Statistical Power and t-test Basics

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Questions and Answers

What is the purpose of a p-value in hypothesis testing?

To determine the probability of observing the data if the null hypothesis is true (correct)

To identify the sample size needed for accurate estimates

To calculate the standard error of the sample

To measure the effect size of a population

Which of the following correctly defines a Type I error?

Incorrectly estimating the standard error in the analysis

Rejecting the null hypothesis when it is true (correct)

Accepting the alternative hypothesis when it is false

Failing to reject the null hypothesis when it is false

How can statistical power be maximized in hypothesis testing?

By decreasing the effect size

By lowering the confidence level

By increasing the sample size (correct)

By rejecting the null hypothesis more often

In the context of statistical testing, what does the term 'alpha' (α) refer to?

The threshold for statistical significance Signup and view all the answers

What does a false negative (Type II error) indicate in hypothesis testing?

The null hypothesis is accepted when it should be rejected Signup and view all the answers

What is the definition of statistical power in a hypothesis test?

The ability to reject the null hypothesis when it is false. Signup and view all the answers

Which factor does NOT directly impact the power of a statistical test?

Accuracy of the data collection method Signup and view all the answers

What is the conventional target power level typically aimed for in studies?

80% Signup and view all the answers

Which of the following statements is true regarding one-sided vs. two-sided tests?

One-sided tests have more power than two-sided tests when the effect is in one direction. Signup and view all the answers

What is the relationship between sample size and statistical power?

Larger sample sizes increase the power. Signup and view all the answers

How can increasing the significance threshold (α) affect statistical power?

It increases power by reducing β. Signup and view all the answers

What does a false negative imply in the context of statistical testing?

Failing to detect an effect when one actually exists. Signup and view all the answers

When planning research, what is a common use of power analysis?

To calculate the sample size required for a desired power level. Signup and view all the answers

What is the primary reason for needing a larger sample size with a smaller effect size when aiming for 80% power?

To detect true effects that are otherwise too small Signup and view all the answers

In the context of hypothesis tests, a two-sided test is used when the alternative hypothesis states what?

The group mean is not equal to a given value Signup and view all the answers

What issue arises from conducting studies with low power?

They may overestimate effect sizes Signup and view all the answers

Why is the z-test not commonly used in practice?

It requires knowing the true population SD Signup and view all the answers

When discussing statistical significance, what must be fixed to ensure the reliability of effect sizes?

Power and alpha level Signup and view all the answers

What is one of the consequences of running underpowered studies?

They inflate the perceived effect sizes Signup and view all the answers

In hypothesis testing, what does the null hypothesis (H0) generally assert?

The group mean equals a specified value Signup and view all the answers

What role does publication bias play in the interpretation of research results?

It leads to fewer significant results being published Signup and view all the answers

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Study Notes

Statistical Power and the t-test

Statistical power is the likelihood of detecting an effect if it truly exists.
Low statistical power leads to a higher chance of missing effects, leading to wasted resources.
Power should be considered when designing studies.
The t-test is a fundamental statistical test for comparing group means.
There are different types of t-tests: one-sample, independent groups, and paired.

Assumptions of the t-test

One-sample t-test: Assumes the sample's mean is compared to a known value. The data needs to be normally distributed.
Independent groups t-test: Assumes that the data is normally distributed and observation within and between groups are independent. Also, the variance between groups must be homogeneous.
Paired t-test: Assumes pairs of observations are independent; difference scores are normally distributed.

Cohen's d

Cohen's d is a measure of effect size.
Values of 0.2, 0.5, and 0.8 are used to describe small, medium, and large effects but are arbitrary and should be contextually interpreted.

Interpretation

Statistical tests can sometimes produce incorrect results.
False positive (Type I error): null hypothesis incorrectly rejected even though it is true
False negative (Type II error): null hypothesis incorrectly accepted despite the alternative hypothesis being true.
These values (alpha and beta) should be reported along with effect sizes to give a complete picture of the significance in a statistical assessment.

Statistical Tests

t-test: This test is frequently used when the standard deviation is unknown. The sample standard deviation is applied to give an approximate estimate.
Z-test: Assumes the population standard deviation is known.

Choosing the Correct Test

One-sided vs two-sided tests: Using a one-sided test will have slightly higher power when you are only interested in one direction of results.
Student's t-test vs. Welch's t-test: By default, R applies Welch's test. While Welch's is generally preferred, Student's t-test assumes homogeneity of variance (a shared variance for each group).

Additional Considerations

Statistical tests and their results should be examined in context to determine significance.
The t-test can be considered to be an outcome in a regression model.
The results should be reviewed with the correct contextual information.

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Description

This quiz covers the key concepts of statistical power and the various types of t-tests used in statistical analysis. Participants will learn about the assumptions of different t-tests and how to interpret effect sizes using Cohen's d. It's essential for researchers to understand these principles for effective study design.