USMLE Step 1 Quiz
Practice Statistical Tests in USMLE Step 1 with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.
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Researchers investigate the association between daily saturated fat intake (in grams) and serum LDL cholesterol levels (in mg/dL). After analyzing the data from their study population, they calculate a Pearson correlation coefficient (r) of 0.70.
Based on this result, what percentage of the variability in serum LDL cholesterol levels can be explained by the variability in daily saturated fat intake?
This quiz focuses on Statistical Tests, giving you a quick way to practice the rules, question types, and explanations that matter most for USMLE Step 1.
Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.
Researchers investigate the association between daily saturated fat intake (in grams) and serum LDL cholesterol levels (in mg/dL). After analyzing the data from their study population, they calculate a Pearson correlation coefficient (r) of 0.70.
Based on this result, what percentage of the variability in serum LDL cholesterol levels can be explained by the variability in daily saturated fat intake?
Explanation: The coefficient of determination, or r-squared (r²), represents the proportion of the variance in the dependent variable that is predictable from the independent variable. To find this value, the correlation coefficient (r) is squared. In this case, r = 0.70, so r² = (0.70)² = 0.49. This means that 49% of the variability in serum LDL cholesterol levels can be explained by the variability in daily saturated fat intake in this study population.
A large observational study in a seaside town finds a strong positive correlation (r = +0.85) between monthly ice cream sales and the number of drowning incidents.
Based on this information, which of the following is the most appropriate conclusion?
Explanation: Correlation does not imply causation. A strong correlation between two variables does not mean that one causes the other. In this classic example, a third factor, or confounding variable (e.g., warm weather), is likely responsible for the increase in both ice cream sales and swimming activities, which in turn leads to more drowning incidents. This is a much more plausible explanation than a direct causal link.
A study is conducted to assess the relationship between body mass index (BMI) and fasting plasma glucose in a group of 500 non-diabetic adults. The analysis yields a Pearson correlation coefficient (r) of +0.60.
Which of the following is the best interpretation of this correlation coefficient?
Explanation: The Pearson correlation coefficient (r) measures the strength and direction of a linear relationship between two continuous variables. A positive value (r = +0.60) indicates a positive association, meaning that as one variable (BMI) increases, the other variable (fasting glucose) tends to increase. The slope of the relationship is determined by regression analysis, not the correlation coefficient itself. The proportion of variance explained is r-squared (r²), which would be 0.36 or 36% in this case. Correlation does not establish causation.
A new lifestyle intervention program aims to reduce systolic blood pressure (SBP) in patients with prehypertension. Researchers measure the SBP of 40 participants at the beginning of the program and again after 12 weeks of participation. They want to assess if the intervention was effective.
Which statistical test is most appropriate for comparing the mean SBP before and after the intervention in this group of participants?
Explanation: A paired t-test is the most appropriate test in this scenario because the measurements are taken from the same group of individuals at two different time points (before and after). This means the data points are paired or dependent. An independent samples t-test would be used if comparing two different groups of people. A chi-square test is for categorical data, and linear regression is for prediction.
A pharmacologist is studying the effect of a new analgesic. A total of 120 subjects with moderate pain are randomly assigned to one of four groups: placebo, 10 mg of the new drug, 20 mg of the new drug, or a standard dose of ibuprofen. The primary outcome is the self-reported pain score on a continuous scale 2 hours after administration.
Which statistical test should be used to determine if there is a significant difference in mean pain scores among the four treatment groups?
Explanation: Analysis of variance (ANOVA) is the appropriate statistical test for comparing the means of a continuous variable across three or more independent groups. Using multiple t-tests to compare each pair of groups would inflate the probability of making a Type I error (falsely concluding there is a difference). ANOVA analyzes the variance between groups relative to the variance within groups to test the null hypothesis that all group means are equal.
A study is conducted to examine the relationship between a specific genetic polymorphism (Allele A present vs. Allele A absent) and the risk of developing Crohn's disease (diagnosed vs. not diagnosed). Data are collected from a large cohort of individuals.
Which statistical test is most suitable for determining if there is a significant association between the presence of Allele A and the diagnosis of Crohn's disease?
Explanation: The Chi-square test is used to assess for an association between two categorical variables. In this scenario, both the genetic polymorphism (present/absent) and the disease status (diagnosed/not diagnosed) are categorical. The test compares the observed frequencies in each category to the frequencies that would be expected if there were no association between the variables.
An investigator wishes to compare the mean weight loss between a diet-only group and a diet-plus-exercise group. Each group has only 12 participants. The distribution of weight loss in the diet-plus-exercise group is noted to be significantly skewed, not following a normal distribution.
