A multiple regression model predicting hospital length of stay includes: age (β = 0.08, p = 0.045), severity score (β = 1.2, p < 0.001), and insurance type (β = -2.1, p = 0.067). The overall model: F(3,156) = 18.7, p < 0.001, R² = 0.26, adjusted R² = 0.25. Which statement about model interpretation is most accurate?
Answer: The model explains 26% of length of stay variance, with severity score being the strongest predictor
When interpreting multiple regression output, you need to distinguish between overall model performance and individual predictor significance. The key metrics here are the regression coefficients (β), their p-values, R², and the overall F-test.
Looking at the model performance, the significant F-test (p < 0.001) confirms the model as a whole is meaningful, and R² = 0.26 indicates it explains 26% of the variance in hospital length of stay. Among the predictors, severity score has the largest absolute coefficient (β = 1.2) and highest significance (p < 0.001), making it the strongest predictor. This reasoning confirms answer C is correct.
Answer A is wrong because overall model significance doesn't guarantee all individual predictors are significant. The F-test evaluates whether the model explains more variance than chance, but individual coefficients must be evaluated separately using their own p-values.
Answer B incorrectly labels insurance type as "marginally significant." With p = 0.067, it fails to reach the conventional α = 0.05 threshold and is technically non-significant, not marginal.
Answer D makes a premature recommendation to remove insurance type. While it's not statistically significant, the decision to remove predictors should consider clinical importance, effect size, and model goals—not just statistical significance. The minimal difference between R² (0.26) and adjusted R² (0.25) actually suggests the model isn't overly complex.
Study tip: In regression interpretation questions, always separate overall model performance from individual predictor effects, and remember that coefficient magnitude indicates practical importance while p-values indicate statistical significance.
A multiple regression analysis predicting weight loss (kg) includes exercise hours per week (β₁ = 1.8, p = 0.003) and dietary restriction score (β₂ = 0.4, p = 0.156). The R² = 0.32, adjusted R² = 0.28. What can be concluded about the dietary restriction variable?
Answer: Dietary restriction is not significantly associated with weight loss when controlling for exercise
When interpreting multiple regression results, you need to understand what each p-value tells you about individual predictors while controlling for other variables in the model.
The dietary restriction variable has β2=0.4 with p=0.156. Since this p-value exceeds the conventional significance threshold of 0.05, we cannot conclude that dietary restriction is significantly associated with weight loss when exercise hours are held constant. This is the key insight: in multiple regression, each coefficient's p-value tests whether that specific variable adds significant predictive value beyond what the other variables already provide.
Option A incorrectly conflates the overall model's explanatory power (R² = 0.32) with the significance of individual predictors. A model can have meaningful overall fit while containing non-significant individual variables. Option B oversimplifies by suggesting no relationship exists - the p-value only indicates we cannot detect a statistically significant relationship in this sample with these controls, not that no relationship exists at all. Option D misinterprets the adjusted R². The comparison between R² (0.32) and adjusted R² (0.28) reflects the penalty for including additional variables, but this alone doesn't determine whether to remove a variable - you'd need to compare models with and without the variable.
Remember this pattern: in multiple regression, each coefficient's p-value tests that variable's unique contribution while controlling for all other predictors in the model. Don't confuse overall model significance with individual predictor significance - they answer different questions.
Based on this regression output, what represents the most appropriate interpretation of the model's explanatory power and individual predictors?
Answer: The model explains 31% of variance after adjustment; age and comorbidity are significant predictors, with comorbidity showing the strongest standardized association
Adjusted R² (31%) is the appropriate measure of explained variance. Age and comorbidity are statistically significant (p < 0.05), surgery type is not. Comorbidity has the largest standardized coefficient (0.48). Choice A uses unadjusted R² and overstates surgery type significance. Choice B incorrectly includes non-significant surgery type in strength ranking. Choice D incorrectly suggests all predictors are meaningful despite surgery type's non-significance.
A correlation analysis between BMI and blood pressure yields r = 0.34, n = 150, p = 0.002, 95% CI for r = (0.18, 0.48). A colleague claims this proves that higher BMI causes higher blood pressure. What does the statistical output actually support?
