Multiple Comparisons Now I want to investigate which differences are significant. Produce the ANOVA table you hand-calculated above in RGuroo or R and report the output. Use it to complete this work. Simultaneous Confidence Intervals using the Bonferroni Method Our α = 0.05 must be divided among the m pairs. Write out each pair among our four treatments and their mean differences. ⚫ (R1, G2) ⚫ (R1, B3) ⚫ (R1, U4) ⚫ (G2, B3) ⚫ (G2, U4) ⚫ (B3, U4) With m = 6 pairs, we will use the formula t (x² - x) ± + MSE 1 + n n (k(k-1)) In addition, use the error degrees of freedom as the degrees of freedom. Construct six simultaneous Bonferroni Confidence Interval. Which population means significantly differ? x-bar 1 = red, x-bar 2 = green, x-bar 3 = blue, x-bar4 = undyed 1. x-barl -x-bar2 = 102 - 105 = -3 +/- 5.68 * √12(+³½³) = -7.63, 1.63 2. x-bar1 -x-bar3 = 102-104 = -2 3. x-barl -x-bar4 = 102 - 111 = −9 +/- 5.68* √12(1½ + ½ ½) = −6.64, 2.64 +/- 5.68 * √/12(1½ ½ + ½ ½) = −13.64, −4.36 |12 ( 1 + 1) == 4. x-bar2 x-bar3 = 105-104 = 1 +/- 5.68 * 5. x-bar2 x-bar4 105-111 = -6 +/- 5.68* 1 = -3.43, 5.64 12(+) = -10.64,−1.36, 6. x-bar3 −x-bar4 = 104-111 = −7 +/- 5.68* √12(³½³½ + ½³½³) = = -11.64, -2.36 Half of the pairs do not contain zeros, thus indicating significant differences in the effects on the breaking strength of cotton thread Tukey's Honest Significant Differences (HSD) Method Then use RGuroo or R to produce all six of Tukey's Honest Significant Differences (HSD) confidence intervals. Provide the output. Which population means significantly differ? Lastly, compare the results of both methods. 7
Multiple Comparisons Now I want to investigate which differences are significant. Produce the ANOVA table you hand-calculated above in RGuroo or R and report the output. Use it to complete this work. Simultaneous Confidence Intervals using the Bonferroni Method Our α = 0.05 must be divided among the m pairs. Write out each pair among our four treatments and their mean differences. ⚫ (R1, G2) ⚫ (R1, B3) ⚫ (R1, U4) ⚫ (G2, B3) ⚫ (G2, U4) ⚫ (B3, U4) With m = 6 pairs, we will use the formula t (x² - x) ± + MSE 1 + n n (k(k-1)) In addition, use the error degrees of freedom as the degrees of freedom. Construct six simultaneous Bonferroni Confidence Interval. Which population means significantly differ? x-bar 1 = red, x-bar 2 = green, x-bar 3 = blue, x-bar4 = undyed 1. x-barl -x-bar2 = 102 - 105 = -3 +/- 5.68 * √12(+³½³) = -7.63, 1.63 2. x-bar1 -x-bar3 = 102-104 = -2 3. x-barl -x-bar4 = 102 - 111 = −9 +/- 5.68* √12(1½ + ½ ½) = −6.64, 2.64 +/- 5.68 * √/12(1½ ½ + ½ ½) = −13.64, −4.36 |12 ( 1 + 1) == 4. x-bar2 x-bar3 = 105-104 = 1 +/- 5.68 * 5. x-bar2 x-bar4 105-111 = -6 +/- 5.68* 1 = -3.43, 5.64 12(+) = -10.64,−1.36, 6. x-bar3 −x-bar4 = 104-111 = −7 +/- 5.68* √12(³½³½ + ½³½³) = = -11.64, -2.36 Half of the pairs do not contain zeros, thus indicating significant differences in the effects on the breaking strength of cotton thread Tukey's Honest Significant Differences (HSD) Method Then use RGuroo or R to produce all six of Tukey's Honest Significant Differences (HSD) confidence intervals. Provide the output. Which population means significantly differ? Lastly, compare the results of both methods. 7
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
Help! I'm not sure how to do the tukey's part I'm very confused please help!
Transcribed Image Text:Multiple Comparisons
Now I want to investigate which differences are significant. Produce the ANOVA table you
hand-calculated above in RGuroo or R and report the output. Use it to complete this work.
Simultaneous Confidence Intervals using the Bonferroni Method
Our α = 0.05 must be divided among the m pairs. Write out each pair among our four treatments
and their mean differences.
⚫ (R1, G2)
⚫
(R1, B3)
⚫ (R1, U4)
⚫
(G2, B3)
⚫ (G2, U4)
⚫ (B3, U4)
With m = 6 pairs, we will use the formula
t
(x² - x) ± +
MSE
1
+
n
n
(k(k-1))
In addition, use the error degrees of freedom as the degrees of freedom.
Construct six simultaneous Bonferroni Confidence Interval. Which population means
significantly differ?
x-bar 1 = red, x-bar 2 = green, x-bar 3 = blue, x-bar4 = undyed
1. x-barl -x-bar2 = 102 - 105 = -3 +/- 5.68 * √12(+³½³) = -7.63, 1.63
2. x-bar1 -x-bar3 = 102-104 = -2
3. x-barl -x-bar4 = 102 - 111 = −9
+/- 5.68* √12(1½ + ½ ½) = −6.64, 2.64
+/- 5.68 * √/12(1½ ½ + ½ ½) = −13.64, −4.36
|12 ( 1 + 1) ==
4. x-bar2 x-bar3 = 105-104 = 1 +/- 5.68 *
5. x-bar2 x-bar4 105-111 = -6 +/- 5.68*
1
= -3.43, 5.64
12(+) = -10.64,−1.36,
6. x-bar3 −x-bar4 = 104-111 = −7 +/- 5.68* √12(³½³½ + ½³½³) =
= -11.64, -2.36
Half of the pairs do not contain zeros, thus indicating significant differences in the effects
on the breaking strength of cotton thread
Tukey's Honest Significant Differences (HSD) Method
Then use RGuroo or R to produce all six of Tukey's Honest Significant Differences (HSD)
confidence intervals. Provide the output. Which population means significantly differ? Lastly,
compare the results of both methods.
7
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