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Determine mean for each group

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Lesson 3: Determine mean for each group Compact cars Midsize cars Full-size cars Determine Test Statistic, F F = MSTR / MSE; k-1 and n-k d.f. Calculate p-value If ... – PowerPoint PPT presentation

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Title: Determine mean for each group


1
Lesson 3
2
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3
  • Determine mean for each group
  • Compact cars
  • Midsize cars
  • Full-size cars

4
  • Determine Test Statistic, F
  • F MSTR / MSE k-1 and n-k d.f.
  • Calculate p-value
  • If p lt alpha, reject null hypothesis

5
  • Summarize data in an ANOVA table

SOURCE DF SS MS F p
Factor
Error
Total
SST SSTR SSE
6
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.

7
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
8
  • Factor weight
  • Treatment levels are 4 populations
  • Mu (sub 1) mean weight of all metal waste
  • Null hypothesis
  • Alternative hypothesis

9
ANOVA TABLE
Source DF SS MS F p
Factor
Error
Total
10
  • Conclusion

11
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.

12
  • Test Stat
  • Reject
  • LSD

13
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)
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