Answer: The output shows a moderate positive association but cannot establish causal direction
When you encounter correlation analysis results, remember that correlation never establishes causation, regardless of statistical significance or effect size. This is a fundamental principle in biostatistics that researchers must always keep in mind.
The statistical output shows r = 0.34, indicating a moderate positive linear relationship between BMI and blood pressure. With p = 0.002 and a confidence interval of (0.18, 0.48) that excludes zero, you can confidently conclude this association is statistically significant and likely represents a real relationship in the population. However, correlation analysis only measures the strength and direction of linear association—it cannot determine which variable influences the other, or whether both are influenced by external factors.
Answer C correctly identifies that while the data demonstrates a moderate positive association, it cannot establish causal direction. The correlation could mean BMI affects blood pressure, blood pressure affects BMI, or both are influenced by confounding variables like genetics, diet, or lifestyle factors.
Answer A incorrectly conflates statistical significance with causation. A p-value only tells you the association is unlikely due to chance. Answer B misinterprets r² (coefficient of determination) as r—the actual explained variance is r² = (0.34)² = 11.6%, not 34%. Answer D incorrectly suggests that excluding zero in the confidence interval indicates reverse causation, when it simply confirms the association isn't due to random variation.
Remember: correlation coefficients measure association strength, never causation. To establish causality, you need experimental designs, temporal relationships, or sophisticated causal inference methods.
A paired t-test comparing pre- and post-treatment blood glucose levels in 25 patients yields: Mean difference = -15.2 mg/dL, SE = 4.8, t = -3.17, df = 24, p = 0.004, 95% CI = (-25.1, -5.3). If the study were repeated with 100 patients and the same effect size, what would happen to the standard error?
Answer: It would become approximately half as large due to the increased sample size
When you encounter questions about how sample size affects statistical measures, focus on the fundamental relationship between sample size and standard error. The standard error measures the precision of your sample estimate, and it has a predictable mathematical relationship with sample size.
The standard error formula includes ns in its structure, where s is the sample standard deviation and n is the sample size. This means standard error is inversely proportional to the square root of sample size. When sample size increases from 25 to 100 patients (a 4-fold increase), the denominator n increases from 25=5 to 100=10. This doubles the denominator, making the standard error approximately half as large.
Choice A incorrectly assumes effect size and standard error are directly related. While effect size remains constant, standard error still decreases with larger samples because you're measuring the same effect with greater precision.
Choice C falls into the common trap of thinking standard error decreases proportionally to sample size increase. Since standard error involves the square root of n, a 4-fold increase in sample size only halves (doesn't quarter) the standard error.
Choice D contradicts the fundamental principle that larger samples provide more precise estimates, not less precise ones.
Remember this key pattern: Standard error always decreases as sample size increases, following the square root relationship. Doubling sample size doesn't halve standard error—you need to quadruple sample size to halve standard error.
Given this survival analysis output, what is the most accurate interpretation of the statistical evidence?
Answer: The evidence suggests a potential protective effect, but the confidence interval includes 1.0, indicating insufficient evidence for statistical significance
The HR < 1 suggests a protective effect, but the CI crossing 1.0 confirms lack of statistical significance, consistent with p > 0.05. This interpretation acknowledges both the direction of effect and the uncertainty. Choice A overstates the evidence by calling it 'strong' when it's not statistically significant. Choice C incorrectly assumes the p-values should be identical (they test slightly different aspects). Choice D incorrectly dismisses any evidence of effect and makes an unsupported claim about CI width.
The Tukey post-hoc results show: Drug A vs Drug B: p = 0.041, Drug A vs Drug C: p = 0.002, Drug B vs Drug C: p = 0.167. Using α = 0.05, which statement correctly summarizes the pairwise comparisons?
Answer: Drug A differs significantly from both Drug B and Drug C, but Drugs B and C do not differ
When you encounter ANOVA followed by post-hoc tests, remember that a significant overall F-test only tells you that some groups differ—it doesn't specify which pairs are significantly different. That's why post-hoc tests like Tukey are essential for pairwise comparisons.
