week 4 class notes
Popular in Statistics In Psychology
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This 3 page Class Notes was uploaded by Nate Dickstein on Friday February 13, 2015. The Class Notes belongs to PSYCH240 at a university taught by Jeffrey Starns in Fall. Since its upload, it has received 172 views.
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Date Created: 02/13/15
being scientific means expressing an appropriate level of confidence in our beliefs if strong evidence is not available the scientific thing to do is acknowledge our uncertainty combining probability addition rule the probability of getting any one of multiple mutually exclusive outcomes is the sum of the individual probabilities of each outcome the probability of getting a 1 on a dice roll is 16th the probability of getting a 2 on a dice roll is 16th the probability of getting either a 1 or a 2 on a dice roll is 26th Multiplication rule the probability of simultaneously observing multiple independent outcomes is the product of the probabilities of each individual outcome always express probabilities as proportions when applying this rule NVOVPC100OV NVOVPC100OV you believe a lot of things and you can39t be completely certain that any of them are true the multiplication rules shows that even if you strongly believe in all the things you believe in the chances are that at least one of them is wrong Percentage change percentage change the difference between the new and old value of a variable divided by the old value times 100 to make it a percentage PC100NVOVOV PCpercent change OVold value NVnew value if the value comes out positive then it is a percentage increase if the value comes out negative then it is a percentage decrease percent change can be over 100 When you have the old value and the percentage change you can figure out the new value increase decrease When you only have information on the percentage change and not the absolute change you should be suspicious If you don t know the original value or the new value then you can t figure out how big the absolute change was in the variable The same percentage change can represent different absolute changes depending on the original value This is especially tricky when the original variable itself is expressed in percentages o increasedecrease means something very different than an increasedecrease of percentage points If 4 of people quit smoking without a therapy program and 6 quit with the therapy program you can either say that there was a 50 increase in quitting or that the rate of quitting increased by 2 percentage points Guess which one advertisers will choose Marginal Probability overall probability of an event in a population the marginal probability of A is denoted pA conditional probability probability of an event just for a subset of the population that has a certain characteristic the conditional probability of A given B is pAB Contingency table table that has all the combinations of 2 or more variables tells you how many of the scores in a population are at an intersection of those variables contingency tables are a good way to demonstrate the difference between marginal and conditional probabilities contingency tables show the number of scores at each combination at the levels of multiple variables You get marginal probabilities by dividing the column or row totals by the grand total You get conditional probabilities by dividing a cell total by a column or row total The condition tells you which column or row total to use The requested probability tells you which cell to use Conditional probabilities can be different depending on which variable you use as a condition pAB does not have to equal pBlA Class 721115 Normal distribution we can define idealized distributions that follow a particular mathematical function these are called formal distributions one famous formal distribution is the normal or Gaussian distribution this is a special distribution that is seen for many natural variables probability density when it is high there is a lot of scores that are near the value of the variable when it is low there is a few scores near the value of the variable the normal curve is symmetrical bell shaped and unimodal because the normal curve is defined mathematically we can also mathematically work out the proportion of scores in a range of values for example what proportion of people have lQ s between 120 and 140 Normal Curve When a variable is normally distributed the following proportion of scores fall between standarddeviation intervals 3 2 1 D 1 2 3 Standard deviations away from the mean 2 scores The length of adult eastern diamondback rattlesnakes is normally distributed with a mean of 45 feet and a standard deviation of 1 foot About what proportion of adults are between 55 and 65 feet first convert the scores to Zscores z 55 45 1 1 z 65 45 1 2 so we need the proportion between 1 standard deviation and 2 standard deviations above the mean next we apply our knowledge about how many scores fall between standard deviations in a normal distribution About 14 of the scores fall in our target region so the answer is 14 Samples and populations populations consist of all possible scores for a variable sample smaller set of scores actually available to a researcher statistic index that is computed from sample data regular letters Sample meanM sample standard deviation S Parameter characteristic of a population as a wholegreek letters population meanu population standard deviation 0 Law of large numbers sample estimates will tend to converge to population values as sample size increases The law of large numbers says that the estimated empirical probability will tend to converge to the true theoretical probability as sample size increases populations don39t have to be infinite Samples should be selected from a population completely at random to sample bias If samples are not random sample statistics give biased estimates of population values That is the sample value tends to come out consistently lower or consistently higher than the population value About test 1 multiple choice section computational section short answer section they are up on moodle 4 of them only 2 will be on the test at random
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