Lesson 13.1 One-Way ANOVA
The purpose of a one-way ANOVA is to determine
the existence of a statistically significant
difference among several independent population
means. Random samples are taken from each
population and the test actually uses standard
deviations to help determine if the means are
equal or not.
Basic Assumptions
- Each population from which a sample is taken
is assumed to be normal.
- All samples are randomly selected and
independent.
- The populations are assumed to have equal
variances.
- The factor is a categorical variable.
- The response is a numerical variable.
Some explanation of #4 and 5 is needed.
Suppose we want to determine if the average weight
of tomatoes grown in different types of soil are
equal or not. The type of soil (bare ground,
ground cover, plastic cover, straw cover, or
compost cover) would be the factor and these are
categorical variables. The weights of the
tomatoes grown in each of these types of soil are
measured and therefore, quantitative continuous
variables.
The Null and Alternate
Hypotheses
The null hypothesis states that all of the
population means are the same. The alternate
hypothesis is that at least one pair of population
means is different.
Ho: µ1 = µ2 =
µ3 = ... = µk
Ha: At least two of the group means
are not equal.
Ultimately, when we do a One-Way ANOVA, if the
null is true it means that the differences between
populations are due to random variations and the
averages are statistically the same. On the
other hand, if the null is not true, the
differences between populations are too large to
be due to random variation so the averages are not
statistically the same.
Please continue to the next section
of this lesson.
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