The use of an independent samples t-test in this situation may be invalid because which of its key assumptions has been violated?
Explanation: The t-test is a parametric test, which means it relies on certain assumptions about the data. A key assumption is that the data are sampled from a population with a normal distribution. While the t-test is robust to minor violations, especially with larger sample sizes, significant skewness in a small sample (n=12) makes its results unreliable. The assumption of independence is met, and the outcome is continuous. While equal variances (homoscedasticity) is an assumption, the violation of normality is the more critical issue here prompting the use of a non-parametric test.
A study evaluates the effect of a mindfulness-based stress reduction program on telomere length in a small group of 15 healthcare workers. Telomere length is measured from leukocytes before the 8-week program and again at its conclusion. The distribution of the differences in telomere length (post-pre) is found to be significantly skewed.
Which statistical test is the most appropriate to determine if there was a significant change in telomere length?
Explanation: This study uses a pre-post design with the same subjects, so the data are paired. The paired t-test is the standard parametric test for this design, but it assumes that the differences between paired measurements are normally distributed. Since this assumption is violated (the differences are skewed), the appropriate nonparametric alternative is the Wilcoxon signed-rank test.
An emergency department physician is comparing the time to pain relief for three different non-opioid analgesics given for acute renal colic. Twenty patients are randomized to each of the three drug groups. The outcome, time to relief, is highly skewed as some patients take a very long time to respond. The physician wishes to see if there is any difference among the three drugs.
What is the most appropriate statistical test to use to compare the central tendency of time to pain relief among the three groups?
Explanation: The Kruskal-Wallis test is the nonparametric alternative to one-way ANOVA. It is used to determine if there are statistically significant differences between two or more independent groups on a continuous or ordinal dependent variable when the assumptions of ANOVA (like normality) are not met. Since the data are highly skewed and there are three independent groups, the Kruskal-Wallis test is the most suitable choice.
An endocrinologist wants to understand the factors affecting bone mineral density (BMD) in postmenopausal women. She plans to analyze the relationship between BMD (a continuous variable) and several factors simultaneously: patient age, daily calcium intake, and vitamin D levels.
Which statistical method would allow the researcher to evaluate the independent contribution of each factor to bone mineral density while controlling for the effects of the others?
Explanation: Multiple linear regression is the appropriate technique when assessing the relationship between a single continuous dependent variable (BMD) and two or more independent variables (age, calcium intake, vitamin D levels). This method allows for the assessment of each variable's independent effect while statistically controlling for the others, which helps to mitigate confounding.
In a hospital, a rare, aggressive bacterial infection is identified in 8 patients. An investigation is launched to determine if the infection is associated with a specific type of intravenous catheter used in the ICU. Of the 8 infected patients, 6 had used the catheter. In a control group of 20 uninfected ICU patients from the same period, only 2 had used the catheter.
Due to the small number of cases, which statistical test would be most appropriate for analyzing the association between catheter use and infection?
Explanation: Fisher's exact test is used to analyze categorical data in a 2x2 table, particularly when the sample size is small and the expected frequencies in any cell are less than 5. In such cases, the Chi-square test, which is an approximation, becomes inaccurate. Given the very small number of cases (8), Fisher's exact test provides a more accurate p-value for the association between the two categorical variables (catheter use and infection status).
A research team wants to develop a model to predict the probability of a patient having a myocardial infarction (MI) within the next 10 years. The outcome is binary (MI or no MI). The potential predictor variables include age, smoking status (yes/no), presence of hypertension (yes/no), and serum cholesterol level.
Which statistical method is most appropriate for building this predictive model?
Explanation: Logistic regression is the appropriate statistical technique when the dependent (outcome) variable is dichotomous or binary, such as the occurrence of an MI (yes/no). It allows for the modeling of how multiple independent variables (both continuous and categorical) predict the probability of the outcome. Multiple linear regression is used for continuous outcomes. A Cox model would be used for time-to-event data, which is more specific than what is described.
Researchers are investigating whether there is an association between the type of infant feeding (exclusively breastfed, mixed-fed, exclusively formula-fed) and the incidence of otitis media in the first year of life (yes/no).
Which statistical test is most appropriate to analyze the relationship between these two variables?
Explanation: This analysis involves two categorical variables: infant feeding type (with three categories) and incidence of otitis media (with two categories). The Chi-square test is the appropriate statistical method to determine if there is a significant association between two categorical variables by comparing observed frequencies to expected frequencies.
