Analysis+of+Variance+%28ANOVA%29

May 15, 2026 18:21 · 4:45 · English · Whisper Turbo · 1 Oradores
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
Let's say you want to find out if the beverage that people drink affects their
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reaction time.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
So you set up an experiment with three groups of people.
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The first group gets water to drink.
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The second group gets some sugary fruit juice.
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And the third group gets coffee.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
Now you test everyone's reaction time.
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And you want to know if there's any difference in reaction time
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between the groups.
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The null hypothesis says that the mean reaction time for all three groups
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is the same.
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If there were only two groups
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you could use a t -test to find out if there's a difference between them.
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But when you have three groups or more you need to use a
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different approach,
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the analysis of variance.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
When you do the experiment the scores won't all be the same.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
The total variation of all the scores is made up of two parts.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
The variation within each group
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
because the people in each group have different reaction times,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
and the variation between the groups,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
because the drinks you gave each group are different.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
Here's an example.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
Look at this set of scores.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
They've been sorted into order to make it easier to see the patterns.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
You can see that there's a lot of variation within each
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
group.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
Some people are faster and some are much slower.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
But all the groups look pretty much alike.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
There's not much variation between the groups.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
In this case,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
you'd say that most of the difference is due to the people,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
and the drink didn't make much of a difference.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
You would accept the null hypothesis,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
that the type of drink doesn't have any effect on reaction time.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
Now let's look at a different set
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
of numbers.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
In this case,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
all the scores within each group are very close to one another.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
There's not a lot of variance within each group.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
But the groups are very different from one another.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
There's a lot of difference between the groups.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
In this case, you would reject the null hypothesis.
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In this case,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
the type of drink makes a big difference.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
So here's the idea behind analysis of
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variance.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
Figure out how much of the total variance comes from the
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
between groups variance and the within groups variance.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
Take the ratio of between
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groups to within groups variance.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
And the larger this number is,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
the more likely it is that the means of the groups really are different,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
and that you should reject the null hypothesis.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
In the examples,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
it was obvious where the variance was.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
Now look at these numbers.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
You probably can't tell if there's a significant effect,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
because it's not clear whether there's more variance within groups,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
or between groups,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
or how much.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
The calculations show that
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the ratio is 4 .27,
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which has a probability of .04.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
So in this case,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
you can reject the null hypothesis.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
With these numbers,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
the drink you give the people does have an effect on their reaction time.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
What's that 2 comma 12 doing
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
there? Those are the degrees of freedom for variance between
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groups and variance within groups.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
And here's how you calculate the degrees of freedom
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when you report results for analysis of variance.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
This trick
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
of separating the variance not only works when you have three or more groups,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
It also works when you have multiple variables.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
For example,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
if you test three groups for reaction time in the morning,
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and you test another three groups in the evening,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
an analysis of variance can tell you if there's a significant
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
effect for the type of drink,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
or if the time of day makes a difference,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
or if there's some interaction.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
For example,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
coffee might be more effective in the morning than in the evening.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
So to recap,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
here's the main idea of analysis of variance.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
you figure how much of the total variance comes from between the
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
groups, and how much comes from within the groups.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
If most of the variation is between groups,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
there's probably a significant effect.
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
If most of the variation is within groups,
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S… Speaker 1 (Analysis+of+Variance+%28ANOVA%29)
there's probably not a significant effect.

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