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

next

• 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.

  next

   

   

  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

next

True or False?

1. The p-value is the probability that the null hypothesis is true.

    

2. The p-value is The probability that the alternative hypothesis is true.

    

3. The p-value is the likelihood of the observed data, given that the null hypothesis is true.

    

4. The p-value is, in future experiments, the probability of obtaining results as "extreme" or more "extreme" given that the null hypothesis is true.

    

5. The p-value is a convenient test statistic.

next

True or False?

1. The p-value is the probability that the null hypothesis is true.

    

2. The p-value is The probability that the alternative hypothesis is true.

    

3. The p-value is the likelihood of the observed data, given that the null hypothesis is true.

    

4. The p-value is, in future experiments, the probability of obtaining results as "extreme" or more "extreme" given that the null hypothesis is true.

    

5. The p-value is a convenient test statistic.

next

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.

next

 

 

• 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

next

The X10 Project

http://www.dartmouth.edu/~matc/X10/X10.html