Question

A researcher used a one-factor ANOVA for independent samples to test the effectiveness of four teaching methods for autistic children. The experiment was conducted with four samples of n = 12 autistic children in each group. The results of the analysis are shown in the following summary table. Source SS df MS Between Treatments ____ ____ ____ F = 5.00 Within Treatments 88 ____ ____ Total ____ ____

A. Fill in all missing values in the table. Show your work (i.e., all computational steps for finding the missing values). Hint: start with the df values and figure out the rest by solving simple equations with one unknown value (refer to the computational formulas for df, MS & F statistic).

B. Do these data indicate any significant differences among the four teaching methods (assume p < .05)? Your answer should include: the null hypothesis H0 & the alternative hypothesis H1 the critical F value used for the decision about H0 if the difference is statistically significant, compute the effect size, η2 the conclusion in APA style format.

Answer 1

ANSWER:

Given that,

a)

Since there are 4 different groups so we have k=4. Therefore degree of freedoms are:

Total number of observations is N = 12*4=48

Now

From F test statistics is

Following is the completed ANOVA table:

Source	SS	df	MS	F
Between treatments	10*3=30	3	5*2=10	5
Within Treatments	88	44	88/44=2
Total	118	47

b)

Hypotheses are:

H0: There is no significant difference among the four teaching method.

Ha: There is a significant difference among the four teaching method.

Critical value of F is : 2.816

Since F> 2.816 so we reject the null hypothesis.

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APA style: