Statistics Part II Power Analysis, Effect, Confidence

• What is Beta (probability of false negative believing something is not true, but it is) influenced by?

  • Sample size
  • Power size
  • Alpha
  • Variability
• 1-beta stands for the power (probability of correctly detecting a ttue effect)
• Alpha level (type I error) is 0.05, and Beta is 0.80 or 80% (power of the test)
• Which type of error is worse to fall under?

  Type I error (0.05) because we may think there is an effect, when there is not an effect
• Power analysis is used to determine the sample size needed in a study to detect an effect of a given size.
• By controlling Beta-1 (power analysis), researchers can minimise the chance of making a Type II error (believing there is no effect, when there actually is).
• What do we want to specify for the effect in a one-sample t-test?

  The difference between the observed means and the expected means
• What do you think we should specify for the effect in a independent-sample t-test?

  Difference between the two groups for effect
• What do we want to specify for the effect in a paired-sample t-test??

  Difference within the two groups (before and after)
• What test statistic do we use to quantify effect size in t-tests?

  Cohen's d (d= difference/ standard deviation)
• Effect size is important because?

  It establishes practical importance in measuring the difference of means within the population, not just observed difference (significance level alpha)
• A cohen's d measure of 0.20 within a t-test would equate to a roughly small effect size
• What does this image describe?

  A cohen's d measure of 0.80 within a t-test would equate to a roughly large effect size by measuring the observed difference/ standard deviations of groups

  
• What does this image describe?

  A Cohen's d measure of 0.50 within a t-test would equate to a roughly moderate effect size by measuring the observed difference/ standard deviations of groups.

  
• The confidence interval quantifies how precise an estimate about your true population mean from the sample taken
• Increasing the sample size will create a more precise estimate (confidence interval) for the true population mean
• one-sample t-test: Confidence interval in which the difference between observed and expected mean likely falls
• independent samples t-test: Confidence interval in which the difference between two groups means likely falls
• Paired samples t-test Confidence interval in which the difference between the two paired groups( before and after) likely falls
• When do we require a non-parametric test?

  When data are not normally distributed
• A Wilcox test is can example of a non-parametric test
• The confidence interval ([0.03, 4.40]) is broad, meaning there's a wide range of values that the true effect could take. This broadness indicates a degree of uncertainty about the size of the effect.
• Power (1 - beta) is the probability that a study will detect an effect when there is an effect to be detected. It is typically established before a study begins. The higher the power(1 - beta).
• The bigger Power B-1 greater the chance of avoiding a Type II error (false negative).