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.
1) 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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2) Many of the data sets we study in psychology have the particular shape shown above – most of the data is centered on a the mean value, with the response frequencies becoming less common as the values move away from the mean. These distributions are often called “normal distributions.” Use the applet to investigate the mean, median, and mode of the normal data set. If you had to choose just one of these values to describe the data, which one would you choose and why? (Select “Normal Data” for the Group to display, and cycle through showing the Mean, Median, and Mode.)
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3) Some measurements, like response time values, are typically skewed. The data in the Positive Skew graph represents a positive skew because the tail of the distribution extends out in the positive direction (towards the right). How does a positive skew change the relative locations of the mean, median, and mode? (Select “Positive Skew” for the Group to display, and cycle through showing the Mean, Median, and Mode.)
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4) Still looking at the graph for positively skewed data, what portion of the data is below the mean of this skewed distribution? (Select “Positive Skew” for the Group to display, and show the Mean.)
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Statistical Lesson. It may come as a surprise that more than half of the values in a distribution can be below (or above) average. You may sometimes hear friends or even professors say something like “75% of all students think that they are above average!”, implying that such a distribution is not possible. However, it is possible, and it is not even unusual. Whenever you are dealing with a skewed distribution, the mean value is pulled towards the tail and more than half of the values – sometimes far more than half of the values – can be above or below average. In fact, most Introductory Psychology classes have exam scores that are negatively skewed, so it’s quite likely that more than half of your classmates will have an above average score on the next exam!
5) If you were analyzing a distribution of response time values that had a positive skew similar to the data in the Positive Skew graph in the previous questions, which measure of central tendency provides the best representation of the data and why?
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6) Suppose that a shady researcher from another university wanted to promote the incorrect belief that the response times for students at other schools were not as fast at performing a response time task as the students at his university. Which measure of central tendency would he be likely to report for the other school’s data and why? (Hint: Keep in mind that slower response times means it took the student more time to complete the task.)
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7) Some measurements, like Introductory Psychology exam scores, are typically skewed. The data in the Negative Skew graph represents a negative skew because the tail of the distribution extends out in the negative direction (towards the left). How does a negative skew change the relative locations of the mean, median, and mode? (Select “Negative Skew” for the Group to display, and cycle through showing the Mean, Median, and Mode.)
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8) How does the measure of central tendency that provides the best representation of the data compare in positively and negatively skewed distributions?
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9) Some aspects of perception, like the perception of bitterness in a particular food, can follow a bimodal distribution – a distribution where the data tends to fall into two distinct ranges or clusters of responses. The textbook says that most of the population are tasters, who would report little to no perception of bitterness when tasting dark green vegetables. But about 25% of the population are supertasters, and their perceptions of bitterness would all be much higher. The resulting distribution might look similar to the one in the Bimodal graph. Which measure of central tendency is the most representative and why? (Select “Bimodal” for the Group to display, and cycle through showing the Mean, Median, and Mode.)
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10) Based on the questions in this applet and information from the text, what should be kept in mind when evaluating the best measure of central tendency to report for data?
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