Medhi,
Assuming that your dependent variables are multivariate normal, you may want to carry out a Multivariate Analysis of Variance (MANOVA) to test the significance of the Level, L1, and two-way Level by L1 interactions. Assuming that your multivariate effects are significant, you could then follow up with univariate ANOVAs for each dependent variable, and then follow-up post-hoc tests to determine which levels of the independent variables are significantly different. There are a couple of caveats to this advice:
1. I am a little puzzled as to how Word Frequency is measured as a single rating. If you have multiple ratings for specific words, or classes of words, then the assumption of normality might not apply to your raw data. You may need to transform frequency count data (e.g., by a log transform). If you are maintaining frequency counts of multiple words or classes of words then you might have multiple Word Frequency variables, and hence you might have too many dependent variables to carry out a MANOVA with adequate statistical power.
2. It has been argued that it is not strictly necessary to obtain a significant MANOVA in order to carry out the univariate ANOVAs, although this practice is still quite common. A critical issue in running ANOVAs with multiple dependent variables is the risk of spuriously rejecting the Null Hypothesis in the process of carrying out multiple tests. The more appropriate way to address this issue is to use a more stringent alph level on the univariate ANOVAs, rather than requiring a significant MANOVA.
Perhaps it would be helpful to provide more information on the Word Frequency variable.
Best Regards,
Stephen Brand, Ph.D.
www.StatisticsDoc.com
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Mehdi Riazi
Sent: Saturday, December 31, 2011 3:05 AM
To: [hidden email]
Subject: Appropriate statistical analyses
Dear all,
Wish you all a healthy 2012. I appreciate your comments for the appropriate analyses for the following data set.
270 written scripts by test takers across three L1 backgrounds: A, B, & C are rated by trained and experienced raters at levels of 5, 6 & 7 as presented in the followig table.
| L1 | ||
Level | A | B | C |
5 | 30 | 30 | 30 |
6 | 30 | 30 | 30 |
7 | 30 | 30 | 30 |
To check the validity of the ratings we've analysed the scripts using some textual features such as Word Frequency, Syntactic complexity, and Cohesion. We now want to find out:
1) Is there a sig. difference between the scripts belonging to levels 5, 6, & 7 in terms of any of the three text features (WF, SC, and Cohesion)?
2) Is there a sig. difference between the scripts at the same level (5, e.g.) across the three L1s (A, B, & C) in terms of the three text features?
3) Is there a sig. difference between the scripts at the three levels (5, 6, 7) for each L1 (A, B, & C)?
Any suggetions for appropriate statistical anslyses to answer these RQs is much appreciated.
Regards;
Mehdi
--
Mehdi Riazi, PhD
Associate Professor & Director HDR
Department of Linguistics
Faculty of Human Sciences
Macquarie University NSW 2109
Room: C5A 575
Phone: +61(02) 98507951
Fax: +61(02) 98509199
www.ling.mq.edu.au
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