Looking at the Tukey results with α = 0.05: Drug A vs Drug B (p = 0.041) is significant since 0.041 < 0.05. Drug A vs Drug C (p = 0.002) is also significant since 0.002 < 0.05. However, Drug B vs Drug C (p = 0.167) is not significant since 0.167 > 0.05. This means Drug A differs from both other medications, but Drugs B and C don't significantly differ from each other.
Choice A incorrectly assumes that a significant overall ANOVA means all pairwise comparisons are significant—this is a common misconception. The F-test only indicates that at least one pair differs significantly.
Choice C is wrong because two comparisons (A vs B and A vs C) are significant, not just one. The Tukey test already adjusts for multiple comparisons, so you simply compare each p-value to your α level.
Choice D misinterprets which drug is driving the differences. While Drug C appears in two comparisons, Drug A is actually the one that differs significantly from the others—Drug C vs Drug B wasn't significant.
Study tip: In post-hoc analysis, examine each pairwise p-value independently against your α level. The drug that appears in multiple significant comparisons is typically the outlier driving the overall ANOVA result.
A repeated measures ANOVA comparing cholesterol levels at 4 time points (baseline, 1 month, 3 months, 6 months) shows: F(3,72) = 12.8, p < 0.001, η² = 0.35. Sphericity was violated (Mauchly's p = 0.032), so Greenhouse-Geisser correction was applied: F(2.1, 50.4) = 12.8, p < 0.001. What should be concluded?
Answer: Cholesterol levels change significantly over time, and the effect explains 35% of the variance
When you encounter repeated measures ANOVA with sphericity violations, the key is understanding that corrections like Greenhouse-Geisser adjust the degrees of freedom to provide valid results, rather than invalidating the analysis.
The results show a significant main effect of time both before and after correction. The original F(3,72) = 12.8, p < 0.001 becomes F(2.1, 50.4) = 12.8, p < 0.001 after Greenhouse-Geisser adjustment. Notice that the F-statistic remains the same (12.8) and the p-value stays highly significant (p < 0.001). The η² = 0.35 indicates that time explains 35% of the variance in cholesterol levels, representing a large effect size. This leads us to conclude that cholesterol levels change significantly over time with substantial practical importance.
Answer A is wrong because sphericity violations don't invalidate results when proper corrections are applied. The Greenhouse-Geisser correction specifically addresses this issue. Answer C misinterprets the correction—the p-value remains < 0.001, so significance is maintained, not lost. Answer D fundamentally misunderstands what the corrected degrees of freedom mean. The 2.1 doesn't indicate that only 2.1 time points differ; it's a mathematical adjustment to account for violated sphericity assumptions while testing differences across all four time points.
Study tip: Remember that sphericity corrections (Greenhouse-Geisser, Huynh-Feldt) fix the problem rather than ruin your analysis. If the corrected p-value remains significant, you can confidently interpret your results using the original effect size measures.
A logistic regression analysis reports an odds ratio of 2.34 (95% CI: 1.12, 4.89) for the association between smoking and lung disease. The baseline probability of lung disease in non-smokers is 8%. What does this output indicate about the absolute risk in smokers?
Answer: Smokers have approximately 16.9% probability of lung disease, representing an absolute risk increase of about 8.9 percentage points
With baseline probability 0.08, baseline odds = 0.08/0.92 = 0.087. Smoker odds = 0.087 × 2.34 = 0.204. Smoker probability = 0.204/1.204 = 0.169 = 16.9%. Absolute risk increase = 16.9% - 8% = 8.9 percentage points. Choice A uses incorrect calculation. Choice C is wrong because absolute risk can be calculated when baseline risk is known. Choice D confuses odds ratio with risk ratio.
A logistic regression predicting hospital readmission (1 = readmitted, 0 = not readmitted) produces the following for age: Coefficient = 0.045, SE = 0.018, Odds Ratio = 1.046, 95% CI for OR = (1.009, 1.084), p = 0.013. What is the correct interpretation of the odds ratio?
Answer: For each year increase in age, the odds of readmission are multiplied by 1.046
When interpreting logistic regression results, you need to understand what an odds ratio represents and how it functions as a multiplicative factor. The odds ratio tells you how the odds change when the predictor variable increases by one unit.
