Week 6: t-tests, confidence intervals, and effect size Flashcards
Describe the research contexts in which one-sample, related-samples, and independent-samples t-tests are most appropriate.
One-sample t-test: Used when comparing the mean of a single sample to a known value (e.g., population mean).
Related-samples t-test: Used when comparing means from the same group at different times (e.g., pre-test and post-test) or matched pairs.
Independent-samples t-test: Used when comparing means from two different groups.
Interpret the results of one-sample, related-samples, and independent-samples t-tests in psychological research.
One-sample t-test: Determines if the sample mean is significantly different from a known value.
Related-samples t-test: Determines if there is a significant difference between paired observations.
Independent-samples t-test: Determines if there is a significant difference between the means of two independent groups.
Define and illustrate the concept of effect size and its relation to hypothesis testing.
Effect size: A measure of the strength of the relationship between two variables. It helps to understand the practical significance of the results.
Relation to hypothesis testing: While p-values indicate if an effect exists, effect size indicates the magnitude of the effect.
Explain the concept of confidence intervals and their role in statistical inference.
Confidence intervals (CI): A range of values that is likely to contain the population parameter with a certain level of confidence (e.g., 95% CI).
Role in statistical inference: Provides an estimate of the parameter and the precision of the estimate, helping to understand the reliability of the results.
Describe the benefits of counterbalancing in repeated measures designs to control for order effects.
Counterbalancing: A method used to control for order effects by varying the order of conditions for participants.
Benefits: Reduces the potential for order effects to confound the results, ensuring that the observed effects are due to the treatment rather than the order of presentation.
When would you use a one-sample z-test?
Used when comparing the mean of a single sample to a known value (e.g., population mean) when the population variance is known.
When would you use a one-sample t-test?
Used when comparing the mean of a single sample to a known value (e.g., population mean) when the population variance is not known and must be estimated.
What is the null hypothesis (H₀) and alternative hypothesis (Hₐ) in hypothesis testing?
Null hypothesis (H₀): A statement that there is no effect or no difference, often represented as H₀: µ = µ₀.
Alternative hypothesis (Hₐ): A statement that there is an effect or a difference, often represented as Hₐ: µ ≠ µ₀ (non-directional) or Hₐ: µ > µ₀ / Hₐ: µ < µ₀ (directional).
How do you calculate the standard error of the mean?
Standard error (SE) = standard deviation (σ) / √n, where n is the sample size.
What is the significance level (α) in hypothesis testing?
The significance level (α) is the probability of rejecting the null hypothesis when it is true. Commonly used values are 0.05, 0.01, and 0.10.
What is the critical value in hypothesis testing?
The critical value is the threshold value that the test statistic must exceed to reject the null hypothesis. It depends on the significance level (α) and the degrees of freedom.
How do you interpret a p-value in hypothesis testing?
The p-value is the probability of obtaining a result as extreme as, or more extreme than, the observed result, assuming the null hypothesis is true. If the p-value is less than the significance level (α), we reject the null hypothesis.
What is a confidence interval (CI)?
A confidence interval is a range of values that is likely to contain the population parameter with a certain level of confidence (e.g., 95% CI).
How do you calculate a 95% confidence interval for the mean?
95% CI = sample mean ± (critical value * standard error). For a 95% CI, the critical value is typically 1.96 for large samples.
What is the effect size and why is it important?
Effect size is a measure of the strength of the relationship between two variables. It is important because it provides information about the practical significance of the results, beyond just statistical significance.
What are the benefits of counterbalancing in repeated measures designs?
Counterbalancing helps control for order effects by varying the order of conditions for participants. This ensures that the observed effects are due to the treatment rather than the order of presentation.
