## Info

Placebo lozenges

### Zinc lozenges

Figure 1.9 Zinc lozenges reduce the duration of colds. This graph illustrates the results of an experiment on the effectiveness of zinc lozenges on decreasing cold duration. Individuals in the experimental group had colds lasting about 4V2 days as opposed to approximately 7V2 days for the placebo group.

Figure 1.9 Zinc lozenges reduce the duration of colds. This graph illustrates the results of an experiment on the effectiveness of zinc lozenges on decreasing cold duration. Individuals in the experimental group had colds lasting about 4V2 days as opposed to approximately 7V2 days for the placebo group.

daily usage. To evaluate the scientific use of the term significance, Jake needs a basic understanding of statistics.

Statistics is a specialized branch of mathematics used in the evaluation of experimental data. An experimental test utilizes a small subgroup, or sample, of a population. Descriptive statistics helps researchers summarize data from the sample—for instance, we can describe the average, or mean, length of colds experienced by experimental and control groups. Inferential statistics allows scientists to extend the results they summarize from their sample to the entire population. Inferential statistics takes the form of statistical tests. When scientists conduct an experiment, they hypothesize that there is a true, underlying effect of their experimental treatment on the entire population. An experiment on a sample of a population can only estimate this true effect, but statistical tests help scientists evaluate whether the results of a single experiment demonstrate the true effect of a treatment. In the experiment with the echinacea tea, statistical tests tell us if the experimental result of a 33% reduction in cold severity is an indication of how well echinacea tea works or if it might be due to chance differences between the experimental and control group.

We can explore the role statistical tests played in a study on another proposed treatment to reduce the severity of colds—lozenges containing zinc. Some forms of zinc can block certain common cold viruses from entering the cells that line the nose. This observation led scientists to hypothesize that consuming zinc at the beginning of a cold decreases the number of cells that become infected, which in turn decreases the length and severity of cold symptoms. To test this hypothesis, a group of researchers at the Cleveland Clinic performed a study using a sample of 100 of their employees who enrolled in the study within 24 hours of developing cold symptoms. The researchers randomly assigned subjects to control or experimental groups. Members of the experimental group received lozenges containing zinc, while members of the control group received placebo lozenges. Members of both groups received the same instructions about use of the lozenges and were asked to rate their symptoms until they had recovered. The experiment was double-blind.

When the data from the experiment were summarized, the researchers observed that the mean length of time to recovery was more than three days shorter in the zinc group than in the placebo group (Figure 1.9). Superficially, this result appears to support the hypothesis. However, a statistical test is necessary because, even with well-designed experiments, chance will always result in some difference between the control and experimental groups. The effect of chance on experimental results is known as sampling error. Even if there is no true effect of an experimental treatment, the results observed in the experimental and control groups will never be exactly the same.

We know that people differ in their ability to recover from a cold infection. If we give zinc lozenges to one volunteer and placebo lozenges to another, it is likely that they will have colds of different lengths. But even if the zinc-taker had a shorter cold than the placebo-taker, you would probably say that the test did not tell us much about our hypothesis—the zinc-taker might just have had a less severe cold for other reasons. Now imagine that we had five volunteers in each group and saw a difference. Or that the difference was only one day instead of three days. Statistical tests allow researchers to look at their data and determine how likely it is that the result is due to sampling error.

Statistical tests actually evaluate the null hypothesis. "Null" means zero, and the null hypothesis is that there is zero difference between the experimental and control populations. In other words, the experimental treatment has no effect. In this case, the null hypothesis is that there is no difference in the length of colds experienced by people who take zinc lozenges and those who take placebo lozenges. A statistical test allows the researchers to evaluate whether the observed data are consistent with this null hypothesis. The logic behind this approach is as follows: As the data from the control and experimental groups diverge from each other, the null hypothesis becomes less and

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