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Analysis of Variance Table Essays

Table 1
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.

SYNTAX
ONEWAY
IQ BY ENGL
/MISSING ANALYSIS
/POSTHOC = TUKEY ALPHA(.05).

OUTPUT Files
ANOVA

IQ Score

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

Multiple Comparisons

Dependent Variable: IQ Score
Tukey HSD

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.

IQ Score

Tukey HSD
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.

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