Don't do drugs! Cocaine addicts need cocaine to feel any...

Don't do drugs! Cocaine addicts need cocaine to feel any pleasure, so perhaps giving them an antidepressant drug will help. A three-year study with 72 chronic cocaine users compared an antidepressant drug called desipramine with lithium (a standard drug to treat cocaine addiction and a placebo. One-third of the subjects were randomly assigned to receive each treatment. Here are the results: $^{.16}$ $$ \begin{array}{lccc} {\text { Drug administered }} \\ \text { Relapsed? } & \text { Desipramine } & \text { Lithium } & \text { Placebo } \\ \text { Yes } & 10 & 18 & 20 \\ \text { No } & 14 & 6 & 4 \\ \hline \end{array} $$ (a) Compare the distributions of relapse status for the three treatments. (b) Are the differences among the three groups statistically significant? Give appropriate evidence to support your answer.

Don't do drugs! Cocaine addicts need cocaine to feel any pleasure, so perhaps giving them an antidepressant drug will help. A three-year study with 72 chronic cocaine users compared an antidepressant drug called desipramine with lithium (a standard drug to treat cocaine addiction and a placebo. One-third of the subjects were randomly assigned to receive each treatment. Here are the results: $^{.16}$
$$
\begin{array}{lccc}
{\text { Drug administered }} \\
\text { Relapsed? } & \text { Desipramine } & \text { Lithium } & \text { Placebo } \\
\text { Yes } & 10 & 18 & 20 \\
\text { No } & 14 & 6 & 4 \\
\hline
\end{array}
$$
(a) Compare the distributions of relapse status for the three treatments.
(b) Are the differences among the three groups statistically significant? Give appropriate evidence to support your answer.

Key Concepts

Contingency Table Analysis

A contingency table is a matrix format used to display the frequency distribution of variables that are categorical in nature. It allows researchers to observe and analyze the relationship between two or more categorical variables by presenting counts in rows and columns, which can then be used for further statistical testing.

Chi-Square Test of Independence

The chi-square test of independence is a statistical method used to determine whether there is a significant association between two categorical variables. By comparing the observed frequencies in a contingency table to the expected frequencies under the assumption of no association, the test produces a p-value that indicates whether the differences between groups are statistically significant.

Randomized Controlled Trial (RCT) Design

A randomized controlled trial is an experimental study design that randomly assigns subjects to different treatment groups. This randomization minimizes selection bias and balancing potential confounding factors, thereby allowing more reliable conclusions about the causal effects of the treatments under investigation.

Statistical Significance

Statistical significance refers to the likelihood that the observed differences between groups are not due to random chance. In hypothesis testing, if the p-value is below a predetermined significance level (often 0.05), it suggests that the differences observed are statistically significant and not likely a result of random variation.

Comparison of Distributions

Comparing the distributions of categorical outcomes across multiple groups involves assessing whether the frequency with which outcomes occur differs among the groups. This comparison is integral to understanding if and how the groups differ in terms of the outcome of interest, and it typically relies on statistical tests like the chi-square test to support the evaluation.

Transcript

00:01 Cocaine addicts need cocaine to feel any pleasure, so perhaps giving them an antidepressant drug will help.

00:05 A three -year study with 72 chronic cocaine users compared an antidepressant drug called, i'm not 100 % sure, but desipranine and lithium, a standard drug to treat cocaine addiction, and a placebo.

00:17 One -third of the subjects were randomly assigned to receive each treatment.

00:20 Here are the results.

00:22 We've got three drugs here, and then a yes or no question.

00:26 Did they relapse? yes.

00:27 Or did they not relapse? so compare the distributions of relapse status for the three treatments.

00:33 So in part a, just kind of a quick overview of what happened.

00:38 So only 10 out of 24, or about 41 .7%, relapsed with the desipramine, compared to lithium, which was 18 out of 24, or 75%, and the placebo, which was the 83 .3%.

01:16 So it appears that desipramine has different results than the placebo or lithium.

01:40 So it just appears that way.

01:42 All right, now in part b, are there differences among the three groups statistically significant? so now we need to use the chi -square test, if i can spell, for homogeneity.

02:00 Okay, so that's what we need to do.

02:01 So with our null hypothesis, the null hypothesis for a chi -square test for homogeneity is that the distributions are the same for the three treatments.

02:10 So the distributions are the same for the three treatments.

02:26 And then the alternative is that the distributions are different, or the distributions are not the same...

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