The coefficient of 0.045 represents the natural log of the odds ratio. When exponentiated, this gives us the odds ratio of 1.046, which means the odds are multiplied by this factor for each one-unit increase in age.
Answer C is correct because it accurately describes this multiplicative relationship. For every additional year of age, you multiply the current odds of readmission by 1.046. This is the fundamental interpretation of odds ratios in logistic regression.
Answer A confuses odds ratios with probability. An odds ratio of 1.046 does not mean a 4.6% increase in probability – probability changes depend on the baseline probability and follow a more complex relationship.
Answer B misinterprets the magnitude. An odds ratio of 1.046 represents a 4.6% increase in odds (1.046 - 1 = 0.046 = 4.6%), not a 46% increase. A 46% increase would correspond to an odds ratio of 1.46.
Answer D incorrectly treats this as a comparison between specific age groups. The odds ratio of 1.046 applies to each single-year increase in age, not to a comparison between 46-year-olds and newborns.
Remember: odds ratios are multiplicative factors that apply to each unit change in the predictor. Always distinguish between odds, probability, and relative comparisons when interpreting logistic regression output.
A Mann-Whitney U test comparing pain scores between two treatments yields: U = 89.5, n₁ = 15, n₂ = 18, p = 0.027, median₁ = 4.2, median₂ = 6.1. The normal approximation z-score is -2.21. What conclusion is most appropriate?
Answer: The pain score distributions differ significantly, with Treatment 1 tending toward lower scores
When you encounter a Mann-Whitney U test question, remember this test compares the distributions of two independent groups without assuming normality—it's about ranking data, not just central tendencies.
The significant p-value (0.027 < 0.05) tells us there's a statistically significant difference between the two treatment groups. The negative z-score (-2.21) combined with the medians (4.2 vs 6.1) indicates Treatment 1 consistently ranks lower than Treatment 2, meaning Treatment 1 tends toward lower pain scores. This supports answer D perfectly.
Let's examine why the other options miss the mark:
Answer A incorrectly focuses on "mean" pain scores. The Mann-Whitney U test doesn't compare means—it's a nonparametric test that compares distributions based on ranks, making no assumptions about means.
Answer B is technically correct that distributions differ significantly, but it's incomplete. It fails to specify the direction of the difference, which is crucial information provided by both the medians and the negative z-score.
Answer C misinterprets the p-value as a confidence level. A p-value of 0.027 doesn't mean "97.3% confidence"—it means there's a 2.7% chance of observing this difference if no true difference existed. Also, while we can infer Treatment 1 has lower scores, the Mann-Whitney test primarily compares entire distributions, not just medians.
Study tip: For Mann-Whitney questions, always remember you're comparing distributions and their tendencies, not specific parameters like means. The direction of the z-score combined with descriptive statistics tells you which group tends higher or lower.
A Cox proportional hazards model analyzing time to hospital readmission includes age as a covariate: β = 0.032, SE = 0.014, HR = 1.033, 95% CI = (1.005, 1.061), p = 0.021. What does the hazard ratio indicate about the effect of age?
Answer: Each year of age multiplies the baseline hazard of readmission by 1.033
When you encounter Cox proportional hazards models, focus on understanding what the hazard ratio represents: it's a multiplicative effect on the baseline hazard function, not an additive probability increase.
The hazard ratio of 1.033 means that for each one-year increase in age, a patient's hazard (instantaneous risk) of readmission is multiplied by 1.033. This is fundamentally different from adding 3.3% to a probability. The Cox model assumes that covariates have multiplicative effects on the baseline hazard function, so if the baseline hazard at time t is h0(t), then a patient one year older has hazard 1.033×h0(t).
Option A incorrectly interprets the hazard ratio as a probability increase. Hazard ratios don't directly translate to probability changes—that would require converting to risk differences. Option B misunderstands what "increases by 3.3%" means; the hazard doesn't increase by 3.3%, it increases by a factor of 1.033 (which is actually a 3.3% relative increase). Option C makes an error about the reference point—hazard ratios in regression represent the effect per unit change in the covariate, not a comparison to age zero.
Study tip: Remember that hazard ratios are always multiplicative factors. An HR > 1 means increased risk, HR < 1 means decreased risk, and the baseline hazard gets multiplied by this factor for each unit increase in the covariate. Don't confuse hazard ratios with probability differences or percentage point increases.
