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ANALYSIS OF VARIANCE. 26 NOVEMBER 2021.
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Objectives Aner c«npJaÉtg this chapter. you shcndd be abk to n use the ore-way ANOVA technque to 'f there B a differnce •rung three or more rnems. which mems differ, lÄng he Sct•Hfe or test rf he repcted in ttr ANOVA Use the ANOVA to detem•tirE ttzre a differnce n mul eff«ts or 12 Analysis of Variance Outline 1.2—1 One-Way AnosisofVuiance 12—2 and the Test 12—3 Two%yhatysis ofWrOnce Summary.
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Figure 9-2 Hypothesis-Testing Situations in the Comparison of Means Sample 1 Sample 2 Population (a) Difference is not significant Do not reject Ho: = since RI — R2 is not significant..
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HYPHOTHESES TESTING. These tests can also be one-tailed, using the following hypotheses: Right-tailed Ho: = or HI: — > O Left-tailed Ho: = or The same critical values used in Section 8—2 are used here. They can be obtained from Table E in Appendix C. If and are not known, the researcher can use the variances from each sample s} and s}, but a t test must be used. This will be explained in Section 9—2. The basic format for hypothesis testing using the traditional method is reviewed here..
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What is a variance?. The variance is the average of the squares of the distance each value is from the mean. The symbol for the population variance is (u is the Greek lowercase letter sigma). The formula for the population variance is where X = individual value = population mean N — population size The standard deviation is the square root of the variance. The symbol for the population standard deviation is u. The corresponding formula for the population standard deviation is.
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Step 1 step 2 step 3 Find the variance and standard deviation for brand B paint data in Example 3—18. The months were 35, 45, 30, 35, 40, 25 Solution —10 Find the mean. EA' 35 + 45 + 30 + 35 + 40+25 210 = — 35 Subtract the mean from each value, and place the result in column B of the table. Square each result and place the squares in column C of the table. 35 45 30 35 25 10 25 25 100.
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Standard Deviation. Formula for the Sample Standard Deviation The standard deviation ofa sample (denoted by s) is s2 = 1 where X = individual value = sample mean n = sample size.
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Objectives Aner this chapter. you shmald be abk to Use the ore-way ANOVA to detemvne there a difference •nong three or more rnems. which mems differ, uung he Sct•Hfe or Tukey test rf he roll retected in the ANOVA Use the two-way ANOVA to determirE f there is a dtfference rnul effects or Analysis of Variance Outline 12—1 0*Way k'Osis ofVuiance 1.2-2 the TIAeyTest 12—3 Two-Way Etatysis ofWrOnce Summary.