Statistical Interpretation - Eppp Knowledge

Which change generally increases power: increasing sample size $n$ or decreasing $n$ ?

Increasing $n$ increases power. Larger samples reduce standard error, improving the precision and likelihood of detecting true effects.
What is the definition of statistical power in null hypothesis significance testing?

The probability of rejecting $H_0$ when $H_0$ is false. Power reflects a test's sensitivity to detect true effects by correctly rejecting the false null hypothesis.
What is the definition of a Type I error ( $\alpha$ ) in hypothesis testing?

Rejecting a true $H_0$ (false positive). Type I error occurs when the null hypothesis is wrongly rejected, representing a false positive result controlled by $\alpha$ .
What is the definition of $r^2$ in correlational analysis?

The proportion of variance in $Y$ explained by $X$ . $r^2$ quantifies the shared variance between variables, indicating explanatory power in regression or correlation.
What is Cohen's $d$ for two independent groups in terms of pooled SD?

$d = \frac{M_1 - M_2}{SD_{pooled}}$ . Cohen's $d$ standardizes the difference between means by dividing by the pooled standard deviation for comparability.
If $p = 0.03$ and $\alpha = 0.05$ , what is the statistical decision about $H_0$ ?

Reject $H_0$ . When the $p$ -value falls below the alpha threshold, evidence suffices to reject the null hypothesis.
What is a minimal clinically important difference (MCID)?

The smallest change in an outcome that patients perceive as beneficial. MCID defines the threshold for patient-noticeable improvement, bridging statistical and practical relevance.
Which design generally has higher power, all else equal: within-subjects or between-subjects?

Within-subjects designs generally have higher power. Within-subjects designs control for individual variability, reducing error variance and boosting statistical power.
What are Cohen's conventional benchmarks for correlation $r$ (small, medium, large)?

Small $= 0.10$ , medium $= 0.30$ , large $= 0.50$ . Cohen's benchmarks classify correlation strengths to evaluate the practical significance of linear relationships.
What is the formula for power in terms of Type II error probability ( $\beta$ )?

Power $= 1 - \beta$ . This formula derives power by subtracting the Type II error rate from 1, yielding the correct detection probability.
What does a $p$ -value represent under the null hypothesis $H_0$ ?

The probability of results at least as extreme as observed, assuming $H_0$ . The $p$ -value assesses how compatible the data are with the null, informing decisions on hypothesis rejection.
If a $95\%$ CI for an odds ratio includes $1$ , what is the conclusion at $\alpha = 0.05$ ?

Not statistically significant at $\alpha = 0.05$ . A 95% CI encompassing 1 suggests no significant difference in odds, failing to reject the null at $\alpha=0.05$ .
What are Cohen's conventional benchmarks for $d$ (small, medium, large)?

Small $= 0.20$ , medium $= 0.50$ , large $= 0.80$ . Cohen's guidelines categorize effect magnitudes to aid interpretation of practical importance in group differences.
Compute $r^2$ when $r = 0.40$ .

$r^2 = 0.16$ . Squaring the correlation coefficient yields the proportion of explained variance between variables.
What are Cohen's conventional benchmarks for $\eta^2$ (small, medium, large)?

Small $= 0.01$ , medium $= 0.06$ , large $= 0.14$ . These values categorize the proportion of variance explained in ANOVA, guiding effect magnitude interpretation.
If a $95\%$ CI for a mean difference includes $0$ , what is the significance at $\alpha = 0.05$ ?

Not statistically significant at $\alpha = 0.05$ . Inclusion of zero in the 95% CI implies the null hypothesis cannot be rejected at the 0.05 level.
Which change generally increases power: lower measurement error or higher measurement error?

Lower measurement error increases power. Reducing error minimizes variability in data, enhancing the signal-to-noise ratio and test sensitivity.
Which change generally increases power: increasing $\alpha$ or decreasing $\alpha$ ?

Increasing $\alpha$ increases power. Raising $\alpha$ lowers the threshold for rejection, thereby enhancing the test's ability to detect true effects.
Which option best indicates a precise effect estimate: wider CI or narrower CI?

A narrower confidence interval indicates more precision. Narrower intervals reflect lower uncertainty and higher reliability in the parameter estimate from the sample.
Which scenario is most plausible: very large $n$ with tiny effect yields significant $p$ , or tiny $n$ with tiny effect yields significant $p$ ?

Very large $n$ with a tiny effect can yield a significant $p$ -value. Large samples amplify test sensitivity, enabling detection of minimal effects despite their trivial magnitude.
Identify the key distinction between statistical significance and clinical significance.

Statistical: unlikely under $H_0$ ; clinical: meaningful real-world benefit. Statistical significance evaluates improbability under the null, whereas clinical significance assesses real-world impact.
Which change generally increases power: larger true effect size or smaller true effect size?

A larger true effect size increases power. Greater effect sizes increase the separation from the null, making true effects easier to detect statistically.
What is the definition of a Type II error ( $\beta$ ) in hypothesis testing?

Failing to reject a false $H_0$ (false negative). Type II error happens when a false null hypothesis is not rejected, missing a true effect and denoted by $\beta$ .
What is the definition of an effect size in psychological research?

A standardized index of the magnitude of a relationship or difference. Effect size quantifies the strength of an association or difference in standardized units, independent of sample size.
If $\beta = 0.20$ , what is statistical power?

Power $= 0.80$ . Power is calculated as 1 minus the Type II error rate, indicating the probability of detecting true effects.

Study these flashcards