Bonferonni-Holm correction

You've seen that comparing many different datasets, even randomly generated ones, can result in "statistically significant relationships" that are anything but! One way around this is to apply a correction to the alpha of your confidence level. In this exercise you'll explore why you should apply this correction and how to do so.

The 1000 p-values you calculated in the previous exercise have been loaded for you in a NumPy array p_values, as has the package NumPy as np.

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Foundations of Inference in Python

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# Compute the Bonferonni-corrected alpha
bonf_alpha = ____

# Check how many p-values were significant at this level
____

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Foundations of Inference in Python

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In this chapter, we'll explore the relationship between samples and statistically justifiable conclusions. Choosing a sample is the basis of making sound statistical decisions, and we’ll explore how the choice of a sample affects the outcome of your inference.

Exercise 1: Statistical inference and random sampling Exercise 2: Sampling and point estimates Exercise 3: Repeated sampling, point estimates and inference Exercise 4: Sampling and bias Exercise 5: Visualizing samples Exercise 6: Inference and bias Exercise 7: Confidence intervals and sampling Exercise 8: Normal sampling distributions Exercise 9: Calculating confidence intervals Exercise 10: Drawing conclusions from samples

Learn all about applying normality tests, correlation tests, and parametric and non-parametric tests for sound inference. Hypothesis tests are tools, and choosing the right tool for the job is critical for statistical decision-making. While you may be familiar with some of these tests in introductory courses, you'll go deeper to enhance your inferential toolkit in this chapter.

Exercise 1: Normality tests Exercise 2: Testing for normality Exercise 3: Distribution of errors Exercise 4: Fitting a normal distribution Exercise 5: Correlation tests Exercise 6: Testing for correlation Exercise 7: Autocorrelation Exercise 8: Explained variance Exercise 9: Parametric tests Exercise 10: Equal variance Exercise 11: Normality of groups Exercise 12: ANOVA Exercise 13: Non-parametric tests Exercise 14: Comparing rankings Exercise 15: Comparing medians

In this chapter, you'll measure and interpret effect size in various situations, encounter the multiple comparisons problem, and explore the power of a test in depth. While p-values tell you if a significant effect is present, they don't tell you how strong that effect is. Effect size measures how strong an effect a treatment has. Master the factors underpinning effect size in this chapter.

Exercise 1: Effect size Exercise 2: Effect size for means Exercise 3: Effect size for correlations Exercise 4: Effect size for categorical variables Exercise 5: Multiple comparisons and corrections Exercise 6: Multiple comparisons problem Exercise 7: Bonferonni-Holm correction

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Exercise 8: Power of a test Exercise 9: What is power anyway?Exercise 10: Power for experimental design Exercise 11: Computing power and sample sizes

You’ll expand your inferential statistics toolkit further with a look at bootstrapping, permutation tests, and methods of combining evidence from p-values. Bootstrapping will provide you with a first look at statistical simulation. In the lesson meta-analysis, you’ll learn all about combining results from multiple studies. You’ll end with a look at permutation tests, a powerful and flexible non-parametric statistical tool.

Exercise 1: Bootstrapping Exercise 2: Bootstrap confidence intervals Exercise 3: Bootstrapping vs. normality Exercise 4: Combining evidence from p-values Exercise 5: Fisher's method in SciPy Exercise 6: Inference using Fisher's method Exercise 7: Summarizing Fisher's method Exercise 8: Permutation tests Exercise 9: Permutation tests for correlations Exercise 10: Permutation tests and bootstrapping Exercise 11: Analyzing skewed data with a permutation test Exercise 12: Course wrap-up video