Question

In: Statistics and Probability

This question uses the "Morphine" data set, available on Canvas. As usual, you have been randomly...

This question uses the "Morphine" data set, available on Canvas. As usual, you have been randomly assigned one of 10 versions of this data. Your version is 3.

2.3          M_S

3.5          M_S

1.1          M_S

8.1          M_S

2.4          M_S

1.9          M_S

4.8          M_S

8.6          M_S

3              M_M

11.6        M_M

12.5        M_M

4.8          M_M

9.4          M_M

10           M_M

12.5        M_M

19.4        M_M

13.4        S_S

6.1          S_S

14.8        S_S

5.2          S_S

20.2        S_S

1.6          S_S

8.9          S_S

20.3        S_S

27.1        S_M

19           S_M

35.4        S_M

20           S_M

25.7        S_M

17.5        S_M

25.4        S_M

17           S_M

24.4        M_M(new)

26.6        M_M(new)

38.8        M_M(new)

31.1        M_M(new)

20.4        M_M(new)

33.4        M_M(new)

25.6        M_M(new)

29.5        M_M(new)

1. Use Analyze / Fit Y by X to tell JMP what your predictor and response variables are. Then select Means / ANOVA from the drop down menu. Report the values of the following statistics:

a. SSG (JMP calls this "Treatment sum of squares"):

b. SSE:

c. MSG:

d. MSE:

e. The test statistic that tests H0:μM_S = μM_M = μS_S = μS_M = μM_M new:

2. Based on the result of this analysis, we can say (select all that apply):

We reject H0 and conclude that all group means are equal

We reject H0 and conclude that all group means differ from one another

We reject H0 and conclude that at least one group mean differs from the rest

The test statistic is bigger than we'd expect it to be if all group means were equal

The test statistic is smaller than we'd expect it to be if all group means were equal

The test statistic is about what we'd expect it to be if all group means were equal

The average between group variation is large relative to the average within group variation

The average between group variation is small relative to the average within group variation

The average between group variation is not very different from the average within group variation

3. From the "Oneway Analysis" drop down menu, select Compare Means / Each Pair, Student's t.

a. Select the pairwise comparisons that are significant, using a comparison-wise error rate of α=0.05

μM_S - μM_M

μM_S - μS_S

μM_S - μS_M

μM_S - μM_M(new)

μM_M - μS_S

μM_M - μS_M

μM_M - μM_M(new)

μS_S - μS_M

μS_S - μM_M(new)

μS_M - μM_M(new)

Solutions

Expert Solution

One-way ANOVA: Latency versus C2

Source DF SS MS F P
C2 4 3232.7 808.2 26.20 0.000
Error 35 1079.6 30.8
Total 39 4312.2

1. a. SSG=3232.7 b. SSE=1079.6 c. MSG=808.2 d. MSE=30.8 e. F=26.20

2. Since p-value<0.05, We reject H0 and conclue that at least one group mean differs from the rest.

3.

Grouping Information Using Fisher Method

C2 N Mean Grouping
M_M(new) 8 27.938 A
S_M 8 24.087 A
S_S 8 10.588 B
M_M 8 9.825 B C
M_S 8 4.575 C

Means that do not share a letter are significantly different.


Fisher 95% Individual Confidence Intervals
All Pairwise Comparisons among Levels of C2

Simultaneous confidence level = 72.67%


C2 = M_M subtracted from:

C2 Lower Center Upper ---------+---------+---------+---------+
M_M(new) 12.475 18.113 23.750 (---*---)
M_S -10.887 -5.250 0.387 (---*--)
S_M 8.625 14.262 19.900 (---*--)
S_S -4.875 0.763 6.400 (---*--)
---------+---------+---------+---------+
-15 0 15 30


C2 = M_M(new) subtracted from:

C2 Lower Center Upper ---------+---------+---------+---------+
M_S -29.000 -23.363 -17.725 (--*---)
S_M -9.487 -3.850 1.787 (--*---)
S_S -22.987 -17.350 -11.713 (--*---)
---------+---------+---------+---------+
-15 0 15 30


C2 = M_S subtracted from:

C2 Lower Center Upper ---------+---------+---------+---------+
S_M 13.875 19.512 25.150 (---*---)
S_S 0.375 6.013 11.650 (---*---)
---------+---------+---------+---------+
-15 0 15 30


C2 = S_M subtracted from:

C2 Lower Center Upper ---------+---------+---------+---------+
S_S -19.137 -13.500 -7.863 (---*---)
---------+---------+---------+---------+
-15 0 15 30

c.

Level N Mean
M_M 8 9.825  
M_M(new) 8 27.938  
M_S 8 4.575  
S_M 8 24.087  
S_S 8 10.588  

d.

Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of C2

Individual confidence level = 99.32%


C2 = M_M subtracted from:

C2 Lower Center Upper +---------+---------+---------+---------
M_M(new) 10.121 18.113 26.104 (----*----)
M_S -13.242 -5.250 2.742 (----*----)
S_M 6.271 14.262 22.254 (----*----)
S_S -7.229 0.763 8.754 (----*----)
+---------+---------+---------+---------
-32 -16 0 16


C2 = M_M(new) subtracted from:

C2 Lower Center Upper +---------+---------+---------+---------
M_S -31.354 -23.363 -15.371 (----*----)
S_M -11.842 -3.850 4.142 (----*----)
S_S -25.342 -17.350 -9.358 (----*----)
+---------+---------+---------+---------
-32 -16 0 16


C2 = M_S subtracted from:

C2 Lower Center Upper +---------+---------+---------+---------
S_M 11.521 19.512 27.504 (----*----)
S_S -1.979 6.013 14.004 (----*----)
+---------+---------+---------+---------
-32 -16 0 16


C2 = S_M subtracted from:

C2 Lower Center Upper +---------+---------+---------+---------
S_S -21.492 -13.500 -5.508 (----*----)
+---------+---------+---------+---------
-32 -16 0 16


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