Quiz Flashcards
What are the permutations of n different elements taken n at a time and what is their number?
Permutations are all the possible linear arrangements of all the elements.
Define the combinations of n different elements taken k at a time in words.
All possible selections of size k of n different elements.
What is the meaning of the (n / k) binomial coefficient? Define it with a formula and with reference to combinatorics.
The binomial coefficient gives the number of ways k elements can be chosen from n different elements without regard to order.
Describe the relationship between the probabilities of event A and its complement event B.
P(A) + P(B) = 1
Define the sum of events A and B.
Sum of A and B is the event which occurs when either A or B or both 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.
and (AB) is the products of events A and B.
Define the product of events A and B.
Product of A and B is the event which occurs when both A and B occur.
Define the complement event of event 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?
It is when AB = 0.
When are events A and B independent of each other?
Only if event B has no effect on the probability of event A and vice versa.
Using the terms of set theory define:
a. the product of events A and B.
b. the sum of events A and B.
a. AB — the intersection of events A and B.
b. A + B — the union of events A and B.
What is the meaning of P(A|B)?
It is a conditional probability of A given B. And the probability of A occurring is dependent on B.
What is the definition of a random variable?
Is the number assigned to a random event.
What is a continuous random variable?
A random variable is continuous if it can assume any value within a specified interval of values.
What is the definition of the cumulative relative frequency of a sample?
Cumulative relative frequency of a sample at x gives the fraction of elements in the sample which are smaller than or equal to x.
Define the mean of a discrete random variable.
xi — is the ith value of the random variable.
pi — is the probability that the random variable assumes the value of xi.
Define the variance of a random variable.
Is the squared deviation of a random variable from its mean.
Define the variance of a sample in words.
A statistic estimating the variance of a random variable or population from which the sample has been taken.
Define the standard deviation (SD) and the standard error of the mean (SEM) of a sample with formulas.
xi — the sample of elements.
x̄ — is the mean of the sample.
n — is the number of elements in the sample.
Define the coefficient of variation (CV) in words, and with a formula.
Coefficient of Variation (CV) is the standard deviation (SD) expressed as the percentage of the mean (x̄):
CV = (SD / x̄) * 100
What is an ordered array?
Is a listing of the values of a sample from the smallest to the largest values.
Define the i-th percentile of a sample.
Is the smallest sample value that is equal to or greater than i% of the observations.
Define the first, second and third quartile (Q1, Q2, Q3) of a sample.
Q1 is the 25th percentile, Q2 is the 50th percentile (or the median), Q3 is the 75th percentile.
Define the mode of a sample.
Is the value which occurs the most frequently.
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 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 1-p:
Give the sum of the elements of a Poisson distribution with parameter λ.
What is a type I error in a statistical test?
True hypothesis (✓) — ACCEPTED
Null hypothesis (✗) — REJECTED
What is a type II error in a statistical test?
True hypothesis (✗) — REJECTED
Null hypothesis (✓) — ACCEPTED
When is a sample representative?
When we use random sampling (i.e. each element of the population has equal probability of being sampled)
What are the most important attributes of the quality of an estimates? Define them briefly.
1. Accuracy or unbiasedness — Value equal to the mean of the estimated parameter.
2. Precision or reproducibility — Value of the SD is small.
Write the null hypothesis for an F test
Variances of the two populations under investigation are equal.
What is the definition of specificity of a clinical diagnostic test?
Specificity is the probability of obtaining a negative test result in a patient without the examined diseases condition (i.e. the reliability of the test in correctly identifying those patients who do not have the condition)
P(T- | D-)
What is the definition of sensitivity 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)
P(T+ | D+)
What is the definition of negative predictive value?
Negative predictive value is the probability that a subject with a negative test result does not have the disease condition.
P(D- | T-)
What is the definition of positive predictive value?
Positive predictive value is the probability that a subject with a positive diagnostic test result has the disease
condition
P(D+ | T+)
Give the kth element of a Poisson distribution with parameter λ and define the probability it means.
Pk — is the probability that the given event occurs k number of times in an infinite number of independent trials.
What is the definition of the cumulative distribution function of a random variable?
Cumulative distribution function (CDF) of a random variable at x gives the probability that the random variable assumes a value smaller than or equal to x
What is the probability that a continuous random variable assumes a value in the interval between a and b?
The probability is equal to the area under the curve of the probability density function between a and b
What is the definition of odds?
Is the ratio of the probability of the occurrence of an event to the probability that it will not occur. If p is the nprobability of occurrence of an event, then:
odds = p/1-p
Define odds ratio from a epidemiological point of view.
Is the ratio of the odds that a risk factor is present in the diseased population to the odds that it is present in the healthy population.
What is relative risk in epidemiological studies?
Relative risk (RR) is the ratio of the probability of a disease in the risk factor-exposed population to the probability of the disease in the risk factor-free population.
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.