What conclusion is most appropriate given this ANOVA and post-hoc analysis output?
Answer: The significant ANOVA indicates group differences exist, but no specific pairwise differences achieve significance after Bonferroni correction
When you encounter ANOVA followed by post-hoc tests, you're dealing with the multiple comparisons problem. The omnibus ANOVA tests whether any groups differ, while post-hoc tests identify specific pairwise differences. However, multiple testing inflates Type I error risk, so corrections like Bonferroni are applied.
The Bonferroni correction divides your alpha level (typically 0.05) by the number of comparisons. With 6 pairwise comparisons here, the adjusted significance threshold becomes 0.05/6=0.0083. This means any p-value must be ≤0.0083 to achieve significance after correction.
Looking at the post-hoc results, all p-values (0.048, 0.072, 0.156, 0.234, 0.288, 0.432) exceed this adjusted threshold of 0.0083. Therefore, no specific pairwise differences reach significance after Bonferroni correction, even though the omnibus ANOVA was significant (p = 0.026).
Answer A correctly captures this scenario: the significant ANOVA indicates group differences exist somewhere, but the conservative Bonferroni correction prevents identification of specific pairs. Answer B is wrong because 0.048 > 0.0083, so Groups 1 and 2 don't significantly differ after correction. Answer C incorrectly suggests the ANOVA is invalid—this situation is actually common and doesn't indicate error. Answer D inappropriately treats the uncorrected p-value of 0.048 as significant and misinterprets "marginal significance."
Remember: when interpreting post-hoc tests, always compare p-values to the adjusted significance threshold, not the original 0.05. The omnibus test and post-hoc results can legitimately disagree due to statistical power differences.
A linear regression of systolic blood pressure (Y) on age (X) produces: Ŷ = 95.2 + 0.8X, R² = 0.41, SE of slope = 0.15, t = 5.33, p < 0.001, n = 85. What is the predicted systolic blood pressure for a 60-year-old person, and what does R² indicate?
Answer: 143.2 mmHg; age explains 41% of the variance in blood pressure in this sample
When you encounter linear regression questions, focus on two key tasks: making predictions using the regression equation and interpreting the coefficient of determination (R²).
To predict systolic blood pressure for a 60-year-old, substitute X = 60 into the equation: Ŷ = 95.2 + 0.8(60) = 95.2 + 48 = 143.2 mmHg. This straightforward calculation gives you the predicted value.
The R² = 0.41 tells you that age explains 41% of the variance in systolic blood pressure within this sample. Think of R² as the proportion of "spread" or variability in blood pressure that can be attributed to differences in age.
Answer A incorrectly interprets R² as applying to individuals rather than variance. R² doesn't tell you what percentage of people are "explained" by the model—it quantifies how much of the overall variability is accounted for.
Answer C confuses R² with correlation. While related, R² (0.41) represents explained variance, not the correlation coefficient itself. The correlation would be 0.41=0.64.
Answer D misinterprets R² as prediction accuracy. R² doesn't indicate that 41% of predictions are within some error range—it measures how well the model explains variability compared to simply using the mean.
Study tip: Remember that R² always represents "proportion of variance explained." When you see R² = 0.41, immediately think "age accounts for 41% of the variability in blood pressure." This interpretation applies universally across regression problems.
An independent samples t-test output shows: Group 1 (n = 25): mean = 78.4, SD = 12.2; Group 2 (n = 30): mean = 82.7, SD = 15.8; t = -1.15, df = 53, p = 0.255, 95% CI = (-11.9, 3.3). What does the 95% confidence interval suggest about the population means?
Answer: The true difference between population means is likely between -11.9 and 3.3 with 95% confidence
When interpreting confidence intervals from independent samples t-tests, you're looking at the plausible range of values for the true difference between population means. The CI of (-11.9, 3.3) represents the difference calculated as Group 1 mean minus Group 2 mean.
Answer B correctly states that we can be 95% confident the true difference between population means falls between -11.9 and 3.3 points. This means Group 1's population mean could be anywhere from 11.9 points lower to 3.3 points higher than Group 2's population mean.
