- Big Ideas
- What you need to know
- Demonstration
- More Web stuff

- Hypotheses:
*Theories or ideas you are trying to test with data. Usually these boil down to particular values for the mean of the distribution of the data .*

- "Null" and "Alternative" Hypotheses
*In the simplest case, the two possibilities for the real mean of data. Often one is zero , and thus is called the "Null". The "Alternative" is usually larger.**What you need to know* - The distribution of statistics such as means or proportions depends on whether the null or alternative hypothesis is true.

- When we perform a statistical test, we decide between the null and alternative hypotheses depending on whether the mean exceeds a certain "critical value"

- The "significance level" of
our test is the probability that we choose the alternative
hypothesis
*when the null hypothesis is true*.

- The "power" of our test is the
probability that we choose the alternative hypothesis
*when the alternative hypothesis is true*

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- The p-value is the probability that the null
hypothesis is true.
- The p-value is The probability that the
alternative hypothesis is true.
- The p-value is the likelihood of the observed
data, given that the null hypothesis is true.
- The p-value is, in future experiments, the
probability of obtaining results as "extreme" or more "extreme"
given that the null hypothesis is true.
- The p-value is a convenient test statistic.

~~The p-value is the probability that the null hypothesis is true.~~~~The p-value is The probability that the alternative hypothesis is true.~~~~The p-value is the likelihood of the observed data, given that the null hypothesis is true.~~- The p-value is, in future
experiments, the probability of obtaining results as "extreme" or
more "extreme" given that the null hypothesis is true.
- The p-value is a convenient
test statistic.

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*The Good*- Tend to be small when the alternative hypothesis is true. Easier to digest than "t-statistics".
*The Bad*- Inadequate as data summary, without more information, ie. the sample size, mean difference, standard error, etc.
*The Ugly*- Oversized studies lead to "significant" p-values with tiny alternatives. Undersized studies lead to "non-significant" p-values with large alternatives.
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- An interactive,Web-based program illustrating concepts in hypothesis testing
- Based on statistics for proportions
- Lets you control the sample size and definitions of the hypotheses
- Simulates data and calculates p-values
- Example:
*20 people are randomly selected for a survey of HIV status. A statistical test is performed to see whether the population proportion is .1 or .3. If it is .3 or higher, a risky live vaccine will be used.* *Local machine, X10*

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The X10 Project