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THC vs Prochloroperazine An article in the New York Times on January 17,1980 reported on the results of an experiment that compared an existing treatment drug (prochloroperazine) with using THC (the active ingredient in marijuana) for combating nausea in patients undergoing chemotherapy for cancer. Patients being treated in a cancer clinic were divided at random into two groups which were then assigned to one of the two drugs (so they did a randomized, double- blind, comparative experiment). Table 6.15 shows how many patients in each group found the treatment to be effective or not effective. (a) Use these results to test whether the proportion of patients helped by THC is significantly higher (no pun intended) than the proportion helped by prochloroperazine. Use a \(1 \%\) significance level since we would require very strong evidence to switch to THC in this case. (b) Why is it important that these data come from a well-designed experiment? $$ \begin{array}{lccc} \hline \text { Treatment } & \text { Sample Size } & \text { Effective } & \text { Not Effective } \\ \hline \text { THC } & 79 & 36 & 43 \\ \text { Prochloroperazine } & 78 & 16 & 62 \\ \hline \end{array} $$

Step by step solution

01

Formulate the Null and Alternative Hypothesis

First, formulate the Null and Alternate Hypothesis. The Null Hypothesis, \(H_0\), is that the proportions of patients helped by both drugs are equal, while the Alternative Hypothesis, \(H_A\), is that the proportion of patients helped by THC is higher than prochloroperazine.

02

Calculate Observed and Expected Counts

Using the given sample size and the amount of effective results, calculate the test statistic for the chi-squared test. The expected count for each treatment can be calculated by multiplying the total sample size by the proportion of success for each group. After that, the observed minus expected counts (O - E) and its square divided by E can be calculated for each cell.

03

Calculate the Test Statistic

Sum up the \((O - E)^2 / E\) for each cell, which gives the test statistic.Usually it follows a \(\chi^2\) distribution with 1 degree of freedom since it is a 2x2 table, but the approximation may not hold in this case due to the small expected counts in the cells.

04

Calculate the P-value

Then calculate the p-value using the test statistic. This is the probability of observing such a considerable difference if the null hypothesis is true. If the p-value is less than the significance level (0.01), reject the null hypothesis, suggesting that THC is a more effective treatment. If the p-value is greater than 0.01, failure to reject the null hypothesis suggests that there is not enough evidence to conclude that there is a difference in the effectiveness of THC and prochloroperazine.

05

Interpret the Result

Interpret the result in the context of the problem. State whether there is significant evidence at the 1% level to justify a switch to THC for treatment based on the test statistic and p-value. A significantly small p-value would indicate that there is a statistically significant difference in the effectiveness of the two treatments.

06

Importance of well-designed experiment

Address the second part of the problem by explaining why it's important that these data come from a well-designed experiment. A well-designed experiment ensures that the difference observed in the treatment effectiveness can be attributed to the treatment itself and not to some confounding variable. Furthermore, the randomized nature of the experiment ensures equal distribution of confounding variables and helps establish a cause-effect relationship.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Randomized Controlled Trial

In research, a randomized controlled trial (RCT) is a powerful method for testing the effectiveness of treatments or interventions. In the exercise about comparing THC and prochloroperazine for nausea treatment, a carefully designed RCT was conducted. Here’s why it's crucial:

• Randomization: Patients were randomly assigned to receive either THC or prochloroperazine. This prevents any bias in assigning treatments, ensuring that each group is similar before treatment starts.
• Control Group: The group receiving prochloroperazine acts as a control against which the effects of THC can be measured.
• Double-Blind: Neither the patients nor the researchers knew which drug was administered to each patient. This eliminates bias in reporting and assessing results.

This setup ensures that the observed effects are due to the treatment and not some other variables, allowing researchers to make more accurate conclusions.

P-value

The p-value is a critical statistic in hypothesis testing. It represents the probability of obtaining results as extreme as those observed, assuming the null hypothesis is true. In the THC versus prochloroperazine trial, this value helps determine the effectiveness of THC.

• Low p-value: If the p-value is less than the significance level (in this case, 1%), it suggests strong evidence against the null hypothesis, indicating that THC might be a more effective treatment.
• High p-value: A p-value greater than 1% would imply insufficient evidence to suggest that THC is more effective than prochloroperazine.

This threshold helps assess whether the result can practically impact treatment choices or if it might be due to random chance.

Chi-squared Test

The chi-squared test is a statistical method used to examine the association between categorical variables. In this exercise, it was employed to compare the effectiveness of THC vs. prochloroperazine.

• Chi-squared Statistic: This value is calculated from the differences between observed and expected frequencies of effective treatments in both groups.
• Distribution: The resulting statistic follows a \(\chi^2\) distribution with degrees of freedom, which helps determine how likely it is that the observed differences could have happened by chance.
• Application: A chi-squared test can reveal if any difference in treatment effectiveness is statistically significant, helping researchers decide whether THC offers a considerable benefit over prochloroperazine.

By understanding this test, one can appreciate how researchers conclude the effectiveness of different treatments through statistical evidence.