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Comparing Birthweights: Tukey-Kramer and Bonferroni Methods, Study notes of Statistics

The results of a statistical analysis comparing birthweights among different smoking groups using the tukey-kramer and bonferroni methods. The analysis includes pairwise comparisons, individual confidence intervals, and significance tests. The document concludes that only the means of the nonsmoker and heavy smoker groups are significantly different.

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Uploaded on 07/23/2009

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STAT 529
Multiple Comparisons
The following output shows all pairwise comparisons (6 pairs) for the birthweight data,
controlling the familywise error rate at most 5% (familywise confidence level at least 95%) by
Tukey-Kramer method and Bonferroni method.
One-way ANOVA: Birthweight versus Smoking
Analysis of Variance for Birthwei
Source DF SS MS F P
Smoking 3 11.673 3.891 4.41 0.014
Error 23 20.304 0.883
Total 26 31.976
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev -------+---------+---------+---------
1 7 7.5857 0.9616 (------*------)
2 5 7.2400 0.9127 (-------*--------)
3 7 6.3286 1.1398 (------*-------)
4 8 6.0125 0.7200 (------*------)
-------+---------+---------+---------
Pooled StDev = 0.9396 6.0 7.0 8.0
1) Tukey-Kramer method
Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of Smoking
Individual confidence level = 98.90%
Smoking = 1 subtracted from:
Smoking Lower Center Upper ---------+---------+---------+---------+
2 -1.8668 -0.3457 1.1753 (---------*---------)
3 -2.6457 -1.2571 0.1314 (---------*--------)
4 -2.9176 -1.5732 -0.2288 (--------*-------)
---------+---------+---------+---------+
-1.5 0.0 1.5 3.0
Smoking = 2 subtracted from:
Smoking Lower Center Upper ---------+---------+---------+---------+
3 -2.4325 -0.9114 0.6096 (---------*---------)
4 -2.7084 -1.2275 0.2534 (---------*---------)
---------+---------+---------+---------+
-1.5 0.0 1.5 3.0
Smoking = 3 subtracted from:
Smoking Lower Center Upper ---------+---------+---------+---------+
4 -1.6605 -0.3161 1.0284 (--------*--------)
---------+---------+---------+---------+
-1.5 0.0 1.5 3.0
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STAT 529

Multiple Comparisons

The following output shows all pairwise comparisons (6 pairs) for the birthweight data,

controlling the familywise error rate at most 5% (familywise confidence level at least 95%) by

Tukey-Kramer method and Bonferroni method.

One-way ANOVA: Birthweight versus Smoking

Analysis of Variance for Birthwei Source DF SS MS F P Smoking 3 11.673 3.891 4.41 0. Error 23 20.304 0. Total 26 31. Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev -------+---------+---------+--------- 1 7 7.5857 0.9616 (------------) 2 5 7.2400 0.9127 (---------------) 3 7 6.3286 1.1398 (-------------) 4 8 6.0125 0.7200 (------------) -------+---------+---------+--------- Pooled StDev = 0.9396 6.0 7.0 8.

1) Tukey-Kramer method

Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons among Levels of Smoking

Individual confidence level = 98.90%

Smoking = 1 subtracted from:

Smoking Lower Center Upper ---------+---------+---------+---------+ 2 -1.8668 -0.3457 1.1753 (------------------) 3 -2.6457 -1.2571 0.1314 (-----------------) 4 -2.9176 -1.5732 -0.2288 (--------*-------) ---------+---------+---------+---------+ -1.5 0.0 1.5 3.

Smoking = 2 subtracted from:

Smoking Lower Center Upper ---------+---------+---------+---------+ 3 -2.4325 -0.9114 0.6096 (------------------) 4 -2.7084 -1.2275 0.2534 (------------------) ---------+---------+---------+---------+ -1.5 0.0 1.5 3.

Smoking = 3 subtracted from:

Smoking Lower Center Upper ---------+---------+---------+---------+ 4 -1.6605 -0.3161 1.0284 (--------*--------) ---------+---------+---------+---------+ -1.5 0.0 1.5 3.

The multiplier of Tukey-Kramer method is 2.76, which is 3.91 (the 95

th

percentile of the

studentized range distribution for 4 groups and 23(=27-4) degrees of freedom) divided by the

square root of 2. With the familywise confidence level at least 95%, only group 1 (nonsmoker)

and group 4 (heavy smoker) are significantly different in the means. The mean birthweight

of babies whose mothers never smoked is estimated to be .229 to 2.918 pounds larger than that of

babies with heavy smoking mothers.

2) Bonferroni method

Fisher 99.17% Individual Confidence Intervals All Pairwise Comparisons among Levels of Smoking

Simultaneous confidence level = 96.14%

Smoking = 1 subtracted from:

Smoking Lower Center Upper +---------+---------+---------+--------- 2 -1.9345 -0.3457 1.2431 (-------------------) 3 -2.7075 -1.2571 0.1932 (-----------------) 4 -2.9775 -1.5732 -0.1689 (---------*--------) +---------+---------+---------+--------- -3.0 -1.5 0.0 1.

Smoking = 2 subtracted from:

Smoking Lower Center Upper +---------+---------+---------+--------- 3 -2.5003 -0.9114 0.6774 (--------------------) 4 -2.7744 -1.2275 0.3194 (------------------) +---------+---------+---------+--------- -3.0 -1.5 0.0 1.

Smoking = 3 subtracted from:

Smoking Lower Center Upper +---------+---------+---------+--------- 4 -1.7204 -0.3161 1.0883 (--------*--------) +---------+---------+---------+--------- -3.0 -1.5 0.0 1.

Setting Fisher’s individual error rate at .05/6=.0083 in Minitab gives simultaneous confidence

intervals with Bonferroni adjustment. Bonferroni method results in the same conclusion as

Tukey-Kramer method in this case.

All pairwise comparisons can be graphically presented by underlining the groups, any pairs of

which are not significantly different.

Sample mean 6.01 6.33 7.24 7.

Group 4 3 2 1

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