In a randomized experiment on treating cocaine addiction, 48 cocaine addicts who were trying to quit were randomly assigned to take either desipramine (a new drug), or Lithium (an existing drug). The response variable is whether or not the person relapsed (which means the person was unable to break out of the cycle of addiction and returned to using cocaine.) We are testing to see if desipramine is better than lithium at treating cocaine addiction. The results are shown in the two-way table.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Section 4.4: Creating Randomization Distributions
Example 1: Evaluating Drugs to Fight Cocaine Addiction
In a randomized experiment on treating cocaine addiction, 48 cocaine addicts who were trying to quit were randomly assigned to take either desipramine (a new drug), or Lithium (an existing drug). The response variable is whether or not the person relapsed (which means the person was unable to break out of the cycle of addiction and returned to using cocaine.) We are testing to see if desipramine is better than lithium at treating cocaine addiction. The results are shown in the two-way table.
|
|
Relapse |
No relapse |
Total |
|
Desipramine |
10 |
14 |
24 |
|
Lithium |
18 |
6 |
24 |
|
Total |
28 |
20 |
48 |
- Using pD for the proportion of desipramine users who relapse and pL for the proportion of lithium users who relapse, write the null and alternative hypotheses.
- Compute the appropriate sample statistic.
- We compute a randomization statistic by assuming the null hypothesis is true. What does that mean in this case?
- How might we compute a randomization sample for this data? What statistic would we compute as the randomization statistic?
- We can use StatKey to generate a randomization dotplot for the difference in proportions based on this sample and what we might see by random chance of the null hypothesis is true. Describe the resulting distribution. Where is it centered?
- How extreme is the sample statistic from part (b) in the randomization distribution? This tells us how unlikely the sample data is if the null hypothesis is true (which is the p-value!) Use the sample statistic calculated in (b) to find the p-value for this test. Use the p-value to make a conclusion.
Example 2: Normal Human Body Temperature
Normal human body temperature is generally considered to be 98.6°F. We wish to test to see if there is evidence that mean body temperature is different from 98.6°F. We collect data from a random sample of 50 people and find = 98.26.
a). State the null and alternative hypotheses.
b). A randomization distribution requires that the null hypothesis is true. What does that mean in this case?
c). Use StatKey to create a randomization distribution for this test, and then use it to find the p-value. Use the p-value to make a conclusion in the test.
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