What can we conclude from data?

To understand how to organize data, we need to understand what kind of data is gathered. For example, data that is gathered about temperatures are numbers. Data based on numbers or quantitative data, like temperature, allows us to conduct certain kinds of analyses, as opposed to gathered data that answers a Yes/No question. Knowing what kind of data are gathered is critical to making correct numerical summaries, such as averages and percentages. Knowing what kind of data are gathered is also necessary for creating correct graphical representations of the data. Creating graphs and numerical summaries about data are known as descriptive statistics.

If data is selected in such a way that it is representative of a population, then conclusions can be drawn about the population. If the data comes from a well-designed experiment, then conclusions can be drawn about cause and effect. Both types of conclusions are known as inferential statistics. Of course, we need a sample that represents the population well. This involves careful planning but also involves chance. For example, if our goal is to determine the percentage of U.S. adults who favor the death penalty, we do not want our sample to contain only Democrats or only Republicans. We can give everyone the same opportunity to be in the sample, but we will let chance select the sample.

For a well-designed experiment, we would want to use chance to assign subjects to treatments, instead of allowing people to choose what treatment to receive. For example, we would not want to let patients choose whether to receive an investigational medication or a traditional medication. If this was done, the sicker patients might choose the investigational medication. This would mean that we would not know how the medication works on all patients with the particular illness.

The main goal of any statistical study is to answer a question about a population based on a sample. Of course, samples will vary due to chance, and we will need to answer our question in spite of this variability. We need to understand how sample results will vary and how sample results relate to the population as a whole when chance is involved. This is where probability comes in. The example that follows shows the entire process of a statistical study, from stating a research question to drawing a conclusion about the population.

Let’s Summarize

A statistical investigation begins with a research question. Then the investigation proceeds with the following steps:

• Produce Data: Determine what to measure, then collect the data.
• Explore the Data: Analyze and summarize the data (also called exploratory data analysis).
• Draw a Conclusion: Use the data, probability, and statistical inference to draw a conclusion about the population.

Types of Statistical Studies and Producing Data

In this first module, we focus on the “produce data” step in a statistical investigation, focusing on randomization in data collection, and what is meant by a well-designed experiment. We also begin to look at some of the exploratory data analysis techniques, including numerical summaries for data and graphs.