# Analysis of Variance Table

Table 1

Analysis of Variance Table

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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

(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.

IQ Score

Tukey HSD

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.