This presentation on data analysis addresses observational studies and randomized controlled trials in two different sections. Types of studies are defined and examples of each study is given to emphasize the differences. Factors and variables are also discussed.
This site describes numerous methods of nonprobability sampling, including accidental, haphazard or convenience sampling and the many types of purposive methods.
This applet simulates rolling dice and displays the outcomes in a histogram. Students can choose to roll 1, 2, 6, or 9 dice either 1, 10, 20, or 100 times. The outcome studied is the sum of the dice and a red line is drawn on the histogram to show expected number of occurences of each outcome.
EasyCharts is a complete library of java chart components, chart applets, and chart servlets that enable programmers to add charts and graphs in java applications, web applications, and web pages with just a few lines of code. The java chart library includes bar charts, line charts, and pie charts and is highly configurable. The java chart library supports charts with multiple data series, overlay charts, drilldown charts, and interactive features such as zooming and scrolling of chart data.
This library contains a plethera of downloadable applets and the components of the applets for use by teachers and students of probability and statistics. These objects (both executable files and source code) can be downloaded, modified if desired, and reused.
The Food and Drug Administration requires pharmaceutical companies to establish a shelf life for all new drug products through a stability analysis. This is done to ensure the quality of the drug taken by an individual is within established levels. The purpose of this out-of-class project or in-class example is to determine the shelf life of a new drug. This is done through using simple linear regression models and correctly interpreting confidence and prediction intervals. An Excel spreadsheet and SAS program are given to help perform the analysis. Key words: prediction interval, confidence interval, stability
This group activity focuses on conducting an experiment to determine which of two brands of paper towels are more absorbent by measuring the amount of water absorbed. A two-sample t-test can be used to analyze the data, or simple graphics and descriptive statistics can be used as an exploratory analysis. Students are asked to think about design issues, and to write a short report stating their results and conclusions, along with an evaluation of the experimental design. Key words: Two-sample t-test
The activity is designed to help students develop a better intuitive understanding of what is meant by variability in statistics. Emphasis is placed on the standard deviation as a measure of variability. As they learn about the standard deviation, many students focus on the variability of bar heights in a histogram when asked to compare the variability of two distributions. For these students, variability refers to the "variation" in bar heights. Other students may focus only on the range of values, or the number of bars in a histogram, and conclude that two distributions are identical in variability even when it is clearly not the case. This activity can help students discover that the standard deviation is a measure of the density of values about the mean of a distribution and to become more aware of how clusters, gaps, and extreme values affect the standard deviation. Key words: Variability, standard deviation
This group activity illustrates the concepts of size and power of a test through simulation. Students simulate binomial data by repeatedly rolling a ten-sided die, and they use their simulated data to estimate the size of a binomial test. They carry out further simulations to estimate the power of the test. After pooling their data with that of other groups, they construct a power curve. A theoretical power curve is also constructed, and the students discuss why there are differences between the expected and estimated curves. Key words: Power, size, hypothesis testing, binomial distribution
This activity is an advanced version of the "Keep your eyes on the ball" activity by Bereska, et al. (1999). Students should gain experience with differentiating between independent and dependent variables, using linear regression to describe the relationship between these variables, and drawing inference about the parameters of the population regression line. Each group of students collects data on the rebound heights of a ball dropped multiple times from each of several different heights. By plotting the data, students quickly recognize the linear relationship. After obtaining the least squares estimate of the population regression line, students can set confidence intervals or test hypotheses on the parameters. Predictions of rebound length can be made for new values of the drop height as well. Data from different groups can be used to test for equality of the intercepts and slopes. By focusing on a particular drop height and multiple types of balls, one can also introduce the concept of analysis of variance. Key words: Linear regression, independent variable, dependent variables, analysis of variance