Answer A misinterprets the interval by treating the bounds as separate, independent statements rather than endpoints of a single range for the difference. While the numerical values seem similar, this phrasing incorrectly suggests two separate possibilities rather than a continuous range.
Answer C commits a classic error: concluding that because the CI includes zero, the means are definitely equal. The CI including zero simply means we cannot rule out equality—it's one possible value among many in the range, not a definitive conclusion.
Answer D confuses confidence intervals about mean differences with prediction intervals about individual scores. This completely misapplies what the CI represents—it's about population parameters, not individual observations.
Study tip: Remember that confidence intervals for mean differences tell you the plausible range for how far apart the true population means could be. If the interval includes zero, you cannot conclude the groups differ significantly, but you also cannot conclude they're identical.
A clinical trial comparing two treatments reports: Treatment A mean = 12.4 (SE = 1.8), Treatment B mean = 15.7 (SE = 2.1), difference = -3.3 (SE = 2.8), p-value = 0.24. The research team concludes there is no significant difference between treatments. What additional information would be most critical for proper interpretation?
Answer: The 95% confidence interval for the difference to assess clinical significance and precision of the estimate beyond the p-value alone
While the p-value indicates no statistical significance, the confidence interval would show the range of plausible differences, helping assess whether clinically meaningful differences could still exist within that range. This addresses both precision and clinical vs. statistical significance. Choice B, while important for calculation verification, doesn't aid interpretation. Choice C focuses on technical verification rather than interpretation. Choice D addresses study design but doesn't help interpret the given statistical output.
A biomarker validation study reports diagnostic performance: Sensitivity = 87% (95% CI: 79-93%), Specificity = 72% (95% CI: 65-78%), PPV = 68% (95% CI: 61-75%), NPV = 89% (95% CI: 83-94%). The prevalence in the study population was 45%. What is the most important limitation when interpreting this output for clinical application?
Answer: The predictive values are specific to the 45% prevalence and will differ substantially in populations with different disease prevalence
When evaluating diagnostic test performance, you need to understand the crucial difference between sensitivity/specificity (which are intrinsic test properties) and predictive values (which depend heavily on disease prevalence in the population being tested).
Answer D is correct because predictive values are fundamentally tied to prevalence through Bayes' theorem. While sensitivity (87%) and specificity (72%) remain constant across populations, the PPV of 68% and NPV of 89% will change dramatically when this biomarker is applied to populations with different disease prevalence. For example, if used in a low-prevalence screening population (say 5% instead of 45%), the PPV would drop substantially, meaning most positive tests would be false positives. Conversely, in a higher-prevalence population, the PPV would increase.
Option A misinterprets confidence interval width—while wider intervals indicate more uncertainty, the 79-93% range for sensitivity is reasonably precise and doesn't represent a fatal flaw. Option B reflects a common misconception; PPV being lower than sensitivity doesn't indicate poor clinical utility—this relationship depends entirely on prevalence and specificity. Option C makes an absolute judgment about specificity without considering the clinical context; 72% specificity might be acceptable depending on the consequences of false positives and the intended use.
Key takeaway: Always remember that sensitivity and specificity are intrinsic test characteristics, while PPV and NPV are population-dependent. When evaluating diagnostic studies, ask yourself: "Will the prevalence in my target population match the study population?" This is critical for translating research findings into clinical practice.
A two-way ANOVA examines the effects of drug type (A vs B) and dose level (low vs high) on blood pressure reduction. Results show: Drug main effect F(1,76) = 8.4, p = 0.005; Dose main effect F(1,76) = 2.1, p = 0.151; Interaction F(1,76) = 6.8, p = 0.011. How should these results be interpreted?
Answer: Drug type has a significant effect, but the significant interaction indicates this effect depends on dose level
When interpreting two-way ANOVA results, you must evaluate main effects and interactions systematically, with special attention to significant interactions since they change how you interpret main effects.
Let's examine each statistical result: The drug main effect is significant (p = 0.005), indicating drug type matters. The dose main effect is non-significant (p = 0.151), suggesting dose level alone doesn't significantly impact blood pressure. However, the interaction effect is significant (p = 0.011), which is crucial for interpretation.
