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Unformatted text preview: Statistics Test #3 Inferential Statistics Inferential statistics allow researchers to estimate whether a sample is representative of a certain population "Statistical significance" reveals whether the characteristics of a sample are likely to exist in the population When a statistic has a corresponding statistical significance estimate of p < . 05, there is less than a 5% chance that the sample represents the population to which it is being compared Statistical Hypothesis Testing Statistical hypothesis testing describes how statistical significance is derived Statistical hypotheses: H : sample does not differ from population (null hypothesis) H a : sample differs from population (alternative hypothesis) Typically, when p < .05, researchers conclude that they can safely reject H Type 1 error : incorrectly rejecting null hypothesis Probability of type 1 error called alpha ( ) Alpha criterion (alpha level) = standard for rejecting null hypo (typical: p must be less than .05) Thus, the likelihood of type 1 error increases when alpha level is high (more likely when alpha criterion = .10 than when alpha criterion = .01) Type 2 error : failing to reject incorrect null hypothesis Type 2 error involves concluding that there is no relationship when a relationship really does exist Probability of type 2 error called beta ( ) Type 2 error most likely when alpha criterion is low or when statist ical power is inadequate Stat ist ical power = ability to detect relat ionships = 1 beta Stat ist ical power determ ined by method, sample size Researcher's Decision Stat ist ical hypothesis test for one sample experiment In a one sample experiment, all sample part icipants receive t reatment. To test the effect of t reatment, the sample mean is compared with a known populat ion mean Example: Populat ion mean = 48 ( SD = 16), sample mean = 45 H 0 = sample represents population with = 48 H a = sample represents population with 48 Does the sample mean differ significantly from the population mean? Hypothetical distribution of means of samples of N = 64 drawn from population with = 48, = 16 Standard error of the mean population standard deviation S.E.M. = ___________________________ square root of sample size In example, SEM = 16 divided by square root of 64 = 2 If the sample mean = 45, should H be rejected? Calculat ing z-score for sample mean in sampling dist ribut ion:...
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- Fall '08