4.1 Sensation and Perception

Topic:

Finding the Best Way to Describe Experimental Data

Statistical concepts covered:

In this applet we will cover various measures of central tendency and how to model the relationships between data values using distributions.

Introduction

When we talk about sensation and perception, psychophysics plays a central role. Not only do we have to have accurate and reliable ways to measure stimuli and physical responses, but we must also be able to describe the results clearly and concisely. Unfortunately, there is not a one-size-fits-all solution when it comes to describing data. While you might think that talking about the average value of a data set is a reasonable approach (and often it is), the truth is that you must understand the shape of your data distribution and the point that you want to convey before you can decide on the best way to represent your data.

In this exercise, you will investigate several different data distributions and think about possible ways to describe the data. It will be helpful to you to review the text’s coverage of graphic representations and descriptive statistics (specifically mean, mode and median). Sometimes the mean value will be a fair and unbiased model of the data, but other times, the mean may misrepresent the data or even be completely uninformative. As you analyze these data and answer the related questions, you should begin to get a feel for how to select the most accurate methods for describing your findings.

Richard Alan Hullinger, Indiana University, Bloomington
Melanie Maggard, University of the Rockies

Question

You have probably learned how to calculate the mean value of a set of numbers, but you may not know how to estimate the mean value by looking at a histogram. The mean value isn’t just the sum of the data values divided by the number of data values. It is also the balancing point of the data – where the “weight” of the data from one side of the distribution balances the “weight” of the other side. Therefore, you can estimate the mean by thinking about trying to balance the entire histogram on your finger. Where would you have to put your finger along the x-axis in order to keep the data balanced? That is the mean of the data. Based on this understanding, what is your estimate for the mean of the distribution? (Be sure the graph is displaying “Normal Data” group.)

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