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  • Let's say you want to find out

  • if the beverage that people drink

  • affects their reaction time.

  • So you set up an experiment with three groups of people.

  • The first group gets water to drink.

  • The second group gets some sugary fruit juice,

  • and the third group gets coffee.

  • Now you test everyone's reaction time.

  • And you want to know if there's any difference

  • in reaction time between the groups.

  • The null hypothesis says that the mean reaction time

  • for all three groups is the same.

  • If there were only two groups,

  • you could use a t-test to find out

  • if there's a difference between them.

  • But when you have three groups or more,

  • you need to use a different approach--

  • the analysis of variance.

  • When you do the experiment,

  • the scores won't all be the same.

  • The total variation of all the scores

  • is made up of two parts:

  • The variation within each group,

  • because the people in each group

  • have different reaction times,

  • and the variation between the groups,

  • because the drinks you gave each group are different.

  • Here's an example.

  • Look at this set of scores.

  • They've been sorted into order

  • to make it easier to see the patterns.

  • You can see that there's a lot of variation

  • within each group;

  • some people are faster and some are much slower.

  • But all the groups look pretty much alike;

  • there's not much variation between the groups.

  • In this case, you'd say that most of the difference

  • is due to the people, and the drink

  • didn't make much of a difference.

  • You can't reject the null hypothesis;

  • which is that the type of drink doesn't have

  • any effect on reaction time.

  • Now let's look at a different set of numbers.

  • In this case, all the scores within each group

  • are very close to one another.

  • There's not a lot of variance within each group,

  • but the groups are very different from one another.

  • There's a lot of difference between the groups.

  • In this case, you would reject the null hypothesis.

  • In this case, the type of drink makes a big difference.

  • So here's the idea behind analysis of variance:

  • Figure out how much of the total variance comes from the between-groups variance

  • and the within-groups variance.

  • Take the ratio of between-groups

  • to within-groups variance,

  • and the larger this number is,

  • the more likely it is

  • that the means of the groups really *are* different,

  • and that you should reject the null hypothesis.

  • In the examples, it was obvious where the variance was.

  • Now look at these numbers.

  • You probably can't tell

  • if there's a significant effect

  • because it's not clear whether there's

  • more variance within groups or between groups,

  • or how much.

  • The calculations show that the ratio is 4.27,

  • which has a probability of .04,

  • so in this case, you can reject the null hypothesis.

  • With these numbers, the drink you give the people

  • does have an effect on their reaction time.

  • What's that "2,12" doing there?

  • Those are the degrees of freedom

  • for variance between groups

  • and variance within groups.

  • And here's how you calculate the degrees of freedom

  • when you report results for analysis of variance.

  • This trick of separating the variance

  • not only when you have three or more groups,

  • it also works when you have multiple variables.

  • For example, if you test three groups

  • for reaction time in the morning,

  • and you test another three groups in the evening,

  • an analysis of variance can tell you

  • if there's a significant effect

  • for the type of drink,

  • or if the time of day makes a difference,

  • or if there's some interaction.

  • For example, coffee might be more effective in the morning than in the evening.

  • So to recap, here's the main idea of analysis of variance:

  • You figure hοw much of the total variance

  • comes from between the groups,

  • and how much comes from within the groups.

  • If most of the variation is between groups,

  • there's probably a significant effect;

  • if most of the variation is within groups,

  • there's probably not a significant effect.

Let's say you want to find out

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B1 中級

分散分析 (ANOVA) (Analysis of Variance (ANOVA))

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    羅紹桀 に公開 2021 年 01 月 14 日
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