APPLICATIONS OF STATISTICS
APPLICATIONS OF STATISTICS STAT 314
Virginia Commonwealth University
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This 2 page Class Notes was uploaded by Verdie Hauck PhD on Wednesday October 28, 2015. The Class Notes belongs to STAT 314 at Virginia Commonwealth University taught by S. Street in Fall. Since its upload, it has received 20 views. For similar materials see /class/230672/stat-314-virginia-commonwealth-university in Statistics at Virginia Commonwealth University.
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Date Created: 10/28/15
One Proportion ZTests in SPSS STAT 314 A certain soft drink bottler claims that less than 20 of its customers drink another brand of soft drink on a regular basis A random sample of 100 customers yielded 18 who did in fact drink another brand of soft drink on a regular basis Do these sample results support the bottler39s claim Use a leVel of significance of 005 Enter the category Values Brand of Drink lother brand 2same brand into one Variable and the observed counts other brand18 same brand82 into another Variable see le gure below Then weight the category Values Variable by the observed counts Variable see two right gures below w Data Iranxmrm Analyze anDatzx 0 Dn nntwelqht case weight case by I 4L 1 mm mm 1 same mm 32 Sun a Iranxpnxz Frznuencyvarlahlz MME FIIES gcnunumunq qr ate urrzntStatux Welqhtcaxeshycnunt 2 Select Analyze 9 Nonparametric Tests 9 ChiASquare see le gure below E Select quotBrand of Drinkquot as the test Variable and enter the Values for the null hypothesis proportions in numerical order by category Value ie Pother brand 020 then Psame brand 080 see right gure below Cnunllcnunll Expulznnanqa zm mum 7 9 6211mm data 0 All catEanIE Equal Ouxexuecmenranqz Valm vwzl39 W E Levene s T est for Equality of Variances Levene s T est for Homogeneity of Variances Levene s Test A homogeneityofvariance test that is less dependent on the assumption of normality than most tests For each case it computes the absolute difference between the value of that case and its cell mean and performs a oneway analysis of variance on those differences Assumptions 1 The samples from the populations under consideration are independent 2 The populations under consideration are approximately normally distributed Checking the assumptions Assumption I 39 Be sure that the samples were taken independently of one another Assumption 2 Construct sidebyside boxplots or Q Q plots by treatment to assess normality Notation OneWay ANOVA t number of treatments t k for oneway ANOVA t kl for twoway ANOVA yij 2 sample observationj from treatment i j l 2 ni and i l 2 t n i number of observations from treatment i at least one ni must be 3 or more N 2 n1 n2 nr 2 total number of pieces of data overall size of combined samples a mean of sample data from treatment i Dij lyij 3 2 absolute deviation of observation j from treatment i mean 5 average of the ni absolute deviations from treatment i 5 average of all N absolute deviations Note At least one of the treatments must have 3 or more observations or else the Levene s statistic will be undefined the denominator will equal zero if each treatment has 1 or 2 observations