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continuous
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random variable that takes all values in some interval of numbers.
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Sampling Distribution
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distribution of values taken by the statistic in all possible samples of the same size from the same population.
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goodness of fit test
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used to help determine whether a population has a certain hypothesized distribution, expressed as proportions of population members falling into various outcome categories.
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variance
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the average squared differences of the values of the variable from their mean.
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chisquare statistic
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measure of how far the observed counts in a two-way table are from the expected counts.
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test of significance
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asseses the evidence provided by data against a null hypothesis in favor of the alternative hypothesis.
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Discrete
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random variable that has a countable number of possible values.
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Matched Pair
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Design in which a before and after of the same subjects are compared., A matched pairs design compares exactly two treatments, either by using a series of individuals that are closely matched two by two or by using each individual twice.
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independent
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when the result of one observation tells you nothing about the other observations.
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random variable
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a variable whose value is a numerical outcome of a random phenomenom.
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Central limit
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theorem stating that the sum of a number of random variables obeying certain conditions will assume a normal distribution as the number of variable becomes large
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mean
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the balance point of the probability histogram or density curve.
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type I
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error that occurs if we reject Ho when it is in fact true.
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exponential
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distribution with mean and standard deviation equal to one.
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geometric
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distribution used when the number of trials is unknown.
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probability histogram
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compares the probability model for random digits with the model given by Benford's Law.
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expected count
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(in any cell of a two-way table when the null hypothesis is true) row total times column total over table total.
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confidence interval
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uses sample data to estimate an unknown population parameter with an indication of how accurate the estimate is and of how confident we are that the result is correct.
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cumulative distribution function
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calculates the sum of the probabilities for 0,1,2,...... up to value X.
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type II
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error that occurs if we accept Ho when in fact Ha is true.
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expected value
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mean of a random variable
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variability
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the spread of a statistic's sampling distribution.
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standard deviation
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square root of variance. measures the variability of the distribution about the mean.
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law of large numbers
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the average of the values of x observed in many trials must approach ?.
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Z Statistic
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used when the population standard deviation is known or used when dealing with proportions.
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expected count
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obtained by multiplying the proportion of the distribution for each category times the sample size.
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chi square
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a family of distributions that take only positive values and are skewed to the right.
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normal distribution
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one type of continuous probability distribution.
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sample
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a selected representation of the population.
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parameter
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a number that describes a population.
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p-value
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probability, computed supposing Ho to be true, that the test statistic will take a value at least as extreme as that actually observed.
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binomial
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distribution that requires a fixed number of trials
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unbiased statistics
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the mean of its sampling distribution is equal to the true value of the parameter being estimated.
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degrees of freedom
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sample size minus 1.
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degrees of freedom
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one parameter which specifies a specific chi square distribution.
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probability distribution
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lists the values and their probabilities; described by a density curve.
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confidence level
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states the probability that the method will give a correct answer.
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bias
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Any variable that can alter the center of a data set, or alter the outcomes.
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standard error
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the result when the standard deviation of a statistic is estimated from the data.
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Probability distribution function
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assigns a probability to each value of X.
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density curve
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describes the probability distribution of a continuous random variable.
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power
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measures a significant test's ability to detect an alternative hypothesis.
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statistic
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a number that can be computed from the sample data.
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alternative
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hypothesis that proposes a change or opposes the claimed hypothesis.
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Least-squares regression
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fits a straight line through data in order to predict a response variable Y from the explanatory variable X.
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statistical inference
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provides methods for drawing conclusions about a population from sample data.
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null
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hypothesis that says there is no effect or change in the population.
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probability model
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overall description of the population.
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