A randomized controlled trial is conducted to evaluate a new medication designed to reduce intraocular pressure (IOP) in patients with glaucoma. Sixty patients are randomly assigned to receive either the new medication or a placebo eye drop. After one month, the mean IOP is measured in each group. The data are approximately normally distributed.
Which statistical test is most appropriate to determine if there is a significant difference in the mean IOP between the medication and placebo groups?
Explanation: An independent samples t-test (or two-sample t-test) is the correct statistical method for comparing the means of a continuous outcome variable (IOP) between two independent, unrelated groups (medication vs. placebo). A paired t-test is used for related samples (e.g., before and after treatment in the same group). ANOVA is used for comparing means of three or more groups. Pearson correlation assesses the association between two continuous variables.
A nephrologist wants to create a model to predict a patient's glomerular filtration rate (GFR) based on their serum creatinine level. Data on both continuous variables are collected from a large patient cohort.
Which of the following statistical methods is most appropriate for developing an equation to estimate GFR from serum creatinine?
Explanation: Simple linear regression is used to model the relationship between two continuous variables and to create a predictive equation. The goal is to predict the value of a dependent variable (GFR) based on the value of an independent variable (serum creatinine). The other options are incorrect: a t-test compares means between two groups, ANOVA compares means among three or more groups, and a chi-square test assesses the association between categorical variables.
A cross-sectional study of 500 adults examines the relationship between weekly hours of vigorous exercise and resting heart rate. The analysis produces a Pearson correlation coefficient of r = -0.45 with a p-value of < 0.001.
Which of the following is the most accurate conclusion based on these results?
Explanation: A p-value of < 0.001 indicates that the observed result is highly statistically significant, meaning it is unlikely to have occurred by random chance. The negative correlation coefficient (r = -0.45) indicates an inverse relationship: as weekly hours of exercise increase, resting heart rate tends to decrease. While the association is strong, this observational study cannot prove causation. The coefficient of determination (r²) is (-0.45)² = 0.2025, meaning about 20% of the variability is explained, not 45%.
A study aims to determine if mean C-reactive protein (CRP) levels, a marker of inflammation, differ between patients with active rheumatoid arthritis (RA) and healthy controls. Blood samples are drawn from 50 patients with active RA and 50 healthy individuals. The CRP levels in both groups are found to be approximately normally distributed.
Which statistical test is the most appropriate to compare the mean CRP levels between the two groups?
Explanation: This study compares the means of a continuous, normally distributed variable (CRP levels) between two distinct, unrelated groups (RA patients and healthy controls). Therefore, the independent samples t-test is the most appropriate statistical method. A paired t-test is for related samples, a chi-square test is for categorical data, and Pearson correlation assesses the relationship between two continuous variables.
An epidemiologist is conducting a study on a new viral illness. They want to determine if there is a relationship between the severity of symptoms (rated as mild, moderate, or severe) and the patient's age (in years). The symptom severity is considered an ordinal variable, and age is continuous but its relationship with severity may not be linear.
Which of the following is the most appropriate statistical test to measure the strength of association between these two variables?
Explanation: Spearman rank correlation is a non-parametric test used to measure the strength and direction of the monotonic relationship between two variables. It is ideal when at least one of the variables is ordinal (like symptom severity) or when the relationship between two continuous variables is not linear. Pearson correlation requires both variables to be continuous and assumes a linear relationship.
A pilot study compares a new anxiolytic drug to a placebo in two groups of 15 patients each. The outcome is measured using the Hamilton Anxiety Rating Scale, which produces scores that are not normally distributed. The researchers want to determine if the median anxiety score differs between the two groups.
Given the non-normal distribution of the data, which of the following is the most appropriate statistical test?
Explanation: The Mann-Whitney U test is the nonparametric alternative to the independent samples t-test. It is used to compare two independent groups when the dependent variable is ordinal or when it is continuous but not normally distributed. Since the anxiety scores are not normally distributed and the groups (drug vs. placebo) are independent, the Mann-Whitney U test is the most appropriate choice. The Kruskal-Wallis test is used for three or more groups.
A clinical trial compares a new antiplatelet agent to aspirin for the prevention of stroke. The primary endpoint is the occurrence of stroke. The null hypothesis (H₀) is that there is no difference in the proportion of patients having a stroke between the two groups. The study results yield a p-value of 0.04.
Which of the following is the most accurate interpretation of this p-value?
Explanation: The p-value is the probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct. A p-value of 0.04 means that if there were truly no difference between the drugs (the null hypothesis), there would only be a 4% chance of seeing the observed difference (or a larger one) just by random variation. Since this probability is low (typically < 5%), we reject the null hypothesis.