Analysis of Variance Results - Research Paper Example

Analysis of Variance Results Table 4. Analysis of Variance for ADD-like Behavior among Participants in the Remedial, General and College Preparatory English Levels.   SS df MS F d Sig. Between Groups 3476.35 2 1738.17 18.5 .72 < .001 Within Groups 20012.14 213 93.95 Total 23488.48 215 The research wanted to answer the question: “Is there a difference in the ADD-like symptoms among participants in the remedial, general, and college preparatory English levels?” In order to answer this question, the following research hypotheses were constructed: H0: µremedial = µgeneral = µcollegeprep H1: The means are not all equal.

When considering the results for an Analysis of Variance, certain assumptions have to be met. First, the normality of the data set must be established. However, the ANOVA provides great leeway when this assumption is violated as long as such a violation is not too serious. Second, equality of variances must be assumed. In cases where variances of the groups are unequal, adjustments are made on the critical values of F and the degrees of freedom in order to accommodate the inequality. The third assumption is that the expected values of the errors are zero and, lastly, the errors must be independent.

Table 4 shows that the ANOVA results were statistically significant, F(2, 213) = 18.5, p < .001. This indicates that the null hypothesis is to be rejected in favor of the alternative hypothesis, and that it may be concluded that there are differences in ADD-like symptoms among the three groups. The strength of the relationship between English level and ADD-like behavior, as indexed by d was strong, with English level accounting for 72% of the variance in ADD-like behavior scores. A follow up Tukey test was performed to examine pair-wise differences because equal variances can be assumed.

Findings indicate that those from the college preparatory group (M = 43.07, SD = 7.8) reported a significantly lower level of ADD like behavior compared with those from the general group (M = 53.81, SD = 9.5) and the remedial group (M = 56.97, SD = 11.7). There was no significant difference in the ADD-like behavior scores between the general group and the remedial group. Therefore, results from the ANOVA test found that participants enrolled in the college preparatory English level differed significantly on ADD-like behavior scores compared to both general English level and remedial English level participants, and that the difference between the groups was large, with college preparatory participants reporting lower ADD-like tendencies than the two other groups.

Oneway Notes Output Created 05-Nov-2011 13:56:58 Comments Input Data C:\Users\User\Documents\AR\Oct30 ADHD t test\Howell_dataset_cleaned.sav Active Dataset DataSet1 Filter Weight Split File N of Rows in Working Data File 216 Missing Value Handling Definition of Missing User-defined missing values are treated as missing. Cases Used Statistics for each analysis are based on cases with no missing data for any variable in the analysis. Syntax ONEWAY ADDSC BY ENGL /MISSING ANALYSIS /POSTHOC=TUKEY ALPHA(0.05). Resources Processor Time 00:00:00.

078 Elapsed Time 00:00:00.214 [DataSet1] C:\Users\User\Documents\AR\Oct30 ADHD t test\Howell_dataset_cleaned.sav ANOVA ADD-like behavior score (mean of 3) Sum of Squares df Mean Square F Sig. Between Groups 3476.346 2 1738.173 18.500 .000 Within Groups 20012.136 213 93.954 Total 23488.481 215 Post Hoc Tests Multiple Comparisons ADD-like behavior score (mean of 3) Tukey HSD (I) 9th Grade English Level (J) 9th Grade English Level Mean Difference (I-J) Std. Error Sig. dimension2 College Prep dimension3 General -10.73623* 1.96211 .

000 Remedial -13.90578* 2.46716 .000 General dimension3 College Prep 10.73623* 1.96211 .000 Remedial -3.16955 1.85935 .206 Remedial dimension3 College Prep 13.90578* 2.46716 .000 General 3.16955 1.85935 .206 *. The mean difference is significant at the 0.05 level. Multiple Comparisons ADD-like behavior score (mean of 3) Tukey HSD (I) 9th Grade English Level (J) 9th Grade English Level 95% Confidence Interval Lower Bound Upper Bound dimension2 College Prep dimension3 General -15.3672 -6.

1052 Remedial -19.7288 -8.0828 General dimension3 College Prep 6.1052 15.3672 Remedial -7.5580 1.2189 Remedial dimension3 College Prep 8.0828 19.7288 General -1.2189 7.5580 Homogeneous Subsets ADD-like behavior score (mean of 3) Tukey HSDa,b 9th Grade English Level N Subset for alpha = 0.05 1 2 dimension1 College Prep 29 43.0690 General 154 53.8052 Remedial 33 56.9747 Sig. 1.000 .293 Means for groups in homogeneous subsets are displayed. a. Uses Harmonic Mean Sample Size = 42.088. b.

The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error levels are not guaranteed.