Permutation Test for the Two Sample Problem we wish to compare results for two groups of experimental units the first group could be some subjects who have been given a treatment, whereas the second group has not in some cases we are unable to assume that
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Wilcoxon Rank-Sum Test, also known as the Mann-Whitney test Rank the data. That is replace, the data values by their ranks, from smallest to largest. For example, the pH samples are: Group 1: Group 2: 8.53 8.52 8.01 7.99 7.93 7.85 7.73 7.58 7.40 7.35 7.
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One-Way Analysis of Variance (ANOVA)
One-Way Analysis of Variance (ANOVA) is a method for comparing the means of a populations. This kind of problem arises in two different settings 1. When a independent random samples are drawn from a populations. 2. W
Subsequent Inferences for one-way ANOVA if the overall F test does not show significant differences among the groups, no further inferences are required if the overall test does show a significant difference, differences between particular means can be te
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Assessing Normality of a Sample normal quantile plots can be used to assess whether the data could have come from a normal distribution these plots are also called QQ or normal scores plots the sorted values are plotted against the values we would expec
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Two-Way Analysis of Variance - no interaction
Example: Tests were conducted to assess the effects of two factors, engine type, and propellant type, on propellant burn rate in fired missiles. Three engine types and four propellant types were tested. Twen
Residual Analysis for two-way ANOVA The twoway model with K replicates, including interaction, is Yijk = ij + ijk = + i + j + ij + ijk with i = 1, . . . , I, j = 1, . . . , J, k = 1, . . . , K. In carrying out the F tests for interaction, and for the main
Randomized Block Example A farmer wishes to compare the growth times of four different varieties of daffodil under a range of different conditions. She decides to use a randomized block design where six fields are split into four equally sized plots and t
Subsequent Inferences for two-way ANOVA the kinds of inferences to be made after the F tests of a two-way ANOVA depend on the results if none of the F tests lead to rejection of the null hypothesis, then you have concluded that none of the means are diffe
ECON 3600
Assignment 1
Due on October 3, 2016 (in class)
Total points: 20
1. (4 points)
Army 1, of country 1, must decide whether to attack army 2, of country 2, which is
currently occupying an island between the two countries. In the event of an attack,
Comparing two means, paired experiment
many studies are comparative they compare outcomes from one group with outcomes from another (e.g. two different medical treatments) in the matched-pairs design each subject in one group is paired with a similar sub
Hypothesis Testing basic ingredients of a hypothesis test are 1. the null hypothesis, denoted Ho 2. the alternative hypothesis, denoted Ha 3. the test statistic 4. the the data 5. the conclusion the hypotheses are usually statements about the values of on
Confidence Intervals A confidence interval provides a simple summary of how precisely a parameter, denoted , is estimated. In many situations, a (1 - )100% confidence interval is of the form ^ ( - s t/2 , ^ where ^ is an estimate of s is its standard erro
American Economic Association
Common Knowledge Author(s): John Geanakoplos Reviewed work(s): Source: The Journal of Economic Perspectives, Vol. 6, No. 4 (Autumn, 1992), pp. 53-82 Published by: American Economic Association Stable URL: http:/www.jstor.org/
ONE SAMPLE T-INTERVAL (95% CI) USING MINITAB MTB > DATA> DATA> MTB > set c1 2.5 3.1 2.2 1.5 2.9 end Onet C1.
One-Sample T: C1 Variable C1 N 5 Mean 2.440 StDev 0.631 SE Mean 0.282 95% CI (1.657, 3.223)
How to look up the critical t-value in Minitab (instea
Hypothesis Testing for one sample using t-distribution. Data is the car speed data used in the teaching notes (data set on course web site) Hypothesis Testing using MINITAB
MTB > Onet 'speed'; SUBC> Test 30; SUBC> Alternative 1. One-Sample T: speed Test o
1 Statistics 2080 - practice midterm questions 1. Independent random samples were drawn from two normal populations assumed to have the same standard deviation, resulting in the following summary statistics. n 1 = 9 S1 = 4 n2 = 11 S2 = 5 Calculate a poole
Computer Code for Pooled-t tests. Uses soil pH example from class MINITAB
R Code (using built-in function t.test)
> # pooled t-test used in notes > > # Clear the workspace > rm(list=ls() > > Loc1 = c(8.53, 8.52, 8.01, 7.99, 7.93, 7.89, 7.85, 7.82, 7.80) >
1 1. Independent random samples were taken from two populations of policemen with blood lead concentration measured in each sample member. One sample of 26 policemen subjected to constant inhalation of automobile exhaust fumes in downtown Vancouver had an
Econ2216 (2012): Carbon Social Cost Benefit Project Groups - If you are listed in a group other than the one you have been meeting with OR if you are not in a group or are in a group of 6 and have not met with the group yet and wish to be moved into group
Introduction, 1 sample t-test and t-interval Central Limit Theorem Let X1 , X2 , . . . , Xn be a random sample from a distribution with mean and variance 2 .Then if n is sufficiently large (Rule of thumb > 30), X has 2 2 approximately a normal distributio
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Atlantic Power Company
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John
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