IIIIII6810555123012 G=48ΣX2 = 294T I=12 TII= 16 TIII= 20SS=526 SSII=530 SSIII=538Assume that the data are from an independent- measures study using three separate samples, each with n = 4 participants, and use an independent- measures ANOVA with an alpha level of .05 to test for signifi- cant differences among the three treatments.Nowassumethatthedataarefromarepeated-mea- sures study using one sample of n = 4 participants and use a repeated-measures ANOVA with a level of .05 to test for significant differences among the three treatments.

Name: IIIIII6810555123012 G=48ΣX2 = 294T I=12 TII= 16 TIII= 20SS=526 SSII=53
Uploaded: 2024-03-20T07:07:00.000Z
Channel: Bartleby
Description: IIIIII6810555123012 G=48ΣX2 = 294T I=12 TII= 16 TIII= 20SS=526 SSII=530 SSIII=538Assume that the data are from an independent- measures study using three separate samples, each with n = 4 participants, and use an independent- measures ANOVA with an a

For an independent measures study, following data is given: I II III 6 8 10 G=48…

Answered: I II III 6 8 10 5 5 5 1 2 3 0 1 2 G=48…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

I	II	III
6	8	10
5	5	5
1	2	3
0	1	2

G=48

ΣX2 = 294

T I=12 TII= 16 TIII= 20

SS=526 SSII=530 SSIII=538

Assume that the data are from an independent- measures study using three separate samples, each with n = 4 participants, and use an independent- measures ANOVA with an alpha level of .05 to test for signifi- cant differences among the three treatments.
Nowassumethatthedataarefromarepeated-mea- sures study using one sample of n = 4 participants and use a repeated-measures ANOVA with a level of .05 to test for significant differences among the three treatments.

Expert Solution

Step 1

For an independent measures study, following data is given:

I	II	III
6	8	10	G=48
5	5	5	∑X2=294
1	2	3
0	1	2
T=12	T=16	T=20
SS=26	SS=30	SS=38

Level of significance is α=0.05.

Step 2

Numbers of participants in each sample are n=4.

For the independent-measures study, the hypotheses are given below:

Null Hypothesis: There are no significant mean differences between treatments.

Alternate Hypothesis: There are significant mean differences between treatments.

Let k represents the numbers of treatments. Then,

k=3

Let N represents total numbers of participants, then

N=k×n=3×4=12

Then, degrees of freedom corresponding to SSbetween are:

dfbetween=k−1=3−1=2

Then, degrees of freedom corresponding to SSwithin are:

dfwithin=N−k=12−3=9

SSwithin is calculated as:

SSwithin=∑SS=26+30+38=94

Sum of squares between treatments is given as:

SSbetween= $\begin{array}{rcl} \sum \frac{T^{2}}{n} - \frac{G^{2}}{N} & = & \frac{{(12)}^{2}}{4} + \frac{{(16)}^{2}}{4} + \frac{{(20)}^{2}}{4} - \frac{{(48)}^{2}}{12} \\ = & 36 + 64 + 100 - 192 \\ = & 8 \end{array}$

F-ratio is calculated as:

$\begin{array}{rcl} F & = & \frac{\frac{S S b e t w e e n}{d f b e t w e e n}}{\frac{S S w i t h i n}{d f w i t h i n}} \\ = & \frac{\frac{8}{2}}{\frac{94}{9}} \\ = & \frac{4}{10.444} \\ = & 0.383 \end{array}$

From the table B.4B.4 of appendix B in the textbook, critical value corresponding to df=2,9 is 4.26.

Since, F-ratio is less than the critical value; therefore, fail to reject the null hypothesis and conclude that there are no significant mean differences between the three treatments.

Conclusion:

There are no significant mean differences between the three treatments.

Step by step

Solved in 3 steps

Knowledge Booster

$Hypothesis Tests and Confidence Intervals for Proportions$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions