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UND - Psyc 241 - Class Notes - Week 6

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Lecture 6: Probability

● Probability

○ In inferential stats, we never deal in certainty because of a sampling error ○ Probability is a method for measuring and quantifying the likelihood of obtaining a specific sample from a specific population

○ Probability = likelihood

○ Defined (mathematically) as a fraction or a proportion

○ Probability of specific outcome determined by ratio comparing frequency of occurrence for that outcome to the total number of possible outcomes

○ p(event) = (# of ways an event can happen)/(# of possible events)

○ What is the probability?

■ p(heart) = (13 hearts in deck)/(52 cards in deck) = 0.25

○ It is impossible to predict with perfect accuracy exactly which score(s) will be obtained when you take a sample from the population

○ Researchers rely on probability to determine the relative likelihood for specific samples

○ You cannot obtain exactly which value(s) will be obtained for a sample, but can determine which outcomes have high vs. low probability

○ When a population of scores is represented by a frequency distribution, probabilities can be defined by proportions of the distribution

○ In graphs, probability can be defined as a proportion of area under the curve ● Probability and the normal distribution

○ If a vertical line is drawn through a normal distribution:

■ The exact location of the line can be specified by a z-score

■ The line divides the distribution into two sections (unless z = 0)

■ Larger section = "body"

■ Smaller section = "tail"

○ The unit normal table lists several different proportions corresponding to each z-score location If you want to learn more check out What are amorphous in silicates?

■ Column A of the table lists z-score values

■ For each z-score location, column B and C list the proportions in the body and tail, respectively

■ Finally, column D lists the proportion between the mean and the z-score

location

○ Because probability is equivalent to proportion, the table values can also be used to determine probabilities

○ To find the probability corresponding to a particular score (X value):

■ 1. transform the score into a z-score

■ 2. look up the z-score in the table

■ 3. read across the row to find the appropriate proportion/probability

○ To find score (X value) corresponding to a particular, If you want to learn more check out What are the major influences on the rise of prisons until the british penitentiary act?

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If you want to learn more check out What is the utility functions

■ 1. first look up the proportion in the table,

■ 2. read across the row to find the corresponding z-score

■ 3. then transform the z-score into an X value

● Percentiles and Percentile Ranks

○ The percentile rank for a specific X value is the percentage of individuals with scores at or below that value

○ When a score is referred to by its rank, the score is called a percentile If you want to learn more check out What is the vespertilionidae?

○ The percentile rank for a score in a normal distribution is the proportion to the left of the score