Statistical POWER and Power Analysis

Biostatistics By Design

13 Jan 201907:16

EducationalLearning

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TLDRThis video script delves into the concept of statistical power in inferential statistics, emphasizing the importance of avoiding type 1 and type 2 errors. It explains type 1 errors as incorrect rejections of the null hypothesis and type 2 errors as failing to reject a false null hypothesis. The script highlights the role of p-values in determining significance and the common threshold of 0.05 for alpha. To increase power and reduce the chance of type 2 errors, it suggests strategies like homogeneous experimental units, distinct treatment levels, and larger sample sizes. Power analysis is introduced as a crucial tool for determining sample size and justifying it in grant applications, with the goal of achieving at least 80% power. The script encourages the use of statistical packages for power analysis and suggests literature reviews or pilot studies for informed estimates.

Takeaways

🧐 The video discusses the concept of 'statistical power' in the context of making decisions about populations based on sample data.
🤔 It introduces the idea of making mistakes in inferential statistics, specifically 'Type 1' and 'Type 2' errors.
🔍 A 'Type 1 error' occurs when one incorrectly rejects the null hypothesis, believing there is a difference when there isn't.
🔎 Conversely, a 'Type 2 error' happens when one fails to reject the null hypothesis and misses a real difference between populations.
📉 The speaker explains that p-values are used to measure the probability of committing a Type 1 error, typically set at a 5% threshold.
💪 'Power' is defined as the probability of correctly rejecting the null hypothesis when there is a true effect (1 minus the probability of a Type 2 error).
📈 To increase statistical power and reduce the chance of a Type 2 error, one can improve experimental design, such as using homogeneous units or larger treatment differences.
🔢 Increasing the sample size also boosts statistical power, which is crucial for detecting true effects.
📊 Power analysis is essential for determining the required sample size to detect an effect of a certain size with confidence.
📝 It's often a requirement in grant applications, especially when the study involves animals or human subjects, to justify the proposed sample size.
🔬 Conducting a power analysis can also help in deciding whether a study is feasible based on the required sample size to detect the desired effect.

Q & A

What is the main topic discussed in the script?
-The main topic discussed in the script is statistical power and its relation to making decisions in inferential statistics, specifically focusing on type 1 and type 2 errors.
What are the two types of mistakes that can be made in inferential statistics?
-The two types of mistakes that can be made in inferential statistics are type 1 error (incorrectly rejecting the null hypothesis when there is no difference) and type 2 error (incorrectly failing to reject the null hypothesis when there is a difference).
What is a type 1 error?
-A type 1 error occurs when you decide that two populations are different when in reality there is no difference. It is made by rejecting the null hypothesis when it is actually true.
What is a type 2 error?
-A type 2 error occurs when you decide that there is no difference between two populations when in fact there is a difference. It is made by failing to reject the null hypothesis when it is false.
What is the p-value in the context of statistical tests?
-The p-value is a conditional probability that measures the probability of observing the difference between two samples, or a more extreme difference, just by chance alone, given that the populations are actually not different. It helps in determining the likelihood of committing a type 1 error.
What is the commonly accepted threshold for the p-value to reject the null hypothesis?
-The most commonly accepted threshold for the p-value is 0.05, or a 5% chance of committing a type 1 error, also known as alpha.
What is statistical power in the context of hypothesis testing?
-Statistical power is the probability of correctly rejecting the null hypothesis when there is a true difference between populations. It is calculated as 1 minus beta (1 - β).
How can one increase their statistical power?
-One can increase their statistical power by improving experimental design, such as using homogeneous experimental units, choosing treatment levels that are more different from each other, and increasing the sample size or the number of experimental or observational units.
What is power analysis and why is it important?
-Power analysis is used to determine the sample size required to detect a difference or effect of a given size with a certain amount of confidence. It is important because it helps in justifying sample size in grant applications, especially when using animals or human subjects, and it can inform whether a study is worth pursuing based on the required sample size.
What are the five pieces of information needed to perform a power analysis?
-The five pieces of information needed to perform a power analysis are sample size, magnitude of the difference between populations or effect size, the amount of natural or random variation within the population, the acceptable level of type one error (alpha), and power.
What is a recommended approach for estimating variance when performing power analysis?
-A recommended approach for estimating variance when performing power analysis is to conduct a literature search to find information about what you hope to measure or to conduct a small pilot study to collect preliminary data that can inform your larger study.

Outlines

00:00

🔍 Understanding Statistical Power and Errors

This paragraph introduces the concept of statistical power and the potential for making mistakes in inferential statistics. It explains the two types of errors: Type 1 error, which occurs when incorrectly rejecting the null hypothesis and claiming a difference where there is none (significance level, alpha, is commonly set at 0.05); and Type 2 error, which happens when failing to reject the null hypothesis when there actually is a difference (beta represents the probability of this error). The paragraph also discusses the importance of p-values, which measure the probability of observing a difference due to chance if there is no actual difference in populations. Increasing statistical power, which is 1 minus beta, reduces the chance of committing a Type 2 error. Strategies to increase power include experimental design, homogeneous units, different treatment levels, and increasing sample size. A power of 80% or more is generally recommended for experimental design.

