In principal a distribution of means can be formed by randomly taking a very large number of samples from a population each of the same size making a distribution of their means The variance of a distribution of means is smaller than the original population variance because extreme scores are less likely to affect a distribution of means The mean variance of a comparison distribution that would be used to test the hypothesis that the mean of 100 o2 25 would be mean 100 variance 2 5 The standard deviation of a distribution of means is sometimes called the standard error of the mean or the standard error because it represents the degree to which particular sample means are in error as estimates of the mean of the population of individual scores If the mean of a comparison distribution is 100 oM 20 the mean sample is 115 what is the Z score of the sample on the distribution of means 75 A 95 confidence interval is figured by finding the cutoff points for the lower figure the raw scores for 1 96 standard errors above below 2 5 and the upper 2 5 The 99 confidence interval is the region in a group of scores that is at and above below the 49 5 on a normal curve This comes to 2 58 Rejecting the null hypothesis when the research hypothesis is false is a Type 1 error Failing to reject the null hypothesis when the research hypothesis is true is a Type 2 error Setting the significance level cutoff at 10 instead of the more usual 05 increases the likelihood of a Type 1 error The probability of deciding that an experiment is inconclusive when the research hypothesis is in fact true is Beta The degree to which the experimental manipulation separates the two populations of the individual score is the effect size One important advantage of using effect size is that they are standard that make comparisons of different studies easier Power is the probability that study will give a significant result if the research hypothesis is true Effect size is one of the 2 major factors that contribute to power the other factor is how many participants are in the study aka sample size While no research hypothesis is ever definitely false failing to reject the null hypothesis in a study that has a high level of power allows one to assume it does not have practical importance Low power leaves the possibility that significant results might show up if power were increased How would a psychologist test the hypothesis that a new stress reduction program really works By trying to reject the hypothesis that it does not work A major misuse of significance tests Is the tendency to decide that if a result is not significant the null hypothesis is shown to be true The distribution that represents the situation in which the null hypothesis is true is the comparison distribution The cutoff sample score on the comparison distribution is the point at which if the null hypothesis is true a result this extreme is unlikely When a psychologist rejects the null hypothesis at this 05 level the results of a study indicate that there is less than 5 chance of getting such an extreme result by chance if the null hypothesis is true If the cutoff z score on the comparison distribution is 1 64 the sample z score is 1 32 on the comparison distribution the correct decision is to fail to reject the null hypothesis A result that is statistically significant at the 05 level would be reported in a research article as p 05 The correct argument for using a two tailed test even if there is a clear basis for predicting a result in a given direction is that if an unexpected result that is opposite of what is predicted occurs it does not have to be ignored If a counseling psychologist wants to know if doubling the number of counseling sessions attended by students experiencing severe test anxiety will reduce or increase the amount of anxiety the students report just before a test the statistical test the psychologist would use would be two tailed because the direction of the effort of increasing the amount of therapy is not predicted Which of the following questions is a psychologist planning to answer by determining the characteristics of the comparison distribution Given a particular sample value what is the probability of obtaining that value if the null hypothesis is true Steps of Hypothesis Testing 1 Restate the question as a research hypothesis a null hypothesis about the population 2 Determine the characteristics for the comparison distribution a Comparison distribution is the distribution that represents the population situation if the null hypothesis is true If null is true distributions of populations 1 2 are the same 3 Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected a What kind of result would be extreme enough to convince us to reject the null hypothesis 4 Determine your sample s score on the comparison distribution 5 Decide whether to reject the null hypothesis a If the z score of the sample individual is 1 but the minimum z score to reject the null is 1 64 the sample score is NOT extreme enough to reject the null One tailed test hypothesis testing procedure for a directional hypothesis situation in which the region of the comparison distribution in which the null hypothesis would be rejected is al on one side tail of the distribution Two tailed test hypothesis testing procedure for a nondirectional hypothesis the situation in which the region of the comparison distribution in which the null hypothesis would be rejected is divided between the two sides tails of the distribution