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### 41 Cards in this Set

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 Describe the relationship between the probabilities of event A and its complement event B! P(A)+P(B)=1 How is the relative frequency and probability of an event are related to each other? The probability of an event is the number around which the relative frequency (k/n) oscillates (n – the total number of experiments; k – the number of experiments in which the event occurred). If the number of experiments is very large (n→∞), the variation of relative frequency becomes negligible. This number is called the probability of the event. How is classical probability defined? If there are N mutually exclusive and equally like outcomes of an event, and k of these posses a trait, E, the probability of E is equal to k/N. Define the sum of events A and B and its probability! The sum of A and B is the event which occurs when either A or B or both of them occur. What is the probability of the sum of events A and B? P(A+B)=P(A)+P(B)-P(AB), where A+B is the sum of events A and B, AB is the product of events A and B. Define the product of events A and B! The product of A and B is the event which occurs when both A and B occur. Define the complement event of event A! The complement of A is the event which occurs when A doesn't occur and the sum of the probabilities of A and its complement event is 1. When are events A and B exclusive? If AB=0. When are events A and B independent of each other? A and B are independent if event B has no effect on the probability of A and vica versa that is P(AB)=P(A)⋅P(B) or P(A⏐B)=P(A) or P(B⏐A)=P(B) What is the meaning of P(A⏐B)? P(A⏐B) is the conditional probability of A given B, i.e. the probability of occurrence of A if only those cases are considered when B occurs. What is the definition of specificity in the case of a clinical diagnostic test? Specificity is the probability of obtaining a negative test result in a patient without the examined disease condition, i.e. the reliability of the test in correctly indentifying those patients who do not have the condition. What is the definition of sensitivity in the case of a clinical diagnostic test? Sensitivity is the probability of obtaining a positive test result in a patient who has the examined disease condition, i.e. the reliability of the test in correctly detecting those patients who have the condition. What is the definition of positive and negative predictive values? Positive predictive value is the probability that a subject with a positive diagnostic test result has the disease condition. Negative predictive value is the probability that a subject with a negative test result does not have the disease condition. What is the definition of random variable? If the values assumed by a variable are determined by chance factors, i.e. they cannot be exactly predicted in advance, the variable is called a random variable. When is a random variable continuous? A continuous random variable can assume any value within a specified interval of values. What is the meaning of the cumulative frequency distribution function Fn(x) of a sample? Fn(x) gives the fraction of elements which are smaller than or equal to x. What is the probability that a continuous random variable is in the (a,b) interval? The probability that a continuous random variable assumes a value in the (a,b) interval is equal to the area under the curve of the probability distribution function between a and b. Define the mean of a discrete random variable! ( ) 1 n i i i Mx xp = = Σ where xi is the ith value of the random variable, and pi is the probability that the random variable assumes the value of xi Define the variance of a random variable! ( ) 1 1 2 2 − − = Σ= n x x S n i i where xi are the values assumed by the random variable in a random sample, x is the mean of the sample, and n is the number of elements in the sample. Give the kth element of a binomial distribution with parameter p (the probability of the first possible outcome of a trial) if the total number of trials is n (k=0,1,2,3...,n), and define the probability it means! Pn,k is the probability that a given event occurs k times in n independent trials with two possible outcomes with probabilities p and q: ( ) ( )( ) , ! 1 ! ! k n k n k P n p p n k k − = − − where n is the number of trials, k is the number of occurrences of one of the two events and p is the probability of the event. When does a random variable follow a standard normal distribution? If it follows a normal distribution and the mean and standard deviation are 0 and 1, respectively. Define the standard deviation (SD) and the standard error of the mean (SEM) of a sample! ( )2 ( )2 1 , 1 1 ( 1) n n i i i i x x x x SD SEM n nn = = − − = = − − Σ Σ xi: the elements of the sample, x is the mean of the sample, n is the number of elements in the sample. What is the difference between the standard deviation (SD) and standard error (SEM) of a sample? The SD of a sample gives an unbiased estimation of the population SD, whereas the SEM is the SD of the sample mean, i.e. it describes how accurately the sample mean approaches the population mean. If the number of elements of the sample increases, the SD approaches the square root of the population variance, the SEM approaches 0. Define the mean of a sample! 1 1 n i i x x n = = Σ where xi symbolyzes the elements of the sample and n is the number of elements in the sample. What is an ordered array? An ordered array is a listing of the values of a sample from the smallest to the largest values. Define the median of a sample! The median of a sample is the value which divides it into two equal parts such that the number of values equal to or greater than the median is equal to the number of values equal to or less than the median. If the number of elements is odd, the median will be the middle value in the ordered array. If the number of elements is even, the median will be the average of the two middle values in the ordered array. Define the mode of a sample! The mode of a sample is the value which occurs most frequently. How can a histogram be constructed? The class intervals are displayed on the horizontal axis. Above each class interval a bar is erected so that the height corresponds to the frequency or the relative frequency of the respective class interval. What is a type I error in a statistical test? A type I error is committed when a true null hypothesis is rejected. What is a type II error in a statistical test? A type II error is committed when a false null hypotheses is not rejected. What is the relationship between the probability of committing a type I error and the level of significance? The level of significance is equal to the probability of committing a type I error if the null hypothesis is true. What is the p value in hypothesis testing? The p value is the probability of obtaining a value of the test statistic as extreme or more extreme than the one actually computed provided the null hypothesis is true. What is a two-sided statistical test? The rejection area is split into two parts in a two-sided statistical test, i.e. the null hypothesis is rejected when the value of the statistic is significantly larger or smaller than according to the null hypothesis. Write down the formula for the statistical test used for single population mean hypothesis testing when the SD of the population is known! z x n μ σ − = where: x = the mean of the sample, μ = the population mean, σ = the standard deviation of the population, n = the number of elements in the sample. What kind of hypothesis testing can the F test be used for? It can be used to compare the standard deviations of two random variables following a normal distribution. What quantities can be compared with a two-sample independent groups t-test? It can be used to compare the means of two independent random variables with normal distribution if the standard deviation of the random variables is not significantly different according to an F test. When does a statistic give an unbiased estimation of a parameter? When the expected value of the statistic and that of the parameter in question are identical. When is a sample representative? When we use random sampling, that is each element of the population has equal probability to be sampled. What are the most important attributes of the quality of an estimate? 1., unbiasedness: the expected value of the statistic has to be equal to the parameter estimated by the statistics. 2., exactness: The statistic has to give a value reasonably close to the value of the parameter that is the standard deviation of the estimate has to be small. If both of the above requirements are met, the statistics is accurate. Define the null hypothesis for a two-sample t test! The means of the two populations under investigation are identical, that is the expected value of x − y is 0. Write down the null hypothesis for an F test! The standard deviations of the two populations under investigation are equal, that is σ1 - σ2 = 0.