfully conduct power analysis to determine sample and effect sizes, all while leveraging Python's powerful libraries to bring your data insights to life.

Exercise 1: Choosing the right statistical test Exercise 2: Choosing the right test: petrochemicals Exercise 3: Choosing the right test: human resources Exercise 4: Choosing the right test: finance Exercise 5: Post-hoc analysis following ANOVA Exercise 6: Anxiety treatments ANOVA Exercise 7: Applying Tukey's HSD Exercise 8: Applying Bonferoni correction

Current Exercise

Exercise 9: P-values, alpha, and errors Exercise 10: Analyzing toy durability Exercise 11: Visualizing durability differences Exercise 12: Role of significance levels Exercise 13: Power analysis: sample and effect size Exercise 14: Effect size purpose Exercise 15: Estimating required sample size for energy study

Hop into the complexities of experimental data analysis. Learn to synthesize insights using pandas, address data issues like heteroscedasticity with scipy.stats, and apply nonparametric tests like Mann-Whitney U. Learn additional techniques for transforming, visualizing, and interpreting complex data, enhancing your ability to conduct robust analyses in various experimental settings.

Exercise 1: Synthesizing insights from complex experiments Exercise 2: Visualizing loan approval yield Exercise 3: Exploring customer satisfaction Exercise 4: Effectively communicating experimental data Exercise 5: Addressing complexities in experimental data Exercise 6: Check for heteroscedasticity in shelf life Exercise 7: Exploring and transforming shelf life data Exercise 8: Applying nonparametric tests in experimental analysis Exercise 9: Visualizing and testing preservation methods Exercise 10: Further analyzing food preservation techniques Exercise 11: Congratulations!