Statistical Significance & Power
What does a p-value < .05 indicate in a research study?
There is less than a 5% probability the results occurred by chance → the finding is statistically significant.
When is an independent t-test used?
To compare the means of two different independent groups.
Define effect size.
A standardized measure of the strength or magnitude of a treatment effect.
What does the r-value represent?
The strength and direction of a linear relationship between two variables.
What does an odds ratio (OR) of 1 mean?
No difference in odds between groups.
Define α (alpha) in inferential statistics.
α(alpha) is the level of risk the researcher is willing to accept for making a Type I error (often set at .05).
When is a paired t-test used?
To compare the means of the same group at two time points (before & after an intervention).
Cohen’s d = 0.8 is considered what magnitude of effect?
Large effect.
Interpret r = 0.5 according to Cohen.
Moderate to strong positive correlation.
In what type of study design is an odds ratio most appropriate?
Cross-sectional or case-control studies (where the event has already occurred).
Explain Type I vs Type II errors.
Type I = reject a true null (false positive); Type II = fail to reject a false null (false negative).
Why would a researcher use ANOVA instead of a t-test?
When comparing means among three or more groups to reduce Type I error risk.
Interpret a 95% confidence interval of 0.88–3.22.
There’s a 95% chance the true population value lies within 0.88–3.22; a wide range = less precision.
What does R² represent in regression analysis?
The percentage of variance in the dependent variable explained by the predictor(s).
A relative risk (RR) of 3 means what?
The exposed group is three times more likely to develop the outcome than the non-exposed group.
What is statistical power and what is its desired value?
Power = probability of detecting a true effect (1 – β); a power of .80 is commonly desired.
What is the purpose of an ANCOVA?
To control for covariates (extraneous variables) that might influence the outcome.
How do effect size and p-value differ in interpretation?
p-value = whether an effect exists; effect size = how strong/important the effect is.
Define a beta (β) weight in multiple regression.
A standardized coefficient showing how many SDs the outcome changes per 1 SD change in the predictor.
How do risk ratios differ from odds ratios?
RR compares probabilities (over time); OR compares odds (after the event).
Name three ways to increase statistical power.
↑ sample size, ↑ effect size, ↑ α level (or reduce measurement error).
A study finds F = 15.6, p < .001 among three groups. What does this mean?
At least one group’s mean differs significantly from the others → reject the null hypothesis.
What are η² (eta squared) and ω² (omega squared) used for?
They measure effect size in ANOVA; η² = 0–.06 small, .06–.14 medium, >.14 large.
What is multicollinearity, and why is it a problem?
When predictors in a regression are highly inter-correlated; it makes β weights unstable and reduces model accuracy.
A hazard ratio (HR) = 0.48 for high physical activity (p < .001). Interpret this.
High activity reduces mortality risk by 52% (1 – 0.48 = 0.52); participants experience events slower over time.