EC124 Revision

amarjotsidhu's version from 2015-05-13 05:47

Section 1

Question Answer
Wilcox sign testmatched pairs; assign values (+ / -) ; consider only + values; H0: p= 0.5 ; follows Bernoulli distribution
Wilcox sign test approximationfor values greater than 25, H0 approximated: X/n~N (0.5, 0.25/n) . Test statistic: (x/n - 0.5) / (0.25/n)^1/2
Wilcox signed rank testmatched pairs; rank absolute differences; sum ranks of absolute differences for positive and negative differences separately; T=min... (choose smallest value); if min value is <= critical value, reject H0
Wilcox signed rank test approximationfor n>25, approximate using normal using mean and variance formulas; test statistic = T - mean / SD
Mann Whitney testsamples from independent random samples; rank all observations from both samples; sum the ranks of first sample (R1)
Mann Whitney test approximationFor n>25, approximate using normal and using the mean and variance. U-n1n2 / SD
Goodness of fit testchecking if what we observe is consistent with what we expect to observe; 'K' categories in random sample of n; observed number of cases in categories (01, 02...); H0 specifies probabilities for an observation falling into a category (p1,p2..); under H0, expected numbers in each category = n x Pi ; reject H0 if test statistic is greater than critical value from chi squared
Contingency tables2 attributes A and B; K categories in A and H in B; cross clarification = number of sample observations to category 'i' of A and 'j' of B; null hypothesis = no attribution between 2 tables; under null, number of observations in each cross clarification = product of marginal probabilities (pi x pj) , pi = Oij / n ; pj = Oij / n ; expected no. of observations - n x pi x pj; look at discrepancy between observed and expected values using formula ; reject H0 if test stat is greater than chi squared critical value

Section 2

Question Answer
Standard rest of meansNormal, known pop. variance ; z= sample mean - pop. mean / (standard deviation / root of n)
Not normal distribution, unknown mean but population variance knownn>30 , use CLT with ~ mean and variance = sample variance / n
Not normal distribution, unknown population variance but sample variance knownif n>30, use CLT
Bernoulli dist, unknown mean and unknown pop varianceif n>30, use CLT. mean = E(X) . Variance = V(X) = (p(1-p)) / n
Normal dist, unknown pop varianceuse t distribution, t= sample mean - pop. mean / (standard SD / root of n) ; for 2 sided test, use t with alpha/2 , n-1
Confidence intervalsmeasure of sample mean +- (critical value x standard deviation). critical values = chi-squared with alpha/2 and 1- alpha/2 ; variance = (n-1) x sample variance) / chi squared alpha, n-1