Individual Text Assignment

12. Explain and give an example for each of the following types of variables: (a) equal-interval, (b) rank-order, (c) nominal, (d) ratio scale, (e) continuous.

(a) An equal-interval variable is variable by which numbers represent numbers stand for almost exact equal amounts of what is being measured (Aron, Aron, & Coups, 2009). An example is the difference between stress ratings of 2 and 4 means about as much as the difference between 5 and 7. (b) A rank-order or ordinal variables is a variable by which numbers stand for relative ranking only (Aron, Aron, & Coups, 2009). An example is a car models’ standing in a safety class ranking. (c) Nominal variable is a variable by which the values are categories or names (Aron, Aron, & Coups, 2009). An example is the nominal variable student; the values are traditional and nontraditional. (d) A ratio scale is a scale of measurement of data, which allows comparisons of the differences of values. An example is the time measured from the "Big Bang" until present is on a ratio scale, because before the “Big Bang” time had not begun on Earth. (e) Aron, Aron, and Coups (2009), “with a continuous variable, there are in theory an infinite number of values between any two values” (p. 4). An example is measuring height because the variables would be continuous. There are an unlimited number of possibilities of height even when only looking at between 4 and 5.2 feet.

15. Following are the speeds of 40 cars clocked by radar on a particular road in an 35-mph zone on a particular afternoon:

30, 36, 42, 36, 30, 52, 36, 34, 36, 33, 30, 32, 35, 32, 37, 34, 36, 31, 35, 20,

24, 46, 23, 31, 32, 45, 34, 37, 28, 40, 34, 38, 40, 52, 31, 33, 15, 27, 36, 40

Make (a) a frequency table and (b) a histogram. Then (c) describe the general shape of the distribution.

(a)    Frequency Table

SPEED	FREQUENCY	PERCENTAGE
15-19	1	2.5
20-24	3	7.5
25-29	2	5
30-34	15	37.5
35-39	11	27.5
40-44	4	10
45-49	2	5
50-54	2	5

(b) Histogram

(c) The general shape of distribution is unimodal.

19. Give an example of something having these distribution shapes: (a) bimodal, (b) approximately rectangular, and (c) positively skewed. Do not use an example given in this book or in class.

(a) Bimodal: an example is a day’s account of new drivers taken the written examination driver test. The majority of participants scored between 85-98%, the second largest category of participants scored between 84-88%, and the remainder of participants scored inconsistently between 55% and 99%.  

(b) Approximately rectangular: an example is an online college classroom of 25 traditional and nontraditional students. 15 of the students were 19 years of age and 10 were 32 years of age, which generates a rectangular distribution.

 (c) Positively skewed: an example is a case study of 25 college seniors, whereas one computes the hours of study spent on coursework daily, which may show positively skewed distribution. In this case study 10 students spent 2-3 hours studying daily, 11 spent 3 hours studying daily, and 3 students spent 4-5 hours studying daily. Giving outcomes positively skewed.   

20. Find an example in a newspaper or magazine of a graph that misleads by failing to use equal interval sizes or by exaggerating proportions.

This graph shows the stock market plummeted the day after President Barack Obama’s re-election but it does not show the trend of losses before the President’s re-election. The plummet started on May, 2008, which is not indicated. This leads individuals to believe the drop resulted from President Barack Obama’s re-election.

21. Nownes (2000) surveyed representatives of interest groups who were registered as lobbyists of three U.S. state legislatures. One of the issues he studied was whether interest groups are in competition with each other. Table 1–10 shows the results for one such question. (a) Using this table as an example, explain the idea of a frequency table to a person who has never had a course in statistics. (b) Explain the general meaning of the pattern of results.

(a) Frequency tables are used to explain data gathered and are a way to display certain factors present. These tables are used to find the mean of a large set of data values. In table 1-10, what is demonstrated is what the specific group encounters competition. 20% experiences no competition, 58% experiences some competition, and 22% experiences a lot of competition. (b) The general meaning of the pattern of results from table 1-10, shows results split up exhibiting a specific frequency of a group which encounters rivalry from similar groups. All responses are represented in percentage and number patterns, which indicate the relationship occurring between the groups.    

22. Mouradian (2001) surveyed college students selected from a screening session to include two groups: (a) “Perpetrators”—students who reported at least one violent act (hitting, shoving, etc.) against their partner in their current or most recent relationship—and (b) “Comparisons”—students who did not report any such uses of violence in any of their last three relationships. At the actual testing session, the students first read a description of an aggressive behavior such as, “Throw something at his or her partner” or “Say something to upset his or her partner.” They then were asked to write “as many examples of circumstances of situations as [they could] in which a person might engage in behaviors or acts of this sort with or towards their significant other.” Table 1–11 shows the “Dominant Category of Explanation” (the category a participant used most) for females and males, broken down by comparisons and perpetrators. (a) Using this table as an example, explain the idea of a frequency table to a person who has never had a course in statistics. (b) Explain the general meaning of the pattern of results.

(a) The information in the frequency table explains by sorting the data briefly and clearly. The table exhibits frequency and the percentage of occurrences team members, male and female experienced in each category situation.

(b) The general meaning of the results shows the trend of outcomes for the table, whereas the majority of women perpetrators (27%) display intimate aggression because of control motives, and the majority of men perpetrators (31%) display expressive aggression. The combined majority of intimate aggression of men and women was rejection of perpetrator or act with 46%, and the combined lowest of intimate aggression of men and women was prosocial/acceptable explanations with 0%.

Reference

Aron, A., Aron, E. N., & Coups, E. (2009). Statistics for psychology (5th ed.). Upper Saddle River, NJ: Pearson Prentice Hall.

Clark, P. (2012). The New York Observer. Retrieved from http://observer.com/2012/11/stocks-fall-on-day-after-obama-reelection-but-not-as-far-as-in-2008/