Analysis of Variance
ANOVA
Mary M. MacPhee
Tuesday, October 23rd, 2012
Two main types of statistical inference
1. Estimation with levels of confidence and
confidence intervals
2. Hypothesis testing using statistical
significance / p-values (Vogt, p.130).
Our purpose: use ANOVA or analysis of variance
to test for statistically significant differences.
SPSS
• Running ANOVA will give you P-value
• & will compute confidence intervals
• ANOVA is commonly used in Psychology and
Educational research
• ANOVA Infers back to the general population
ANOVA analysis of variance
Tests for statistically significant differences
between mean results of 2 or more groups.
There is a comparison or analysis
Differences or variances
Between group means
Question we are asking
• How much more variance or difference is
there between groups than within
groups?
Four Assumptions
1) Normal distribution within randomly chosen
sample for DV
2) Homogeneity of variance (Levene’s)
3) Comparing independent cases
4) IV is categorical DV is quantitative
Homogeneity Assumption
• Levene’s test for homogeneity
• Higher than 0.05 (opposite to statistical
significance),
When Assumptions Not Met
• Welch or the Brown and Forsythe test.
• Krusal- Wallis H test,
(which is non-parametric, instead of using
ANOVA, which is parametric) (LAERD).
Inferential statistics
• F-test
• T2 = F
(ANOVA)
• t-test
•
𝐹=𝑡
• most widely used tests of
statistical significance
• most widely used tests of
statistical significance
• yields p-value
• yields p-value
• 2-3 or more groups
• 2 groups of cases
• Type 1 Error decreased
ANOVA
• One-way ANOVA – 1 IV
independent groups
3 or more
• multifactor or factorial design:
Two-way or Three-way ANOVA- 2 or 3 IV
Ratios
• Between group difference
Within group difference
• MSeffect
MSerror
explained variance
unexplained variance
The big F
• An omnibus test; if not which
• The larger the F statistic
• The more likely a statistically significant finding
• Smaller F statistic, then null hypothesis
• …no statistically significant difference between
the group means can still be important!
Where is the difference?
• Post-hoc, an a-posteriori (afterwards) test
• Tukey HSD
• Making multiple comparisons (Vogt, p.136)
Strengths
Robust against violations of assumptions
Reduces type I error compared to multiple
t-tests
Ease of interpretation
Greater versatility than t-tests
Study multiple IV with multiple groups
Weaknesses
Requires approximately equal cell sizes (#).
Cannot be used to establish more complex
models such as can be done with regression.
Requires post-hoc testing to tease out where
the differences are.
Let’s do it
• 1)bring up data
• 2)click Analyze >> compare means > one way
ANOVA
• 3) drag and drop ( DV) into the dependent variable box
• 4) drag and drop independent variable (status) into the
factor box
• 5)click Post Hoc and Tukey 6) click continue
• 7)click options - descriptive & homogeneity variance
• 8) continue – ok
Doing ANOVA /2
• Look at your descriptive statistics table, then
go to multiple comparisons/ANOVA table
• If statistically significant go to Tukey.
Graphing
• Use bar chart with standard deviation bars for
Graphing ANOVA ( LAERD)
References
Vogt, P. (2007). Quantitative Research
Methods for Professionals. Boston, MA:
Pearson.
Collican, H., (2004). Research Methods
and Statistics in Psychology. (4th Ed.).
London, UK: Hodder & Stoughton.
https://statistics.laerd.com/
www.statsoft.com