Significance, errors & choosing tests flashcards
15 high-yield MRCP Part 1 cards from the Intellect Medicos Basic sciences & statistics course. Try to answer each question before you open it — then study them properly with spaced repetition, which brings each card back just before you would forget it.
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What is a type I error, and what symbol denotes its probability?
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Rejecting the null hypothesis when it is true (a false positive); its probability is alpha (α).
Why? Alpha is the significance level, usually set at 0.05.
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What is a type II error, and what symbol denotes its probability?
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Failing to reject a false null hypothesis - missing a real difference (a false negative); its probability is beta (β).
Why? Type II errors are most likely in small, underpowered studies.
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How is the power of a study defined, and what is the main way to increase it?
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Power = 1 − β: the probability of correctly rejecting a false null hypothesis. Increase it mainly by increasing the sample size.
Why? A larger sample reduces random error, making a real difference easier to detect. Studies are usually designed for at least 80% power.
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A trial reports p = 0.03. What does this mean?
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If the null hypothesis were true, there would be a 3% probability of getting a result at least this extreme by chance.
Why? p < 0.05 is conventionally called statistically significant, so the null hypothesis is rejected.
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A study measures systolic BP in 100 patients: mean 120 mmHg, standard deviation 10 mmHg. Calculate the standard error of the mean and the 95% confidence interval.
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SEM = SD/√n = 10/√100 = 1 mmHg. 95% CI = mean ± 1.96 × SEM = 118.04 to 121.96 mmHg.
Why? SEM shrinks as the sample size grows, so larger studies give narrower confidence intervals.
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Which test compares the means of two independent groups of normally distributed data?
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Unpaired (independent samples) t-test.
Why? Parametric tests suit normally distributed continuous data and compare means.
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Which test compares two independent groups when the data are skewed or ordinal?
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Mann-Whitney U test.
Why? It is the non-parametric equivalent of the unpaired t-test and compares ranks rather than means.
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Which test compares proportions between groups of categorical data, and which is used when the sample is small?
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Chi-squared test; Fisher's exact test for small samples.
Why? Categorical outcomes (e.g. alive/dead by treatment group) are compared as counts or proportions, not means.
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In a positively (right-) skewed distribution, how are the mean, median and mode ordered?
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Mean > median > mode.
Why? The long tail of high values pulls the mean upwards. The median resists outliers, so skewed data are summarised with median and interquartile range.
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A doctor sees this many patients over 7 days: 5, 7, 8, 5, 10, 7, 6. Calculate the mean, median, mode and range.
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Mean = 48/7 ≈ 6.9; median = 7; modes = 5 and 7 (bimodal); range = 10 − 5 = 5.
Why? Order the data first (5, 5, 6, 7, 7, 8, 10): the median is the middle (4th) value.
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In a normal distribution, roughly what percentage of values lie within 1 SD of the mean, and within 1.96 SD?
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About 68% within ±1 SD; 95% within ±1.96 SD (about 99.7% within ±3 SD).
Why? This is why a 95% confidence interval is the estimate ± 1.96 standard errors.
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Blood pressure is measured in 30 patients before and after starting a new drug. The differences are normally distributed. Which statistical test should be used?
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Paired t-test.
Why? The same patients are measured twice, so the before and after values are linked (paired), not independent.
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Which test compares the means of three or more independent groups of normally distributed data?
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One-way ANOVA (analysis of variance).
Why? Repeated t-tests between pairs would inflate the type I error rate.
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What is the range of Pearson's correlation coefficient (r), and which coefficient replaces it for skewed or ordinal data?
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r runs from −1 (perfect negative) through 0 (no linear relationship) to +1 (perfect positive). Spearman's rank coefficient (rs) is used for non-parametric data.
Why? Correlation measures how closely two variables move together; regression (Y = a + bX) predicts one from the other.
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A pain score from 0 to 10 is recorded. What type of data is this, and which family of tests suits it?
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Ordinal data; non-parametric tests (e.g. Mann–Whitney U for two independent groups).
Why? Ordinal data are ranked, but the gaps between points are not necessarily equal, so means and t-tests are not appropriate.