Investigating the World Around us with the Scientific Method

Investigating the World Around Us with the Scientific Method

Hi! Welcome to your statistics course. In this course, we will cover many statistical techniques and analyses, but before we delve into any specific topics, it is important that we understand why we do statistics. In short, we do statistics to investigate the world around us.

We begin a statistical investigation with a research question. The research question is frequently something we want to know about a population. The population can be people or other things, such as animals or objects. For example, we might want to know the answer to questions such as:

• What percentage of U.S. adults supports the death penalty? (Population: U.S. adults)

• Do cell phones affect bees? (Population: bees)

• Do cars get better gas mileage with a new gasoline additive? (Population: cars)

The population is the entire group that we want to know something about:

In most cases, the population is a large group. Often, the population is so large that we cannot collect information from every individual in the population. So we select a sample from the population. Then we collect data from this sample. This is the first step in the statistical investigation. We call this step producing data.

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. So we can give everyone the same opportunity to be in the sample.

At this step of the investigation we also carefully define what kind of information we plan to gather. Then we collect the data.

Data is often a long list of information. To make sense of the data, we explore it and summarize it using graphs and different numerical measures, such as percentages or averages. We call this step exploratory data analysis.

Remember, our goal 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. So 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.

Probability is the “machinery” behind the last step in the process called inference. We infer something about a population based on a sample. This inference is the conclusion we reach from our sample data that answers our original question about the population.

Let’s Summarize

A statistical investigation 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.

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