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FIRST INCLASS ANOVA EXAMPLE WITH WRITEUP
Let's say we have three different ways of teaching columnar addition. One way emphasizes
rote memorization of a sequence of steps, one way uses manipulatives such as Popsicle sticks,
and the last way uses a calculator. We teach 3 groups of 2nd graders, 5 to a group for a whole
semester, then give a posttest of 20 addition problems. Here are the scores of each group:
ROTE
7
5
3
4
1
Sum of X = 20
Mean = 4
MANIP
5
9
12
12
7
Sum of X = 45
Mean = 9
CALCULAT
21
15
17
18
14
Sum of X = 85
Mean = 17
1. Write the research hypothesis in English. In the populations from which the samples were drawn,
there are differences in at least one pair of mean math scores across the three classes (rote method,
mainipulatives method, and calculator method).
2. Write the null hypothesis in English: In the populations from which the samples were drawn,
there are no differences in mean math scores across the three classes (rote method, mainipulatives
method, and calculator method).
3. Write the name of the statistical test you think is appropriate.
One way ANOVA followed by a multiple comparison test.
4. Write a narrative paragraph or two summarizing the results, assuming no table in the article. Be
sure to indicate whether one class scored higher than any other as well as how each class did relative
to the others.
Three second-grade classes were taught columnar addition for a semester by three different methods.
After instruction, a one-way analysis of variance (ANOVA) was conducted on the mean addition
scores of the three groups of participants. One group was taught using the rote memory method (M =
4.00, SD = 2.24), one group was taught with manipulatives (M = 9.00, SD = 3.08), and one group was
taught with the calculator method (M = 17.00, SD = 2.74). This analysis produced a significant
analysis of variance (F(2,12) = 29.32, p <.001), indicating that there were differences among these
means. Eta squared was .83, indicating a strong effect size. Multiple comparisons with the Tukey
HSD test revealed that differences exist among all pairwise comparison of means with the mean for
the calculator group being highest, the mean for the manipulatives group in the middle, and the
mean for the rote memory group lowest (p < .05). Thus, the null hypothesis of no differences among
the means was rejected. This study produced support for the idea that the best method for teaching
columnar addition to second graders is the calculator method, while the poorest method is rote
memory.
8. Write a narrative paragraph or two summarizing the results, but including one or more tables.
Three second-grade classes were taught columnar addition for a semester by three different methods.
After instruction, a one-way analysis of variance (ANOVA) was conducted on the mean addition
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scores of the three groups of participants. Table 1 presents the means and standard deviations of
these three groups.
Class: The old, 4th edition of the APA manual called for the following to be placed in text at this
point, with the table itself on a separate sheet at the end of the manuscript:
_________________________
Insert Table 1 About Here
_________________________
Some journals still require this. Consult their author guidelines. The new, 5th edition has done away
with this. You should still place each table on a separate sheet at the end of the manuscript, but you
need not use "Insert Table About Here."
A one-way analysis of variance (ANOVA) was calculated on these mean scores. Table 2 presents the
source table for this analysis.
Again, the old manual would require:
_________________________
Insert Table 2 About Here
_________________________
Inspection of this table reveals a significant F ratio, indicating that the three means were not equal.
Eta squared was .83, indicating a strong effect size. Tukey's test for Honestly Significant Differences
(HSD) was then calculated to determine which means differed. This test revealed significant
differences among all pairs of means, with the mean for the calculator group being highest, the mean
for the manipulatives group in the middle, and the mean for the rote memory group lowest. Thus, the
null hypothesis was rejected, and the research hypothesis for the study was accepted. This study
produced support for the idea that the best method for teaching columnar addition to second graders
is the calculator method, while the poorest method is rote memory.
NOTE: THE TABLES GO LAST IN THE MANUSCRIPT, AFTER THE REFERENCE PAGE/S,
ONE TABLE TO A PAGE, DOUBLE-SPACED, NO VERTICAL LINES, PAGES
CONTINUOUSLY NUMBERED WITH THE REST OF THE MANUSCRIPT.
Table 1
Mean Number of Correct Answers for Three Groups of Second Grade Students on a Test of Columnar
Addition
__________________________________________________________________________________
Group
n
M
SD
__________________________________________________________________________________
Rote Memory
5
4.00
2.24
Manipulatives
5
9.00
3.08
Calculator
5
17.00
2.74
__________________________________________________________________________________
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Table 2
Analysis of Variance of Math Scores After Three Different Methods of Instruction
________________________________________________________________________
Source
SS
df
MS
F
p
_______________________________________________________________
Between
Within
Total
430.30
2
215.00
88.00
12
7.33
518.00
14
29.32
.001
________________________________________________________________________