Lecture 6: 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 Don't forget about the age old question of What are crystals in silicates
○ 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:
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■ 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
■ 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 Don't forget about the age old question of What is emphasized by femininity?
■ Finally, column D lists the proportion between the mean and the z-score
○ 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,
■ 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 Don't forget about the age old question of What is the molossidae?
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○ When a score is referred to by its rank, the score is called a percentile
○ The percentile rank for a score in a normal distribution is the proportion to the left of the score