Homework Help is Here – Start Your Trial Now!
Math
Statistics
A researcher conducted a repeated measures study comparing three treatment conditions. Refer to attached images and tale to answer a to d.   Mean Std. Deviation N Treatment I 1.00 1.414 5 Treatment II 5.00 2.345 5 Treatment III 6.00 1.581 5     In APA format, report the F-ratio related to the treatment effect: Is this treatment effect significant? What is the partial η2  value for the treatment effect? Is this a weak, moderate, or strong effect?

A researcher conducted a repeated measures study comparing three treatment conditions. Refer to attached images and tale to answer a to d.   Mean Std. Deviation N Treatment I 1.00 1.414 5 Treatment II 5.00 2.345 5 Treatment III 6.00 1.581 5     In APA format, report the F-ratio related to the treatment effect: Is this treatment effect significant? What is the partial η2  value for the treatment effect? Is this a weak, moderate, or strong effect?

MATLAB: An Introduction with Applications
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
icon
Related questions
Question

A researcher conducted a repeated measures study comparing three treatment conditions. Refer to attached images and tale to answer a to d.

  Mean Std. Deviation N
Treatment I 1.00 1.414 5
Treatment II 5.00 2.345 5
Treatment III 6.00 1.581 5

 

 

In APA format, report the F-ratio related to the treatment effect:

Is this treatment effect significant?

What is the partial η2  value for the treatment effect?

Is this a weak, moderate, or strong effect?

 

### Mauchly's Test of Sphericity **Measure:** MEASURE_1 | Within Subjects Effect | Mauchly's W | Approx. Chi-Square | df | Sig. | Greenhouse-Geisser | Huynh-Feldt | Lower-bound | |------------------------|-------------|---------------------|----|-----|--------------------|-------------|-------------| | treatment | 0.360 | 3.065 | 2 | 0.216| 0.610 | 0.737 | 0.500 | **Explanation:** Mauchly's test is utilized to verify the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix. This means it checks sphericity, which is the condition where variances of the differences between all combinations of related groups (levels) are equal. - **Design:** - Intercept - Within Subjects Design: treatment - **Notes:** - Mauchly's W is the test statistic. - Approx. Chi-Square indicates the Chi-Square approximation. - df stands for degrees of freedom. - Sig. indicates the p-value for the test. - Greenhouse-Geisser and Huynh-Feldt are used to adjust the degrees of freedom for the averaged tests of significance due to violations of sphericity. Corrected tests are found in the Tests of Within-Subjects Effects table. - Lower-bound provides the minimum possible value of epsilon, a measure related to the degree of non-sphericity. This test is crucial in ensuring the validity of within-subjects ANOVA results and corrections are applied when sphericity is violated.
Transcribed Image Text:### Mauchly's Test of Sphericity **Measure:** MEASURE_1 | Within Subjects Effect | Mauchly's W | Approx. Chi-Square | df | Sig. | Greenhouse-Geisser | Huynh-Feldt | Lower-bound | |------------------------|-------------|---------------------|----|-----|--------------------|-------------|-------------| | treatment | 0.360 | 3.065 | 2 | 0.216| 0.610 | 0.737 | 0.500 | **Explanation:** Mauchly's test is utilized to verify the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix. This means it checks sphericity, which is the condition where variances of the differences between all combinations of related groups (levels) are equal. - **Design:** - Intercept - Within Subjects Design: treatment - **Notes:** - Mauchly's W is the test statistic. - Approx. Chi-Square indicates the Chi-Square approximation. - df stands for degrees of freedom. - Sig. indicates the p-value for the test. - Greenhouse-Geisser and Huynh-Feldt are used to adjust the degrees of freedom for the averaged tests of significance due to violations of sphericity. Corrected tests are found in the Tests of Within-Subjects Effects table. - Lower-bound provides the minimum possible value of epsilon, a measure related to the degree of non-sphericity. This test is crucial in ensuring the validity of within-subjects ANOVA results and corrections are applied when sphericity is violated.
The table titled "Tests of Within-Subjects Effects" is related to the measure named "MEASURE_1." It provides statistical results for a repeated measures analysis of variance (ANOVA). The table is divided into two main sources: "treatment" and "Error(treatment)." Each source has several corrections applied for sphericity: Sphericity Assumed, Greenhouse-Geisser, Huynh-Feldt, and Lower-bound. ### Explanation of Columns: - **Source**: Indicates the variable being analyzed. Two sources are noted: the main effect of "treatment" and its associated error. - **Type III Sum of Squares**: Measures the total variability for the source. It is constant (70.000) for treatment and (10.000) for error across all corrections. - **df (degrees of freedom)**: Indicates the number of independent values. For treatment, it varies depending on the correction method (2, 1.220, 1.474, 1.000), while for error, it remains at 8 across corrections. - **Mean Square**: Calculated by dividing the Type III Sum of Squares by df, representing an average amount of variability. Varies across methods, showing highest value for Lower-bound under treatment (70.000). - **F**: The F-ratio, which compares the model to the error, showing a value of 28.000 across all corrections for treatment. - **Sig. (Significance)**: The p-value indicating statistical significance, with values ranging between <.001 and .006 for treatment, suggesting significant effects. - **Partial Eta Squared**: Provides a measure of effect size. It is consistently .875 for treatment across methods, indicating a large effect size. This table helps assess the influence of the "treatment" factor, demonstrating significant results across different corrections for sphericity.
Transcribed Image Text:The table titled "Tests of Within-Subjects Effects" is related to the measure named "MEASURE_1." It provides statistical results for a repeated measures analysis of variance (ANOVA). The table is divided into two main sources: "treatment" and "Error(treatment)." Each source has several corrections applied for sphericity: Sphericity Assumed, Greenhouse-Geisser, Huynh-Feldt, and Lower-bound. ### Explanation of Columns: - **Source**: Indicates the variable being analyzed. Two sources are noted: the main effect of "treatment" and its associated error. - **Type III Sum of Squares**: Measures the total variability for the source. It is constant (70.000) for treatment and (10.000) for error across all corrections. - **df (degrees of freedom)**: Indicates the number of independent values. For treatment, it varies depending on the correction method (2, 1.220, 1.474, 1.000), while for error, it remains at 8 across corrections. - **Mean Square**: Calculated by dividing the Type III Sum of Squares by df, representing an average amount of variability. Varies across methods, showing highest value for Lower-bound under treatment (70.000). - **F**: The F-ratio, which compares the model to the error, showing a value of 28.000 across all corrections for treatment. - **Sig. (Significance)**: The p-value indicating statistical significance, with values ranging between <.001 and .006 for treatment, suggesting significant effects. - **Partial Eta Squared**: Provides a measure of effect size. It is consistently .875 for treatment across methods, indicating a large effect size. This table helps assess the influence of the "treatment" factor, demonstrating significant results across different corrections for sphericity.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS