The data below are from an independent-measures experiment comparing three different treatment conditions regarding attention scores. Treatment 1 Treatment 2 Treatment 3 0 2 4 0 3 2 0 1 4 3 3 3 0 2 4 0 1 4 n = n = n = N = T = T = T = G = 36 M = M = M = k = ∑X2 ∑X2 ∑X2 ∑X21,2,3 = 114 SS = SS = SS = Explain why an ANOVA should be used instead of a series of t tests to evaluate the mean differences among the three treatment conditions. Use an analysis of variance (ANOVA) with α = .05 to determine whether these data indicate any significant mean differences among the treatment conditions. State the hypothesis using symbols and words. Find critical region. Find degrees of freedom: Total Between Within Calculate the F-Ratio SS total SS within SS between MS between MS within F Ratio Compute η2, the percentage of variance accounted for by the treatments and state it in the context of the scenario Write the results of the analysis of variance as appropriate for a statistical report. Conduct Tukey's Honestly Significant Difference (HSD) Test Find q Conduct HSD Interpret HSD in the context of the scenario -- attention scores

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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The data below are from an independent-measures experiment comparing three different treatment conditions regarding attention scores.

Treatment 1	Treatment 2	Treatment 3
0	2	4
0	3	2
0	1	4
3	3	3
0	2	4
0	1	4
n =	n =	n =	N =
T =	T =	T =	G = 36
M =	M =	M =	k =
∑X²	∑X²	∑X²	∑X²_¹^,2,³^₌ 114
SS =	SS =	SS =

Explain why an ANOVA should be used instead of a series of t tests to evaluate the mean differences among the three treatment conditions.
Use an analysis of variance (ANOVA) with α = .05 to determine whether these data indicate any significant mean differences among the treatment conditions.
- State the hypothesis using symbols and words.
- Find critical region.
- Find degrees of freedom:
  - Total
  - Between
  - Within
- Calculate the F-Ratio
  - SS total
  - SS within
  - SS between
  - MS between
  - MS within
  - F Ratio
Compute η2, the percentage of variance accounted for by the treatments and state it in the context of the scenario
Write the results of the analysis of variance as appropriate for a statistical report.

Find q
Conduct HSD
Interpret HSD in the context of the scenario -- attention scores

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 + ...

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