Sensation and Perception

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 is more than 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. In essence, 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 to keep the data balanced? That value is the mean of the data. Based on this understanding, what is your estimate for the mean response to the question about individuals’ perception of their most bitter experience? (Be sure the graph is displaying the “Most Bitter Experience” data.)

One of the other pieces of data that Dr. Bartoshuk collected on her questionnaires was the height of the individual answering the survey. Switch to the histogram that shows the height data. Many of the data sets we study in psychology have the particular shape shown in this histogram: Most of the data are centered on, or piled up around, the mean value, with the response frequencies becoming less common as the values move away from the mean in either direction. Such distributions are called symmetric distributions because they have roughly the same shape above and below the mean value. Use the applet to investigate the mean, median, and mode of this data set. If you had to choose just one of these values to describe the data, which one would you choose and why? (Select “Height” for the group to display, and cycle through showing the mean, median, and mode.)

Not all cases are so simple, though. In psychology, many measurements are not symmetric. For example, some histograms may have more responses trailing off in one direction or the other—a shape we refer to as skewed. Look at the distribution of responses when people were asked to report their perception of the bitterness of celery. We would classify this distribution as positively skewed because the tail of the distribution extends out in the positive direction (toward the right). How does a positive skew change the relative locations of the mean, median, and mode? (Select “Bitterness of Celery” for the data to display, and investigate the mean, median, and mode.)

Still looking at the graph for the bitterness of celery, which portion of the data is below (less than) the mean of this skewed distribution?

If you were analyzing a distribution of response time values that had a positive skew, similar to the skew of the responses for the bitterness of celery, which measure of central tendency would provide the best representation of the data and why?

Suppose that a shady marketer from the (fictional) Carrot Farmers Alliance wanted to promote the incorrect belief that celery is a very bitter vegetable (and insinuate that parents should buy their children carrots instead). Using the data collected and without changing any of the data, which measure of central tendency would the marketer be likely to report about celery’s bitterness and why? (Hint: Higher scores indicate a stronger perception of bitterness.)

In addition to distributions with positive skews, we can collect data sets that have a negative skew. Investigate the remaining data distributions and look for a histogram that shows most of the responses at the high end of the response scale, with a smaller number of responses trailing off toward the lower end of the distribution. Which of the following distributions shows the strongest negative skew?

The data in the Strongest Pain Experienced graph have a negative skew, as shown by the tail of the distribution extending out in the negative direction (toward the left). How does a negative skew change the relative locations of the mean, median, and mode?

When presented with a data distribution that is strongly skewed (positively or negatively), which measure of central tendency should be used to present the most representative description of the data?

Based on the questions in this applet and the information from the text, which point should be kept in mind when evaluating the best measure of central tendency to report for data?

The standard deviation is a measure of how spread out the data in a particular distribution are. Roughly speaking, it is the average distance away from the mean value of any single data point in the distribution. If all of the data values are very close to together, then the average distance from the mean value would be small. If the data are very spread out, however, then many of the data points could be far away from the mean value, and the standard deviation would be much larger. Look at the graph that shows people’s perceptions of their most bitter experience. That data set has a mean value of approximately 56, but quite a few individuals gave scores down around 20 or up around 90—that is, the data are very spread out. Compare this distribution to the distribution of scores for the perception of a loud whisper. Which of the following statements best describes the variability of those two data sets?

Look at all of the data sets that are available in this exercise. When examining each graph, think about whether each graph shows data with a high level of variability or a low level of variability. Be sure to pay attention to the x-axis, as it may differ from graph to graph! After looking at each graph, predict (estimate) which data set will have the largest standard deviation. Then go back and use the controls on the graph to display the standard deviation and double-check your intuition. Which data set has the largest standard deviation?