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27 Cards in this Set
- Front
- Back
What is Inferential Statistics?
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Using data or scores to make a statement about a characteristic of the population. Two statements: hypothesis testing and Parameter estimation.
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What is hypothesis testing?
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Experimenter is collecting data in an experiment to validate some hypthesis involving population.
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What is parameter estimation?
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Experimenter is interested in determining the magnitude of a population characteristic. Ex. economist interested in what the amount of money a college student spent on food.
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What is random sampling?
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sample selected from the population by a process that ensures 1. each possible sample of given size has an equal chance of being selected and 2. all members of population have an equal chance of being selected into sample
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What is sampling with replacement?
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Sampling from population one score at a time and then placing it back into the population before drawing again.
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Sampling without replacement
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method of sampling in which the members of the sample are not returned to the population before subsequent members are selected.
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Two ways probability may be approached?
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1. Priori, or classical viewpoint
2. Posteriori, emperical viewpoint |
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Formula for computing Priori probability?
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# of A events
p(A)= ---------------------- Total # of events |
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Formula for Posteriori?
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# times A occurs
p(A) = ------------------------------- Total # of occurrences |
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Properties of Probability
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1. A proportion ranging from 0.00 to 1.00.
2. Expressed as fraction or decimal # 3. Expressed chances in 100 or p(A) = 0.05 (5 chances in 100) |
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Probability of occurrence of A or B
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equal to the probability of occurrence of A plus the probability of occurrence of B minus the probability of occurrence of both A and B.
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Formual for addition rule is
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p(A or B)=p(A) + p(B) - p(A&B)
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Two events are mutually exclusive
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if both CANNOT occur together or if the occurrence of one precludes the occurrence of the other. Ex: Rolling a 1 and a 2 in one roll of a die is mutually exclusive, if it rolls a 1 then it cannot be a 2.
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Mutually exclusive formula
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p(A or B) = p(A) + p(B)
always = 0 because the probability of both events occurring together is impossible |
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What is exhaustive?
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A set of events that includes all of the possible events.
Ex: Rolling a die once, set of events of getting 1, 2, 3, 4, 5, 6, is exhaustive because set includes all possible events. |
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Multiplication rule
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concerned with joint or successive occurrence of several events
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Probability of occurrence of both A and B
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equal to the probability of occurrence of A times the probability of occurrence of B given A has occurred
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Multiplication rule equation
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p(A and B) = p(A) p(B/A)
p(B/A) means "probability of occurrence of B given A has occurred.) |
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Multiplication rule: Mutually exclusive events
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p(A and B) = 0
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Two events are Independent
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if the occurrence of one has no effect on the probability of occurrence of the other
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Ex of two events being independent
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Suppose we draw two cards, one at a time, with replacement, from ordinary deck of cards. Let A be first card drawn and B be second card. Since A is replaced before drawing B the occurrence of A on first draw has no effect on probability of occurrence of B
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Equation for multiplication rule with independent events
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p (A and B) =p (A) p (B/A) = P(A)p(B)
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Multiplication with dependent events
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When A and B are dependent the probability of occurrence of B is affected by the occurrence of A
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Equation for multiplication rule with dependent events
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p(A and B) = p(A) p (B/A)
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Ex of dependent events
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Suppose we draw two cards one at a time, without replacement. A is an ace on first draw and B is an ace on the second draw.
p(an ace on the first draw and an ace on the second draw) = p(an ace on the first draw) p(an ace on the second draw, given an ace was obatained on first draw) |
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Multiplication and addition rules
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p(A) = p(5 die 1 & 6 die 2)
= p(5 die 1) p(6 die 2) = (1/6) (1/6) = 1/36 p(B) = p(6 die 1 and 5 die 2) = p(6 die 1) p(5 die 2) = (1/6) (1/6) = 1/36 p(+ of 11)=p(A or B)=p(A)+p(B) |
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Probability and Normally distributed continuous variables
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Area under curve corres A
------------------------------------- Total area under curve |