Analysis of Variance Table
Source SS df MS F η2 p
Between 3686.73 2 1843.367 12.99 0.16 <.05
Within 30217.231 213 141.860
The research question examined was “Are the IQ scores of students related to their 9th grade English level proficiency”. The hypothesis tested were:
H0: µremedial = µgeneral = µcollege
H1: The means are not all equal.
The assumptions for the analysis of variance (ANOVA) are a) the subjects are sampled randomly, (b) the groups are independent and (c) that null hypothesis has to be tested.
The results of the test indicated that it has no statistical significance since F computed is (12.99) lower than the F critical (19.49) which means that the null hypothesis is accepted. The strength of the relationship was determined by computing effect size which is by η2 0.16, according to Cohen (1988) this is fairly small and can be accounted for by the normal distribution of the sample population.
A follow up Tukey test was done to identify the difference in IQ scores in each English level; it was found that equal variances cannot be proven for this data thus an analysis of means showed that the average IQ score (M: 102.354) indicates that the student sample is performing well and that those who had college level status in English (111.0345) had higher IQ’s than the rest of the group. It was also found that the mean difference for the three English levels were significant at 0.05 level of confidence. It was found that IQ scores of those who had remedial, general and college English levels were significantly different from each other at 0.05 alpha, while as a whole there is no statistical relationship between English level and IQ.
IQ BY ENGL
/POSTHOC = TUKEY ALPHA(.05).
Sum of Squares df Mean Square F Sig. Between Groups 3686.734 2 1843.367 12.994 .000 Within Groups 30217.422 213 141.866 Total 33904.156 215
Dependent Variable: IQ Score
(I) 9th Grade English Level
(J) 9th Grade English Level
Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound Upper Bound Lower Bound Upper Bound Lower Bound College Prep General 8.87215(*) 2.41104 .001 3.1816 14.5627 Remedial 15.41327(*) 3.03165 .000 8.2579 22.5686 General College Prep -8.87215(*) 2.41104 .001 -14.5627 -3.1816 Remedial 6.54113(*) 2.28477 .013 1.1486 11.9337 Remedial College Prep -15.41327(*) 3.03165 .000 -22.5686 -8.2579 General -6.54113(*) 2.28477 .013 -11.9337 -1.1486 * The mean difference is significant at the .05 level.
9th Grade English Level N Subset for alpha = .05 12 3 1 Remedial 33 95.6212 General 154 102.1623 College Prep 29 111.0345 Sig. 1.0001.000 1.000 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.