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Suppose the director a drug rehabilitation center selected 30 individuals from the population of applicants to...

Suppose the director a drug rehabilitation center selected 30 individuals from the population of applicants to her program and randomly assigned 10 to treatment 1, 10 to treatment 2 and 10 to treatment 3. After 5 weeks of treatment, a manual dexterity test is administered for which a higher score indicates greater manual dexterity. Suppose the scores on the manual dexterity test are as follows:

Treatment 1

Treatment 2

Treatment 3

6

4

6

10

2

2

8

3

2

6

5

6

9

1

4

8

3

5

7

2

3

5

2

5

6

4

3

5

4

4
  1. State the assumptions necessary for an ANOVA
  2. State the null hypothesis in this study.
  3. State the alternate hypothesis in this study.
  4. Compute the ANOVA for the data using SPSS.
math   Statistics-And-Probability   
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Answer #1

(a) The number of assumpti ons are * Each group sample is drawn from a normally distributed populati on * All populations have a comm on variance * All samples are drawn independently of each other * Within each sample, the observations are sampled randomly and independently of each other * Factor effects are fixed model of ANOVA (b) The null hypothesis is that the three treatm ent means are equal (c) The altemative hypothesis is that the three treatment means are not equal (d) The Step-by-Step instructi ons to obtain One-way Anova output using SPSS17 Enter the data into the SPSS17 w orksheet * Click on Analyze Compare Means -One-way Anova. * Select the response vari able into the dependent list. * Select the factor variable into the factor Cick ok. The One-way Anova output using SPSSI

Oneway ANOVA Sum of Squares df Mean Square Si Between Groups Within Groups Total 86.667 60.000 146.667 43.33319.500 27 29 2.222

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Step1 The null and alternative hypotheses are There is no signficant ifference between the three treatment means There is signficant difference between the three treatm ent means Ho : μ1 = μ2 = μ3 Step2 The level of significance is a-0.05 Step3 The critical value of the F- test is If F 2 3.354131. Reject H0 otherwise do not reject Ho Step4 The formula for calculating the test statistic is MS MSgror 43.33333 2.222222 19.5 F 19.5 Step5 Decision Rule Since, the test stati stic is F-19.5> F We reject the null hypothesis Ho Hence, we conclude that the treatment treatm ent means differ Or There is signficant difference between the treatment means

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