Statistics level of significance

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SUMMARY

This discussion focuses on determining the required sample size for a two-sided one-sample t-test with an effect size of 0.20 and a sample variance of σ² = 1.0, aiming for a power of 0.80. The level of significance is set at α = 0.05 and α = 0.01. Additionally, the conversation addresses the calculation of sample size when the population size is N = 350, suggesting the use of binomial distribution for this scenario. Participants express confusion over the statistical equations and seek guidance on implementing these concepts.

PREREQUISITES
  • Understanding of two-sided one-sample t-tests
  • Knowledge of effect size and sample variance
  • Familiarity with statistical power and significance levels
  • Basic concepts of binomial distribution
NEXT STEPS
  • Calculate sample size using G*Power for t-tests
  • Explore the relationship between effect size and sample size
  • Learn about the implications of different significance levels (α = 0.05 vs. α = 0.01)
  • Study the application of binomial distribution in sample size determination
USEFUL FOR

Statisticians, data analysts, researchers conducting hypothesis testing, and students seeking clarity on sample size calculations in statistical studies.

tedpark1212
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I need help with these statistics problems. Can anyone guide me through them? I would greatly appreciate it. I am completely lost on where to start.

1. Suppose you want to show the significance of an effect size of 0.20 between your sample mean and a hypothesized mean. You intend to conduct a two-sided one-sample t-test. The sample variance is σ2 = 1.0. You assume that the population is large, or effectively infinite. If you want the test to have a power of 0.80, what is the required sample size for the following?

So for here I would use standard normal distribution, correct?

• A level of significance of α = 0.05


• A level of significance of α = 0.01



2. After some research, you determine that the size of the population is N = 350. If you want the test to have a power of 0.80, what is the required sample size for the following?

For question 2 I would use binominal distribution? I'm really confused on how to work the equations.

• A level of significance of α = 0.05


• A level of significance of α = 0.01


3. Comment on the sample sizes required for questions 3 and 4. Explain the differences and similarities.
 
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tedpark1212 said:
I need help with these statistics problems. Can anyone guide me through them? I would greatly appreciate it. I am completely lost on where to start.

1. Suppose you want to show the significance of an effect size of 0.20 between your sample mean and a hypothesized mean. You intend to conduct a two-sided one-sample t-test. The sample variance is σ2 = 1.0. You assume that the population is large, or effectively infinite. If you want the test to have a power of 0.80, what is the required sample size for the following?

So for here I would use standard normal distribution, correct?

• A level of significance of α = 0.05


• A level of significance of α = 0.01



2. After some research, you determine that the size of the population is N = 350. If you want the test to have a power of 0.80, what is the required sample size for the following?

For question 2 I would use binominal distribution? I'm really confused on how to work the equations.

• A level of significance of α = 0.05


• A level of significance of α = 0.01


3. Comment on the sample sizes required for questions 3 and 4. Explain the differences and similarities.

PF rules require you to show some effort. What have you done on this so far?
 
I have yet only established an idea of only which approach to use, but I am unable to implement it in my work.
 

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