Standard deviation
=> graphs can have the same mean but different standard deviations (sd)
=> how much the data varies
Standard error
=> sd: how well the mean represents the sample data
standard error: “standard deviation of sample means”
Measures how representative a sample is likely to be of the population
Large standard error => lot of variability between the means of different samples (sample may not be representative of population)
Confidence intervals
Different approach to assessing the accuracy of the sample mean
Basic idea is to construct a range of values within which we think the population value falls
95% or 99%
If we collect 100 samples, calculate the mean and then calculate a confidence interval for the mean, for 95 of these samples, the confidence intervals we constructed would contain the true value of the mean in the population.
X (+/-) (1.96 x SE)
SE = Standard error
=> confidence interval does not mean we are 95% confident that the population mean will fall in the interval
Test statistics
=> fit statistical models to the data that represent the hypotheses that we want to test
Test statistic = variance explained by the model / variance not explained by the model = effect / error
One- and two-tailed tests
directional hypothesis: one-tailed (0.05)
non-directional hypothesis: two-tailed (0.025)
Type I and II error
Type I error: We believe there is a genuine effect in our population, when in fact there isn´t = alpha
Type II error: We believe there is no effect in the population, when in reality there is = beta
=> trade-off between both errors: if we lower the probability of accepting alpha, we increase ß
—> trade-off depends on the content, e.g. pharmacy
Effect size
Linked to
sample size
probability level
ability of a test to detect an effect (statistical power)
Types of effect sizes
Cohen´s d
Persons correlation coefficient r
Odds ratio
Statistical power
= ß / beta
calculate the sample size necessary to achieve a given level of power
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