What are the degrees of freedom for the variance?
Provide a response to the following questions.
1. The Wilcox & Keselman (2003) article from this week’s electronic readings discusses two problems with measures of central tendency: skewness of the data and outliers. Discuss each of these issues and how they affect measures of central tendency.
2. For the following scores, find the mean, median, and mode. Which would be the most appropriate measure for this data set? You may use Microsoft^{®} Excel^{®} data anlysis to compute these statistics. You may copy your output from Microsoft^{®} Excel^{®} into this worksheet.
2, 2, 0, 5,1, 4,1, 3, 0, 0, 1, 4, 4, 0,1, 4, 3, 4, 2, 1
3. Based on the scale of measurement for each variable listed below, which measure of central tendency is most appropriate for describing the data?
a. The time (in years) it takes a sample of students to graduate college.
b. The blood type (such as A, B, AB, or O) of a group of participants.
c. The rankings of college undergraduate academic programs.
4. How do the sample mean and the population mean differ? What is the symbol for each type of mean?
5. An expert reviews a sample of 10 scientific articles (n = 10) and records the following numbers of error in each article: 0, 4, 2, 8, 2, 3, 1, 0, 5, and 7. Compute the SS, the variance, and the standard deviation for this sample using the definitional and computational formulas. You may use Microsoft^{®} Excel^{®} data anlysis to compute these statistics. You may copy your output from Microsoft^{®} Excel^{®} into this worksheet.
6. A psychologist interested in political behavior measured the square footage of the desks in the official office of four U.S. governors and of four CEOs of major U.S. corporations. The figures for the governors were 44, 36, 52, and 40 square feet. The figures for the CEOs were 32, 60, 48, 36 square feet.
a. Figure the means and standard deviations for the each group: governors and CEOs.
b. Explain, to a person who has never had a course in statistics, what you have done.
c. Note the ways in which the means and standard deviations differ, and speculate on the possible meaning of these differences, presuming they are representative of U.S. governors and large corporations’ CEOs in general.
7. Radel and colleagues (2011) conducted a study of how feeling overly controlled makes you desire—even unconsciously—more freedom. In their study, 52 Canadian undergraduates played a video game in a laboratory and were randomly assigned to one1 of the following:
- · An automony deprivation condition, in which they were told to follow instructions precisely, constantly given instructions over a loudspeaker, and carefully observed on everything they did.
- · A neutral condition, which was much more laid back.
After this activity, they were asked to do a lexical decision task (a standard approach for measuring unconscious responses), in which they were shown a series of words and nonwords in random order and had to press C if it was a real word or N if not. Half of the real words were related to autonomy (such as freedom and choice), and half were neutral (such as whisper and hammer). The key focus of the study was on how long it took people to press the button (response latency) for each kind of real word, averaged over the many words of each type. The table below shows the mean and standard deviation across the participants of these four categories of results. For example, 782 milliseconds (thousandths of a second) is the average time it took participants in the autonomy-deprived condition to respond to the autonomy-related words, and 211 is the standard deviation across the 26 participants’ average response time in that condition. Explain the numbers in this table to a person who has never taken a course in statistics. (Be sure to explain some specific numbers, as well as the general principle of the mean and standard deviation.) For your interest, the pattern of results shown here supported the researchers’ hypothesis: “Relative to a neutral instructional climate, a controlling climate thwarting the need for autonomy…enhanced accessibility for autonomy-related words” (p. 924).
Mean Latencies (in Milliseconds) in the Lexical Task Assessing Accessibility for Autonomy-Related Constructs (Experiment 1) | |||||
Condition | |||||
Autonomy Deprivation | Neutral | ||||
Construct | M | SD | M | SD | |
Autonomy-related words | 782 | 211 | 857 | 243 | |
Neutral words | 835 | 258 | 841 | 301 |
8. A researcher records the levels of attraction for various fashion models among college students. He finds that mean levels of attraction are much higher than the median and the mode for these data.
a. What is the shape of the distribution for the data in this study?
b. What measure of central tendency is most appropriate for describing these data? Why?
9. An organizational psychologist measures levels of job satisfaction in a sample of 30 participants. To measure the variance of job satisfaction, it is calculated that the SS = 120 for this sample.
- What are the degrees of freedom for the variance?
- Compute the variance and standard deviation (you will have to do this one by hand).
10. State the three empirical rules for a normal distribution with any mean and varaince.
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