ANOVA Project
You will be researching one-way analysis of variance (ANOVA). One-way analysis of
variance is a method of testing the equality of three or more population means by analyzing
sample variances from these populations. You may use any resources that you like. If you
Google one-way ANOVA you’ll find a plethora of information that will help you complete this
project. I will have some resources posted on D2L in the Announcements page, but feel free to
ignore them in favor of your sources.
This project is worth a letter grade and I’ll be looking at your work carefully, so please
take the time and do this well. It MUST be typed and completely filled in to receive any
credit. Every question must be answered. This is worth a lot of points, so again 0lease put
in an appropriate amount of effort.
____________________________________________________________________________
1. What is meant by the Grand Mean in ANOVA?
2. Please explain what the difference is between the two concepts below.
Between Group Variability vs Within Group Variability
3. What is the F distribution and how is it related to ANOVA and between group variance and
within group variance?
Please answer the following questions, and fill in the table related to the data set below. You’ll
most likely want to use and ANOVA calculator on-line like this one.
https://www.socscistatistics.com/tests/anova/default2.aspx
First-born children tend to develop language skills faster than their younger siblings. One
possible explanation for this phenomenon is that first-born children have undivided attention
from their parents. If this explanation is correct, then it is also reasonable that twins should show
slower language development than single children and that triplets should be even slower. In
1937, Davis found exactly this result. The following hypothetical data demonstrate this
relationship. The dependent variable is a measure of language skill at age three. Do the data
provide evidence for significant differences between the three populations? Test at the .05 level.
Single Child
9
8
9
7
9
Twin Child
7
6
7
4
9
Triplet Child
3
5
8
1
3
State the null and alternative hypothesis.
Fill in the following table of descriptive statistics.
Descriptive Statistics
N
Mean
SD
Single
Twin
Triplet
Also, complete the following ANOVA table.
Analysis of Variance of Sociability Data
Source
SS
df
Between Groups
Within Groups
MS
F
If the F is statistically significant at p < .05 place an asterisk next to it and go on to compute a
post-hoc test to determine which pairs of means are significantly different.
Write a brief conclusion (interpretation) of the results.

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