05:01

📊 The Importance of Power Analysis in Research

This paragraph delves into the importance and application of power analysis in research. Power analysis is crucial for determining the necessary sample size to detect a given effect size with confidence. It is often a requirement in grant applications, especially when the study involves animals or human subjects, to justify the proposed sample size. Power analysis can also help researchers decide whether a study is feasible based on the required sample size. The process involves understanding the relationship between sample size, effect size, variability within the population, the acceptable type 1 error rate (alpha), and power. Researchers are advised to use statistical software for power analysis and may need to estimate certain parameters like variance, possibly through literature review or pilot studies. The paragraph also encourages viewers to watch an example of power analysis for a two-sample t-test and subscribe for more educational content.

Mindmap

Keywords

💡Statistical Power

Statistical power refers to the probability that a test will correctly reject a false null hypothesis, i.e., detect a true effect when it exists. In the video, it is the main focus as the speaker discusses how to avoid making incorrect decisions in inferential statistics. The script emphasizes the importance of increasing statistical power to reduce the chance of committing a type 2 error, which is a failure to detect a difference when one actually exists.

💡Type 1 Error

A type 1 error occurs when a study incorrectly rejects the null hypothesis, concluding that there is a difference between populations when in reality there is none. The video script uses the example of comparing two populations and mistakenly declaring a difference when there is none, which would be a type 1 error. The significance level, or alpha, is set to protect against this error, commonly at a 5% threshold.

💡Type 2 Error

A type 2 error is the mistake of failing to reject the null hypothesis when there actually is a difference between populations. The script explains that type 2 errors happen when the study does not detect a difference that truly exists, and increasing statistical power can help reduce the likelihood of committing this type of error.

💡Null Hypothesis

The null hypothesis is a statement of no effect or no difference that researchers test in an experiment. In the script, the null hypothesis is mentioned in the context of making decisions about population differences. Rejecting the null hypothesis implies a type 1 error risk, while failing to reject it implies a type 2 error risk.

💡P-value

The p-value is a statistical measure that indicates the probability of obtaining results as extreme as the observed results, assuming the null hypothesis is true. The video script explains that p-values range from zero to one and are used to determine if the observed difference is likely due to chance or a true effect. A common threshold for significance is p < 0.05.

💡Beta

Beta represents the probability of committing a type 2 error, which is the chance of failing to detect a true effect. The script mentions that power is equal to 1 minus beta, indicating that increasing power decreases the likelihood of a type 2 error.

💡Sample Size

Sample size refers to the number of observations or subjects included in a study. The video script discusses the importance of sample size in increasing statistical power and how power analysis can be used to determine the necessary sample size to detect an effect with a certain level of confidence.

💡Power Analysis

Power analysis is a method used to determine the sample size needed to detect an effect of a certain size with a given level of confidence. The script emphasizes the importance of power analysis in experimental design, grant applications, and deciding whether a study is feasible based on the required sample size.

💡Effect Size

Effect size is a measure of the magnitude of a difference or effect in a study. The video script mentions that power analysis takes into account the effect size, which is one of the factors that determine the required sample size to detect a significant difference.

💡Alpha

Alpha is the probability of making a type 1 error, commonly set at 0.05. The script explains that researchers protect against type 1 errors by rejecting the null hypothesis only when the p-value is less than alpha.

💡Experimental Design

Experimental design refers to the process of planning and conducting an experiment to ensure valid results. The script discusses strategies for maximizing statistical power through experimental design, such as using homogeneous experimental units and choosing treatment levels that maximize differences.

Highlights

Introduction to the concept of power in statistical analysis

Explaining the inevitability of making mistakes in inferential statistics

Definition and explanation of Type 1 error

Clarification on when Type 1 errors occur

Definition and explanation of Type 2 error

Conditions under which Type 2 errors occur

Importance of avoiding mistakes in research

Introduction to p-values and their significance

Explanation of p-values as conditional probabilities

Commonly accepted Type 1 error rate (alpha)

How researchers use p-values to protect against Type 1 errors

Introduction to the concept of power and beta

Strategies to increase statistical power

Role of experimental design in maximizing power

Importance of sample size in increasing power

Recommendation for a minimum of 80% power in experimental design

Explanation of power analysis and its purpose

Necessity of power analysis in grant applications

Use of power analysis to determine feasibility of a study

Components needed for power analysis and their interrelation

Recommendation to use statistical packages for power analysis

Suggestion to conduct a literature search or pilot study for preliminary data

Invitation to view an example of power analysis for a two-sample t-test

Encouragement to subscribe for more informative videos

Transcripts

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Takeaways

Q & A

What is the main topic discussed in the script?

What are the two types of mistakes that can be made in inferential statistics?

What is a type 1 error?

What is a type 2 error?

What is the p-value in the context of statistical tests?

What is the commonly accepted threshold for the p-value to reject the null hypothesis?

What is statistical power in the context of hypothesis testing?

How can one increase their statistical power?

What is power analysis and why is it important?

What are the five pieces of information needed to perform a power analysis?

What is a recommended approach for estimating variance when performing power analysis?