Anova test help
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 Garter
 Posts: 15
 Joined: Fri Oct 12, 2007 7:58 pm
Anova test help
Can some please explain the results? What is the P or F Value and how can I reject the null hypothesis?
(The experiment is to test two popular anti bacterial agents in Petri dishes and see whether they indeed kill bacteria or not. Our hypothesis is that the two anti bacterial agents will indeed kill the bacteria and will not allow the bacteria to grow even in favorable conditions. The null hypothesis here, is the assertion that the mean diameter of the experimental discs is the same as the mean diameter of the control discs.)

Anova findings:
Source of Sum of d.f. Mean F
Variation Squares Squares
between 4166. 2 2083. 209.2
error 378.4 38 9.958
total 4544. 40
The probability of this result, assuming the null hypothesis, is less than .0001.
Group A: Number of items= 18
15.0 15.0 15.0 20.0 20.0 20.0 20.0 21.0 21.0 21.0 22.0 22.0 22.0 22.0 25.0 26.0 28.0 28.0
Mean = 21.278
95% confidence interval for Mean: 19.77 thru 22.78
Standard Deviation = 3.86
High = 28.00 Low = 15.00
Median = 21.00
Average Absolute Deviation from Median = 2.72
Clorox
Group B: Number of items= 5
10.0 10.0 14.0 20.0 22.0
Mean = 15.200
95% confidence interval for Mean: 12.34 thru 18.06
Standard Deviation = 5.59
High = 22.00 Low = 10.00
Median = 14.00
Average Absolute Deviation from Median = 4.40
Dial
Group C: Number of items= 18
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Mean = 0.0000
95% confidence interval for Mean: 1.506 thru 1.506
Standard Deviation = 0.00
High = 0.000 Low = 0.000
Median = 0.000
Average Absolute Deviation from Median = 0.00
Control
(The experiment is to test two popular anti bacterial agents in Petri dishes and see whether they indeed kill bacteria or not. Our hypothesis is that the two anti bacterial agents will indeed kill the bacteria and will not allow the bacteria to grow even in favorable conditions. The null hypothesis here, is the assertion that the mean diameter of the experimental discs is the same as the mean diameter of the control discs.)

Anova findings:
Source of Sum of d.f. Mean F
Variation Squares Squares
between 4166. 2 2083. 209.2
error 378.4 38 9.958
total 4544. 40
The probability of this result, assuming the null hypothesis, is less than .0001.
Group A: Number of items= 18
15.0 15.0 15.0 20.0 20.0 20.0 20.0 21.0 21.0 21.0 22.0 22.0 22.0 22.0 25.0 26.0 28.0 28.0
Mean = 21.278
95% confidence interval for Mean: 19.77 thru 22.78
Standard Deviation = 3.86
High = 28.00 Low = 15.00
Median = 21.00
Average Absolute Deviation from Median = 2.72
Clorox
Group B: Number of items= 5
10.0 10.0 14.0 20.0 22.0
Mean = 15.200
95% confidence interval for Mean: 12.34 thru 18.06
Standard Deviation = 5.59
High = 22.00 Low = 10.00
Median = 14.00
Average Absolute Deviation from Median = 4.40
Dial
Group C: Number of items= 18
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Mean = 0.0000
95% confidence interval for Mean: 1.506 thru 1.506
Standard Deviation = 0.00
High = 0.000 Low = 0.000
Median = 0.000
Average Absolute Deviation from Median = 0.00
Control
The overall Ftest for the particular 1way ANOVA design tests the null that all group means are equal against the alternative that at least one group mean is different. The overall Ftest doesn’t tell you which one (or more) mean is different, only that some mean is different. Group C looks dubious to me. I find it hard to believe there is absolutely no statistical variation between the observations. You can reject the overall null of equal means at the p=0.001 level, but I don’t believe the test is valid when it includes Group C. I also don’t understand the output listed at the top, which I assume is summarizing the overall Ftest. I can’t follow it very well. There is a moreorless standard format for the output of an Ftest that allows you to quickly identify the MSE due to groups, the residual MSE, and the Fstatistic and its df. Maybe they’re all there, but I don’t recognize them easily. You can test the significance of the difference between group means with ANOVA (sometimes called pairwise analysis—which is what I think canalon was getting at), but you need to do Fisher exact Ttests, I think they’re called, or some sort of contrast. It’s possible that the confidence intervals about the group means were meant to be used as contrasts, but I don’t know how they were calculated here. You need to spend some time staring at a statistics text book. My favorite is Afifi and Azen, which is probably out of print by now, but even Snedecor (yuck) would be helpful.
You might find the following useful: http://davidmlane.com/hyperstat/intro_ANOVA.html
There are several options for comparing the means within the context of an ANOVA. They are essentially, if not explicitly, ttests. The Fisher LSD (not the Exact testmy mistake) and the Tukey HSD are the two I'm most familiar with. There are several others discussed in the link. Most ANOVA software gives you the option to perform some kind of pairwise analysis of the group means. I still have my doubts about the validity of your Group C. It looks really odd to me.
There are several options for comparing the means within the context of an ANOVA. They are essentially, if not explicitly, ttests. The Fisher LSD (not the Exact testmy mistake) and the Tukey HSD are the two I'm most familiar with. There are several others discussed in the link. Most ANOVA software gives you the option to perform some kind of pairwise analysis of the group means. I still have my doubts about the validity of your Group C. It looks really odd to me.
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