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Cloze Statistics for the life sciences::Lecture 9 From a sample to a claim: standard error, confidence intervals and p-values Population mean: the true average of the whole population is written with the Greek letter {{c1::mu}}, a parameter. The population is everybody the question is about. Its true average is a parameter. Lecture 9 @ 00:01:35, slide 2 "That group, everybody we care about, is the population, and the true average for that whole population gets a Greek letter, mu." Statistics-for-the-life-sciences::Lecture-9 population-sample-and-the-sampling-distribution
Basic Statistics for the life sciences::Lecture 9 From a sample to a claim: standard error, confidence intervals and p-values Sampling distribution of the mean: how is it built? Histogram of sample means from thousands of repeated surveys
Each survey uses a fresh sample. The lecturer called it the most important idea in the course. Lecture 9 @ 00:04:45, slide 3 "It is the sampling distribution of the mean, and it is the most important idea in this course." Statistics-for-the-life-sciences::Lecture-9 population-sample-and-the-sampling-distribution
Basic Statistics for the life sciences::Lecture 9 From a sample to a claim: standard error, confidence intervals and p-values Standard deviation: what does a standard deviation of 1.6 hours describe in the student survey? How much individual students differ from each other
It describes spread between individuals, not the precision of the sample mean. Lecture 9 @ 00:07:36, slide 4 "The standard deviation, one point six hours, tells you how much individual students differ from each other." Statistics-for-the-life-sciences::Lecture-9 standard-error-and-95-confidence-intervals
Basic Statistics for the life sciences::Lecture 9 From a sample to a claim: standard error, confidence intervals and p-values Standard error: what does a standard error of 0.2 hours describe? How much the sample mean varies between surveys
Confusing it with the standard deviation is the most common exam mistake. Lecture 9 @ 00:07:44, slide 4 "The standard error, zero point two hours, tells you how much the sample mean would differ from survey to survey." Statistics-for-the-life-sciences::Lecture-9 standard-error-and-95-confidence-intervals
Cloze Statistics for the life sciences::Lecture 9 From a sample to a claim: standard error, confidence intervals and p-values 95% confidence interval: sample mean plus or minus {{c1::1.96}} times the standard error. Lecture 9 @ 00:09:54, slide 5 "the sample mean, plus or minus one point nine six times the standard error." Statistics-for-the-life-sciences::Lecture-9 standard-error-and-95-confidence-intervals
Cloze Statistics for the life sciences::Lecture 9 From a sample to a claim: standard error, confidence intervals and p-values Hypothesis test: a sample 3.5 standard errors from the claimed value, in either direction, has p of about {{c1::0.0005}}. The p-value asks how often, if the null were true, a sample would land this far away or further. Lecture 9 @ 00:18:12, slide 8 "If the null were true, how often would a sample land three and a half standard errors away or further, in either direction?" Statistics-for-the-life-sciences::Lecture-9 small-sample-t-and-hypothesis-testing
Basic Statistics for the life sciences::Lecture 9 From a sample to a claim: standard error, confidence intervals and p-values Confidence interval: a 95% interval is the set of which values, in hypothesis-testing terms? Those a 5% level test would not reject
In the example, 7.5 lay outside the interval and was rejected; 7 lay inside and was not. Lecture 9 @ 00:20:11, slide 8 "The ninety-five percent confidence interval is exactly the set of values that a test at the five percent level would not reject." Statistics-for-the-life-sciences::Lecture-9 small-sample-t-and-hypothesis-testing
Cloze Statistics for the life sciences::Lecture 9 From a sample to a claim: standard error, confidence intervals and p-values p-value: the probability of data at least as {{c1::extreme}} as observed, assuming the null hypothesis is true. Lecture 9 @ 00:20:50, slide 9 "The p-value is the probability of getting data at least as extreme as yours, if the null hypothesis is true." Statistics-for-the-life-sciences::Lecture-9 misreading-p-values-error-types-multiple-tests
Basic Statistics for the life sciences::Lecture 9 From a sample to a claim: standard error, confidence intervals and p-values Bonferroni correction: how is the per-test threshold found from alpha? Divide alpha by the number of tests
For 20 tests, each must beat 0.05/20 = 0.0025. Strict but honest. Lecture 9 @ 00:25:49, slide 10 "You divide alpha by the number of tests. Twenty tests, zero point zero five over twenty" Statistics-for-the-life-sciences::Lecture-9 misreading-p-values-error-types-multiple-tests