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# STATISTICAL METHODS STAT 303

Texas A&M

GPA 3.5

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This 2 page Class Notes was uploaded by Celestino Bergnaum on Wednesday October 21, 2015. The Class Notes belongs to STAT 303 at Texas A&M University taught by J. Carroll in Fall. Since its upload, it has received 18 views. For similar materials see /class/225745/stat-303-texas-a-m-university in Statistics at Texas A&M University.

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Date Created: 10/21/15

Hypothesis Testing Overview Steps involved 1 Pick H0 and HA H0 always contains HA matches the question asked it is what we re trying to prove Remember we assume H0 is true and we re trying to prove it false meaning prove H A is true Either H0 or HA must be true making the other false 2 Pick an oclevel by determining which is more critical a Type I error then use on 001 or a Type 11 error use on 010 If all else fails use on 005 on indicates how much evidence we must have to prove HA true 3 Pick which test to use see Flowchart and details below and calculate the pvalue 4 State the conclusion If the pvalue lt X reject H0 and conclude H A is true If the pvalue is NOT lt on do NOT reject H0 fail to reject and we can NOT conclude H A is true there is insuf cient evidence to prove H A is true Numeric data means averages or expected values One mean H0 1 HA can be gt lt or i depending on what we want to prove 7 1 sample z test 1 on owchart must have normal data and KNOWN oz 7 1 sample t test 2 on owchart must have normal data but oz is unknown and we must use s2 7 If n gt30 we don t have to have normal data fwill be approx normal so we can use a ttest 3 on owchart 7 Ifn lt30 we can t use a z or a t we would have to use a nonparametric test Two means H0 ul uz ul 7 Hz 0 HA is again gt lt or i 7 Matched paired t test 10 on owchart IF the samples are dependent there is some link between the 2 samples by units we create a sample of differences which must be normal if ngt30 and use a 1 sample ttest using the mean standard deviation and number of differences This is the most powerful of the 3 tests here because we eliminate a source of variability df mm 7 1 the number of differences minus 1 7 2 sample t test 9 on the owchart we must have normal data or ngt30 for both samples and independent samples We use s12 and s22 for 612 and 022 df minn171 and 11271 7 pooled t test 8 on owchart we must have normal data or ngt30 for both samples independent samples and the variances must be equal We pool s12 and s22 to get a better estimate of oz spz df r1171 r1271 9 larger degrees of freedom so more power than 2 sample I 7 if m or 112 are NOT gt 30 we must use a nonparametric procedure Multiple means H0 ul uz uk k different populations HA not all the means are equal 7 ANOVA F test normal data independent samples and equal 62 s same as pooled ttest We compare the variation between the means the f s with the variation within the data sp2 estimates oz the true variance of the data F smmsZspz the larger it is the further apart the means are dfnum of groups 7 1 dfdenom total 7 of groups Categorical data proportions percents and fractions One proportion H0 71 HA can be gt lt or i depending on what we want to prove 7 1 sample z test 6 on owchart must have rm and n177I 2 10 7 exact binomial test 5 on owchart if mt OR n177I lt 10 we have to do a binomial test Two proportions H0 711 112111 7 n2 0 HA is again gt lt or i 7 2 sample z test 11 on owchart must have 111711 11117111 112712 11217712 2 10 although it s often relaxed to 5 Multiple proportions H0 711 n2 71k HA not all proportions are equal test for homogeneity OR H0 row and column variables are independent HA row and column variables are related test for independence 7 x2 test all cells rowcolumn combinations must have a count of at least 5 For tables larger than 2 x 2 we can use the approximation whenever the average of the expected counts is 5 or more and the smallest is at least 1 IPS p626 The expected count within a cell Eij ProwPcoluann is based on the rows and columns being independent so the further the expected is from the observed count the larger the X2 test statistic is the less we believe the null df r 7 1c 7 1 where r is the number of rows and c is the number of columns Hypothesis Testing Template First write down all of the numbers given in the problem Second gure out what statistic or parameter is associated with each number This will help you with the four steps of hypothesis testing quot1 x1 51 H1 61 1 12 f2 52 H2 52 or for categorical data nl pl n1 n2 p2 n2 Step 1 State H0 and HA 9 H0 vs HA Step 2 Pick an oclevel H0 true 9 H0 false 9 Reject H0 9 Fail to reject H0 9 Type I error 9 Type 11 error 9 Signi cance level on Step 3 Pick the appropriate teststatistic based on whether the data satis es the teststatistic s assumptions Start by listing the assumptions for the test below Check if each assumption is met by the data Then nd the pValue Use the owchart for this part Assumptions TS pValue lt Step 4 State the conclusion including whether you rejected or failed to reject AND what this means in terms of your decision

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