Analysis of variance (ANOVA) is a statistical test used to identify differences between sample means. It partitions variability, attributing portions to the effect of an independent variable on a dependent measure. The ANOVA yields an F ratio statistic determined by dividing between-groups variance by within-groups variance. This ratio indicates whether differences among two or more means are statistically significant or likely due to random error.

1. MEAN COMPARISON II
Desmond Ayim-Aboagye, Ph.D
ONE-VARIABLE ANALYSIS OF
VARIANCE

2. Analysis of Variance (ANOVA)
• It is the most familiar procedure for
behavioural scientists.
• It was originated by Statistician known as
Fisher.
• F distribution used to test hypothesis
regarding significant differences among two or
more means.

3. ANOVA
• The ANOVA and its F test can search for
reliable differences among the magnitudes of
two, three, four, or even more means
simultaneously.
• The ANOVA enables investigators to analyze
data addressing complex questions (i.e.,
beyond those posed by standard two-group
experiments).

4. OVERVIEW OF ANOVA
• The analysis of variance (ANOVA) is a
statistical test used to identify differences
between or among distinct sample means. As
a statistical technique, the ANOVA partitions
or divides variability, attributing portions of it
to the effect of an independent variable on a
dependent measure.

5. TOTAL VARIANCE
• Variance of all participants‘ scores from the
three samples combined would be labeled the
total variance. (each sample is exposed to
one– and only one– level of independent
variable.)
• Total variance entails the combined variance
of all the scores or observations within an
experiment.

6. F Ratio
• The ANOVA yields an F Ratio, a t test statistic
that is determined by dividing between-
groups variance (largely based on an
independent variable) by within-groups
variance (random error).

7. ANOVA
• The ANOVA provides a statistic, the F ratio,
comprised of two elements:
• 1. The numerator of the F ratio indicates the
variability between or among means of two or
more samples (i.e., between-group variance)
• The denominator of the F ratio identifies the
variability among the observations within
each sample (i.e., within-group variance)

8. F Ratio
• F = between-group variance
• within-group variance