A significant interaction means the effect of one factor depends on the level of the other factor. Here, while drug type shows an overall main effect, this effect varies depending on the dose level. You cannot simply say "drug A is better than drug B" without specifying the dose, because the drug effectiveness might differ dramatically between low and high doses.
Answer A is incorrect because dose level alone is not significant (p = 0.151). Answer B misses the critical significant interaction effect, oversimplifying the findings. Answer D goes too far by claiming interactions "override" main effects entirely—significant main effects still provide valuable information, but must be interpreted within the context of the interaction.
Answer C correctly captures that drug type has a significant effect, but this effect is qualified by the significant interaction, meaning the drug's effectiveness depends on the dose level.
Study tip: When you see a significant interaction in ANOVA, always interpret main effects cautiously—the interaction tells you the story is more complex than main effects alone suggest.
A McNemar's test compares the effectiveness of two diagnostic tests on the same 120 patients. The results show: discordant pairs = 28, χ² = 6.12, df = 1, p = 0.013. Test A was positive in 15 cases where Test B was negative, while Test B was positive in 13 cases where Test A was negative. What conclusion is appropriate?
Answer: There is a significant difference in the diagnostic performance of the two tests
When you encounter McNemar's test questions, focus on what this test actually measures: whether two paired tests perform significantly differently on the same subjects, not which test is "better" or what type of performance differs.
The key evidence here is the significant p-value (0.013 < 0.05), which tells you there's a statistically significant difference between the two tests' performance. McNemar's test uses only the discordant pairs (cases where the tests disagree) to determine if one test systematically performs differently than the other. With χ2=6.12 and p=0.013, you can conclude the tests perform significantly differently.
Option A incorrectly assumes that Test A is "better" because it detected 2 more positive cases (15 vs 13). However, without knowing the true disease status, you can't determine which test is more accurate or sensitive. Those extra positives could be true positives or false positives.
Option C makes an unsupported claim about specificity. McNemar's test tells you the tests differ significantly, but it doesn't specify whether the difference is in sensitivity, specificity, or both. The discordant pairs alone don't reveal which aspect of performance differs.
Option D contradicts the statistical results. The p-value of 0.013 clearly indicates the difference IS statistically meaningful, making this option factually incorrect.
Option B correctly interprets the results: there's a significant difference in diagnostic performance without making assumptions about which test is superior or which performance metric differs.
Study tip: Remember that McNemar's test detects significant differences between paired tests, but it doesn't tell you which test is better or what aspect of performance differs.
A clinical trial uses a chi-square test to compare cure rates between a new drug (48/60 cured) and standard therapy (35/55 cured). The output shows: χ² = 2.89, df = 1, p = 0.089, OR = 1.85, 95% CI for OR = (0.91, 3.77). How should these results be interpreted?
Answer: The new drug shows promise but the difference is not statistically significant at α = 0.05
When interpreting clinical trial results, you need to consider both statistical significance and clinical meaningfulness together. Statistical significance tells you whether the observed difference is likely due to chance, while effect size and confidence intervals reveal the magnitude and precision of that difference.
The correct interpretation is B because the data shows a promising trend that falls short of statistical significance. The odds ratio of 1.85 indicates the new drug has 85% higher odds of cure compared to standard therapy - a clinically meaningful difference. However, with p = 0.089 > 0.05, this difference doesn't reach conventional statistical significance, meaning we cannot rule out chance as an explanation.
Choice A incorrectly conflates effect size with statistical significance. While OR = 1.85 does suggest higher cure rates, the p-value shows this difference isn't statistically significant. Choice C misinterprets the confidence interval. Though the 95% CI (0.91, 3.77) includes 1.0 (indicating potential for no difference), it doesn't include values below 1.0 that would suggest harm - the lower bound is 0.91. Choice D is overly pessimistic, incorrectly concluding "no effect" when the p-value simply indicates insufficient evidence for statistical significance.
Study tip: Remember that p > 0.05 doesn't prove "no difference" - it means "insufficient evidence for a difference." Look for answer choices that acknowledge promising trends while respecting statistical significance thresholds. The phrase "shows promise but not statistically significant" is often correct in borderline results like p = 0.089.
