Determine mean for each group

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Lesson 3
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• Determine mean for each group
• Compact cars
• Midsize cars
• Full-size cars

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• Determine Test Statistic, F
• F MSTR / MSE k-1 and n-k d.f.
• Calculate p-value
• If p lt alpha, reject null hypothesis

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• Summarize data in an ANOVA table

SOURCE DF SS MS F p
Factor
Error
Total
SST SSTR SSE
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Example 2

• The City Resource Recovery Co. (CRRC) collects
  the waste discarded by households in a region.
  The waste must be separated into metals, paper,
  plastic and glass. In planning for the equipment
  needs to collect and process the garbage, CRRC
  uses the sample information below. The weights
  are in pounds. At a significance level of 5,
  test the claim that the four specified garbage
  population have the same mean.

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Metal Paper Plastic Glass
Sample size, n 62 62 62 62
Mean 2.218 9.428 1.911 3.752
Std. Dev 1.001 4.168 1.065 3.108
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• Factor weight
• Treatment levels are 4 populations
• Mu (sub 1) mean weight of all metal waste
• Null hypothesis
• Alternative hypothesis

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ANOVA TABLE
Source DF SS MS F p
Factor
Error
Total
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• Conclusion

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Fishers LSD (Least Significant Difference)

• ONLY USED if you reject null hypothesis
• If we reject the null and conclude that not all
  population means are the same, we still dont
  know exactly where those differences lie. We
  could do individual 2-sample t-tests on each pair
  of population means OR a better way (and easier)
  is to calculate the difference in means and
  compare it to Fishers LSD statistic.

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• Test Stat
• Reject
• LSD

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Example 2 cont.
Populations Dif. Of means LSD Difference?
Metal Paper (1 2)
Metal Plastic (1 3)
Metal Glass (1 4)
Paper Plastic (2 3)
Paper Glass (2 4)
Plastic Glass (3 4)