BNAD277 Chapter 13a Notes
BNAD277 Chapter 13a Notes BNAD277
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This 4 page Class Notes was uploaded by Kristin Koelewyn on Monday April 11, 2016. The Class Notes belongs to BNAD277 at University of Arizona taught by Dr. S. Umashankar in Spring 2016. Since its upload, it has received 10 views. For similar materials see Business Statistics in Business at University of Arizona.
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Date Created: 04/11/16
Bnad277: Chapter 13a Notes Experimental Design and Analysis of Variance - An Introduction to Experimental Design and Analysis of Variance o Statistical studies can be classified as being either experimental or observational. o In an experimental study, one or more factors are controlled so that data can be obtained about how the factors influence the variables of interest. o In an observational study, no attempt is made to control the factors. o Cause-and-effect relationships are easier to establish in experimental studies than in observational studies. o Analysis of variance (ANOVA) can be used to analyze the data obtained from experimental or observational studies. o In this chapter three types of experimental designs are introduced. ▯ a completely randomized design ▯ a randomized block design ▯ a factorial experiment o A factor is a variable that the experimenter has selected for investigation. o A treatment is a level of a factor. o Experimental units are the objects of interest in the experiment. o A completely randomized design is an experimental design in which the treatments are randomly assigned to the experimental units. o o ▯ For each population, the response (dependent) variable is normally distributed. 2 ▯ The variance of the response variable, denoted s is the same for all of the populations. ▯ The observations must be independent. - Analysis of Variance and the Completely Randomized Design o Between-Treatments Estimate 2f Population Variance ▯ The estimate of s based on the variation of the sample means is called the mean square due to treatments and is denoted by MSTR. ▯ o Within-Treatments Estimate of Population Variance ▯ The estimate of s based on the variation of the sample observations within each sample is called the mean square error and is denoted by MSE. ▯ o Comparing the Variance Estimates: The F Test ▯ If the null hypothesis is true and the ANOVA assumptions are valid, the sampling distribution of MSTR/MSE is an F distribution with MSTR d.f. equal to k - 1 and MSE d.f. equal to nT- k. ▯ If the means of the k populations are not equal, the value of MSTR/MSE will be inflated because MSTR overestimates s 2. o ANOVA Table ▯ With the entire data set as one sample, the formula for computing the total sum of squares, SST, is: o Test for the Equality of k Population Means ▯ Rejection Rule: ▯ P-value approach: Reject Ho id p-value </ s ▯ Critical Value approach: Reject Ho if F>/Fs - Multiple Comparison Procedures o Suppose that analysis of variance has provided statistical evidence to reject the null hypothesis of equal population means. o Fisher’s least significant difference (LSD) procedure can be used to determine where the differences occur. - Fisher’s LSD Procedure o Hypotheses: o Test Statistic: o Rejection Rule: ▯ P-value approach: Reject Ho is p-value </s ▯ Critical Value approach: Reject H0 if t<-t(a/2) 0r t>t(a/2) - Fisher’s LSD Procedure Based on the Test Statistic x bar i – x bar j o Hypotheses: o Test Statistic: o Rejection Rule: - Type 1 Error Rates: o The comparison-wise Type I error rate a indicates the level of significance associated with a single pairwise comparison. o The experiment-wise Type I error rate a EW is the probability of making a Type I error on at least one of the (k – 1)! pairwise comparisons. ▯ o The experiment-wise Type I error rate gets larger for problems with more populations (larger k).
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