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# Unit Normal Table Psyc-21621

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This 3 page Class Notes was uploaded by Amy Turk on Wednesday April 27, 2016. The Class Notes belongs to Psyc-21621 at Kent State University taught by Dr. Gordon in Spring 2016. Since its upload, it has received 4 views. For similar materials see Quantitative Methods Psych I in Psychlogy at Kent State University.

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Date Created: 04/27/16

Psych Stats Powerpoint 6 ● we can identify important sections of the normal distribution using z- scores ● because we know what percent of scores falls in each part of the distribution, we can define the normal distribution in terms of proportions ○ these percentages/proportions apply to any normal distribution, regardless of the values for the mean and SD ● 68-95-99.7% rule ● if you know the z-score, you can find the proportion above or below that score using the unit normal table Unit Normal Table ● lists proportions of the normal distribution for a range of possible z- score values ● imagine you draw a line at a particular z-score ○ this line seperates the distribution into a larger segment (the body) and a smaller segment (the tail) ○ the table provides proportions for these segments ● proportions will be exactly the same on the negative and positive side ● proportion of scores greater than (in the tail) z = 2.0 is the same as the proportion of scores less than (in the tail) z = -2.0 ● finding the proportion using the table ○ determine the z-score ○ locate the z-score in the table ■ find the approximate row ■ you are looking for the closest z-score ○ find the proportion of interest ■ body = b ■ tail = c ■ between the mean = d ● finding the probability between 2 scores ○ take the larger probability from the mean and subtract the smaller probability from the mean ● find the proportion between the mean and the z-scores and subtract them ● probability is used in inferential stats ○ determine whether an outcome (score) is noteworthy (significant) ■ if individuals have scores around the mean, we conclude the treatment has no effect ■ if individuals have scores noticeably different from the mean, we can conclude the treatment has had an effect ● we use probabilities to determine what is “noticeably different” from the mean ● we use the extreme 5% boundary as proof that the treatment has had an effect ○ scores that are very unlikely to be obtained from the original population ○ if someone falls into this area after the treatment, we conclude that the treatment had an effect ○ the magic p<.05 value ● middle 95% = high probability values, indicating that the treatment has no effect ● probability = the likelihood that a particular outcome will occur out of several possible outcomes ● expressed as a fraction or proportion ● probability of A = number of outcomes classified as A divided by the total number of possible outcomes ● frequency = how many times something happens ● relative frequency = the number of times something happens relative to the number of times it could have happened (expressed as a proportion) ● expected relative frequency = the number of outcomes divided by the total number you would expect over a long period of time ● probability is an expectation, not a fact ○ tells us what is likely to happen, not what will happen Why Study Probability? ● fundamental to inferential stats ○ every conclusion we draw from data is based on probability ○ helps us make decisions based on the probability of events ● quantify randomness or uncertainty ● understanding the likelihood of events Math Definitions ● probability model = a mathematical description of a random phenomenon ● event = one specific outcome ○ event probability always between 0 and 1 ● sample space = all of the possible events ○ sample space probability always equals 1 Random Sampling ● an assumption of most psychological research and of stats ● requires that each person has an equal chance of being selected ● the probability of being selected stays constant ● the probability that an event does not happen is 1 minus the probability the event does happen ○ p(not A) = 1 - p(A) ● if two events are disjoint, the probability that one or the other occurs is the sum of the probabilities that both occur ● p(A or B) = p(A) + p(B) ● if event A happens, then event B cannot happen ○ if someone is male, then he cannot be female ● if two events are independent, the probability that both occur is the product of the probabilities that each occurs ○ p(A & B) = p(A) * p(B) ● independent events = result of event A does not influence the result of event B ● most variables we analyze in psychology are continuous variables ● we can assess the probability of a certain score (outcome) by using z- scores and the normal distribution

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