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27 Cards in this Set
- Front
- Back
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How reliable are the results? |
Answer via setting confidence limits bounds to our estimates of population parameters use standard errors |
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How probable that the results are due to chance alone? |
answer by evaluating differences between observed and expected results |
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Notes on stats |
as sample size increases, range of sample means calculated from the sample decreases, and precision of the estimate increases |
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Standard error |
the standard deviation of the estimate's sampling distribution is its standard error every estimate of any stat has a sampling distribution with a standard error measure of reliability (precision) of the estimate standard error of the mean is easy to calc and should always be reported with the mean SE of mean= standard deviation over the square root of the number of observations as sample size increases, se of estimated mean decreases |
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Note on sample means |
Sample means based on large samples should be close to the parametric mean and will not vary as much as will means based on small samples |
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confidence interval |
range of values surrounding the sample estimate that is likely to contain the population parameter (most plausible range for pop mean; beyond range less plausible) Use SE of mean to calc confidence interval |
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Correct ways to state confidence intervals |
We are 95% confident that the true mean lies between bla and bla units. There is a 95% probability that our confidence interval covers the true mean. As ss increases, it narrows the confidence interval and increases the precision because se is decreasing |
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2 se rule of thumb |
rough approx of 95% confidence interval for pop mean mean +/- 2 se of mean |
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To reduce width of confidence interval |
decrease measurement error use better controls in lab but can't change natural populations sd in nature for small samples use t-table distribution values instead of normal distribution values |
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estimation |
putting reasonable bounds on value of parameter |
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hypothesis testing |
determining whether parameter differs from some null expectation biggest use for stats in biology |
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null hypo |
stat hypo being tested no real differences |
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alt hypo |
sometimes can be specific but usually not just opposite of null |
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Reject null |
if data differs so much from expectations that it would be very unlikely to get such data if null were true |
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test stat |
calculated to evaluate whether data agrees with the null expectation increase in deviations increase test stat number calc to represent the match between the data and null hypo, which can be compared to a general distribution to infer probability |
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Null distribution |
sampling distribution of the outcomes expected for a test stat if null were true Theoretical distributions like normal, chi squared, t ,etc. |
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p-value |
probability that any difference is merely due to chance probability of getting data that differs as much from the expected results simply by chance |
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significance level a |
probability chosen as the criterion for rejecting the null typically a=0.05 |
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reject null |
saying sample is significantly different from expected at P is lesser than or equal to alpha if P is lesser than or equal to 0.05 we reject null (if p is greater than 0.05) not significant and fail to reject might be because null is true or null is false but there wasn't enough power to show it confidence intervals for estimates are useful for NS situations large confidence interval suggests power was low small confidence interval suggests truly not much difference |
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Reporting results |
always include test-statistic value, sample size, P-value also good to report confidence intervals or standard errors for parameters |
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How P-values are determined |
Simulation, parametric tests, re-sampling |
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Type 1 error |
rejecting a true null hypo a= acceptable prob of this mistake significance level set arbitrarily by convention |
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Type 2 error |
Failing to reject a false null. B= prob of this mistake rarely able to estimate decreasing a makes it harder to ever reject null as decrease a, b increases |
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Power of test |
sensitivity of test 1-B (probability of rejecting null when false) want as large as possible for given test (B as small as possible) |
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Increase power |
increase sample size, use different statistical procedure, increasing effect size, decreasing variance in population (error variance) intended a may not be actual a, for some tests actual a may be greater than intended a (liberal test, rejecting null and saying things are sig. diff. too often) actual a may be less than intended a (conservative test, accepting null too often) |
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Two-tailed |
alternative hypo can be on either side of null value most tests are two tailed deviation in either direction would reject null a is divided into a/2 on one side and a/2 on the other |
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One-tailed |
alternative hypo value on just one side of null value only rejected if data depart from it in direction stated by H alt more powerful but often unfair must have a very good biological reason to do this all of a comes from one tail only used when other tail is nonsensical |
