1. Using the LEAD dataset (and STATA), conduct an analysis of variance to determ

Question

1. Using the LEAD dataset (and STATA), conduct an analysis of variance to determine if the response variable performance IQ (IQP) differs by the subject’s lead group (LEAD_GRP).

2. If a difference exists in the mean performance IQ over the three levels of lead exposure, conduct a multiple comparison test and explain the difference you detect.

Here's the excel link for the data --> https://drive.google.com/open?id=1kaJlYEZWhZdCZUYdAFmv6PNTMjdM4e4n

Here's the PDF link for the data dictionary --> https://drive.google.com/open?id=1XcWQSRalbbxkEOQzJ6O2Iy980ssafO5W

Explanation / Answer

in every respected we consider significance as 0.05 , and we have the ANOVA table as

One-way ANOVA: iqp versus lead_grp

Source DF SS MS F P
lead_grp 2 1774 887 3.62 0.030
Error 121 29688 245
Total 123 31462

S = 15.66 R-Sq = 5.64% R-Sq(adj) = 4.08%

here p-value=0.03<0.05 so we can reject H0 that is all groups are not has the same effect. hence there is significant effect of gropus.

b) now will procceds to the multiple comparison test by Tukey

Individual 95% CIs For Mean Based on
Pooled StDev
Level N Mean StDev -----+---------+---------+---------+----
1 78 102.71 16.79 (------*------)
2 24 95.67 11.34 (-----------*------------)
3 22 94.14 15.48 (------------*------------)
-----+---------+---------+---------+----
90.0 95.0 100.0 105.0

Pooled StDev = 15.66

Grouping Information Using Tukey Method

lead_grp N Mean Grouping
1 78 102.71 A
2 24 95.67 A
3 22 94.14 A

Means that do not share a letter are significantly different.

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

Individual confidence level = 98.09%

lead_grp = 1 subtracted from:

lead_grp Lower Center Upper --+---------+---------+---------+-------
2 -15.73 -7.04 1.65 (----------*----------)
3 -17.55 -8.57 0.42 (----------*-----------)
--+---------+---------+---------+-------
-16.0 -8.0 0.0 8.0

lead_grp = 2 subtracted from:

lead_grp Lower Center Upper --+---------+---------+---------+-------
3 -12.51 -1.53 9.45 (-------------*-------------)
--+---------+---------+---------+-------
-16.0 -8.0 0.0 8.0

here we can easily seen that group A is significanly leager mean than other two groups. but the difference is not statistically significant as we can see from the above output all the confidence interval contains zero. so there is no significant difference between groups.

hence this contradicts the previous answer. the reason is there is difference of chance in significance level in b)

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