Answered: Now assume that the data are from a…

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

The following data are from an experiment comparing three different treatment conditions

	Treatment
I	II	III	P
6	9	12	27	N = 18
8	8	8	24	G = 108
5	7	9	21	ΣX² = 800
0	4	8	12
2	3	4	9
3	5	7	15
M = 4	M = 6	M = 8
T = 24	T = 36	T = 48
SS =42	SS = 28	SS = 34

Now assume that the data are from a repeated- measures study using the same sample of n = 6 participants in all three treatment conditions. Use a repeated-measures ANOVA with α = .05 to test the significance of the mean differences. (follow the four-step procedure)

Compute partial eta square for part A. Report your results of the hypothesis test and effect size in APA format

Conduct a post hoc analysis for part A using HSD

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1

(A)

Step 2

Result Details
Source	Sum of Squares SS	Degree of freedom df	Mean Square MS	F Statistic (The F statistic formula is: F Statistic = variance of the group means / mean of the within group variances)
Between-treatments	48	2	24	F = 3.46154
Within-treatments	104	15	6.9333
Total	152	17

The f-ratio value is 3.46154. The p-value is 0.058066

Hypothesis Results : Conclusion

The p-value corresponding to the F-statistic of one-way ANOVA is higher than 0.05, suggesting that the treatments are not significantly different for that level of significance. The Tukey HSD test, as well as other multiple comparison tests like Scheffe or Bonferroni, might not narrow down which of the pairs of treatments are significantly different.

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