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What is the primary purpose of inferential statistics?
To draw conclusions about a population based on sample data through hypothesis testing.
What does the null hypothesis (H0) state?
That there is no effect or difference.
What is the common threshold for significance, known as the alpha level (α)?
0.05.
How is the p-value interpreted in hypothesis testing?
A p-value indicates the likelihood that the observed results are due to chance; a small p-value suggests strong evidence against the null hypothesis.
What are Type I and Type II errors in the context of hypothesis testing?
Type I Error: Rejecting the null hypothesis when it is true. Type II Error: Failing to reject the null hypothesis when it is false.
What is the difference between statistical significance and effect size?
Statistical significance indicates if results are likely true, while effect size measures practical significance or the magnitude of the effect.
Define a 95% confidence interval.
A range of values that describes the likely range of population parameters; if sampled repeatedly, 95% of intervals will include the true value.
What factors affect the statistical power of a study?
Alpha level, size of the effect, variance, sample size, and choice of design and analysis methods.
What constitutes an underpowered study?
A study with a small sample size that may lead to undetected effects.
What is the relationship between sample size and variance in the context of power analysis?
Larger samples reduce variance and increase the power of the study.
What is the significance of effect sizes in research analysis?
Effect sizes measure the practical significance or magnitude of an effect, independent from sample size.
What does a power analysis aim to achieve in research design?
To ensure that studies are adequately powered, typically targeting 80% power.
What does the alternative hypothesis (H1) propose?
That there is some effect or difference.
What is the implication of having a p-value less than 0.05?
It suggests enough evidence to confidently reject the null hypothesis.
What are point estimates and how do they differ from interval estimates?
Point estimates are single-value estimates (e.g., mean), while interval estimates provide a range of possible values.
