Download Understanding Hypothesis Testing & Sampling Distributions in Probability and more Slides Statistics in PDF only on Docsity! Hypothesis Testing docsity.com Probability • Review • P = number of times an even can occur/ • Total number of possible event • Bounding rule of probability • Minimum value is 0 • Maximum value is 1 docsity.com Multiplication rule • What is the probability of A and B occurring? • If the events are independent of one another, they can be multiplied • What is the p of having both schizophrenia and epilepsy? docsity.com Probability distributions • A probability distribution is theoretical—we expect it based on the laws of probability • That is different from an empirical distribution—one which we actually observe docsity.com Normal probability distribution • Probability distribution for continuous events • Probability of an event occurring is higher in the center of the curve • Declines for events at each of the two ends (tails) of the distribution • Neither of the tails touches the x axis (infinity) docsity.com Variations • Skewness • Skewed to the right or the left, as opposed to symmetry • Kurtosis: degree of “peakedness” or “flatness” docsity.com Area under the normal curve • Remember that for any continuous distribution there is a mean and SD • Example: Mean = 10 and SD = 2 • If the distribution is not skewed, the majority (2/3) of scores will be from 8 to 12 • 8 and 12 are each one SD from the mean • See p. 225 docsity.com Area under the normal curve • If a distribution is normal, we can express standard deviation in terms of z scores • A z score = (a score – the mean)/SD • If we convert all our raw scores to z scores, then we get what is call the standard normal distribution • It STANDARDIZES our scores docsity.com Standard normal distribution • A minus sign means the score is less than the mean • The z score also tell about magnitude—the larger the z score, the further from the mean, and the smaller the z score, the closer to the mean docsity.com Standard normal distribution • We can also make statements about where an individual score is in relation to the rest of the distribution • .3413 (or 34.13%) of scores will fall between the mean and 1 SD • .3413 (or 34.13%) of scores will fall between the mean and – 1 SD docsity.com Standard normal distribution • .6826 (0r 68.26) of scores will be between -1 and + 1 SD on a normal distribution • Thus, when we see a mean and SD, if it is normally distributed, about 2/3 of the scores will fall between the mean – the SD and the mean + the SD docsity.com Standardized normal • SAT scores, mean = 500, SD = 100 • Illustrate • Use of z table, p. 724 • Reading the table docsity.com Utility of the normal distribution • Use of the normal distribution underlies many statistical tests • Many variables not normally distributed • However, the normal distribution useful anyway because of the apparently validity of the Central Limit Theorem docsity.com Sampling distributions • To understand the Central Limit Theorem, need to understand sampling distributions • Say we draw many samples, and calculate a statistic for each sample, such as a mean • When we draw the samples, the mean will not be the same each time—there will be variation docsity.com
