Learn how to describe the distribution of a variable, make inferences about the population parameters, and exclude observations from analysis.
Simon Newcomb measured the time required for light to travel from his laboratory on the Potomac River to a mirror at the base of the Washington Monument and back, a total distance of about 7400 meters. The data are used to estimate the speed of light. For more information see DASL Story: Estimating the Speed of Light
In this tutorial you will perform the following tasks:
Before summarizing data with descriptive statistics or making inferences about parameters it is important to look at the data. It is hard to see any patterns by looking at a list of hundreds of numbers. Equally, a single descriptive statistic in isolation can be misleading and give the wrong impression of the data. A plot of the data is therefore essential.
The histogram of the data shows a normal distribution except for two outliers.
It is often not enough to simply describe a set of data. Instead you want to make inferences about the parameters of the population the sample of data is drawn from. An inference may be an estimate of a parameter, or a hypothesis test if a parameter is equal to a specific value.
The mean estimate is 26.2 and a 95% confidence interval estimate 23.6 to 28.9.
Some statistics can be badly affected by outliers in the data, while others are robust. It is often worth considering how the results are affected by such observations.
After excluding the outliers the mean estimate has changed from 26.2 to 27.8 and the confidence interval is narrower.
Sometimes it is necessary to make changes to individual plots or tables on an analysis report before it is ready for publication.
The histogram now has better class intervals and the Normal distribution curve shows that the distribution is roughly normal.
