Question

A researcher is interested in whether the phonics method of teaching reading is more or less effective than the sight method, depending on what grade the child is in. Twenty children were randomly selected from each of three grades: kindergarten (K), first grade (1), and second grade. Achievement was measured in terms of reading comprehension where higher scores indicate better comprehension. Within each grade, 10 children were assigned to each of two methods of teaching reading - phonics or sight. The data are as follows:

                        Grade Levels

                        K         1          2                                              K         1                2

                        14        25        49                                            17        35            34

                        20        29        49                                            22        36            33

                        16        27        46                                            19        40            34

Sight    21        31        46                   Phonics           20        34            39

                        20        27        44                                            26        37            38

                        14        34        43                                            18        41            33

                        21        32        50                                            26        42            35

                        23        34        43                                            18        33            42

                        14        35        48                                            25        34            42

                        15        28        52                                            23        43            38

1. State the Null hypotheses for each main effect and interaction – 5 points
2. Present the means and SD for each level of each factor– 5 points.
3. Test the null hypothesis for both main effects and interactions and present the ANOVA source table with all relevant statistics– 15 points.

Tests of Between-Subjects ANOVA source Table
Dependent Variable: RC
Source	Type III Sum of Squares	df	Mean Square	F	Sig.	Partial Eta Squared
method
grade
method * grade
Error
Total
Corrected Total
a. R Squared = (Adjusted R Squared = . Sig = 0 means p is < .001. SPSS takes out the probability value to 8 decimals. So, reporting Sig as .000 means the probability (p) is less than or below the .001 level.

4. Specify all variables– 5 points.
5. Compute, report and explain results from the HSD post hoc follow-up test– 10 points..
6. Present a graph of the interaction of the two factors– 5 points.
7. Write a statement as to your conclusions– 5 points..

Note. This is a Two-Way ANOVA (i.e., 2 IVs). One IV has two levels and one IV has three levels. Thus, a 2 X 3 ANOVA that will produce 6 cell means, 2 row means and 3 column means.

Answer 1

SOlUTION

SUMMARY	K	Grade1	Grade2	Total
Count	10	10	10	30
Sum	178	312	470	960
Average	17.8	31.2	47	32
Variance	12.4	17.29	9.56	159.52
Count	10	10	10	30
Sum	214	375	368	957
Average	21.4	37.5	36.8	31.9
Variance	12.04	13.61	12.18	68.85
Total
Count	20	20	20
Sum	392	687	838
Average	19.6	34.35	41.9
Variance	14.99	25.08	37.67
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	0.15	1	0.15	0.012	0.914	4.020
Columns	5145.7	2	2572.85	200.280	0.000	3.168
Interaction	783.3	2	391.65	30.487	0.000	3.168
Within	693.7	54	12.85
Total	6622.85	59

Main Effects:

There is no significant difference between Sight and Phonics as the p-value is 0.914, which is greater than 0.05.

Between the grades K grade 1 and grade 2 there is a significant difference, the p-value associated with it is 0.000 less than 0.05.

Interactions: The interaction is also significant as the p-value genrated is 0.000 which is less tahn 0.05.

for d-e, refer to the 2 images below.