Practice statistical language for research: 'statistically significant', p-value communication, 'we observe that', 'correlation does not imply causation', confidence intervals, and effect sizes.
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'The improvement was _____ significant (p < 0.05).' What does this phrase mean in a research paper?
'Statistically significant' means the observed result is unlikely to be due to random chance, given the chosen significance threshold (alpha). p < 0.05 means there is less than a 5% probability of seeing this result if the null hypothesis were true. Important: statistical significance does not mean practical significance — a tiny, unimportant difference can be statistically significant with a large enough sample.
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'We report a p-value of 0.003.' How should this be interpreted?
A p-value is the probability of observing data at least as extreme as the sample results, assuming the null hypothesis is true. p = 0.003 means this outcome would occur only 0.3% of the time by chance under H0 — strong evidence against the null. Common misreading: the p-value is NOT the probability that H0 is true, and NOT the probability the result will replicate.
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'We _____ that latency increases sharply above 1,000 concurrent connections.' Which verb is appropriate for reporting an empirical observation in a results section?
'We observe that' is the standard, epistemically careful phrase for reporting what was measured in an experiment. It does not claim causality or generalisability beyond the observed data. 'We prove' is too strong (proof belongs to mathematics). 'We discover' implies a novel finding not everyone uses. 'We observe' is neutral and precise.
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'Higher ice cream sales correlate with higher drowning rates. Therefore, ice cream causes drowning.' What fundamental principle of statistical reasoning does this violate?
'Correlation does not imply causation' is one of the most important phrases in research English. Both ice cream sales and drowning increase in hot weather — the confound is temperature. In research papers: 'We observe a positive correlation between X and Y (r = 0.72), though we caution that this does not establish a causal relationship.' To establish causation you need a controlled experiment, not just correlation.
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'The 95% _____ interval for the mean response time is [142 ms, 158 ms].' What does this interval communicate?
A 95% confidence interval means: if we repeated this study many times, 95% of the computed intervals would contain the true population parameter. It expresses estimation uncertainty. Narrower CI = more precise estimate (larger sample). Wider CI = more uncertainty (smaller sample). Correct language: 'the 95% CI [142, 158]' — not 'there is a 95% probability the true mean is in this interval' (a Bayesian interpretation).