1. Suppose that in a study involving only 40 participants, researchers look at self-esteem differences between two groups. They find a small, but statistically significant, difference between the self-esteem of the two groups. Based on this information, would you infer that the measure’s reliability was low or high? Why?
· The measure is obviously sensitive. Would a sensitive measure’s reliability be low or high?
· If, as the book suggests, random error is like fog, static, and noise, what does random error due to sensitivity? What is the relationship between reliability and random error?
· See pages 199-200.
2. List the scales of measurement in order from least to most accurate and informative.
Nominal, ordinal, interval, and ratio.
3. Becky wants to know how much students drink.
· What level of measurement could Becky get? Why?
Hints: Could she measure a true zero? Could she make ratio statements like Jim drinks 2 times as much as Tom. If so, she should be able to get a measure that allows her to make ratio statements about how much students drink.
· Becky asks participants: How much do you drink:
a) drinks; b) 1-3 drinks; c) 3-4 drinks, d) more than 4 drinks. What scale of measurement does she have?
Hints: Is there an order to the measure? If so, it is at least ordinal. Are there equal distances (intervals) between the scores? If so, it is interval. If not, it is not interval—and cannot be ratio.
· Becky ranks participants according to how much they drink. What scale of measurement does she have?
Hints: If she can order participants from lowest to highest, she has at least an ordinal scale of measurement. To do more, she must be able to tell how much of a difference there is between participants. Can she do that? For more help, see pages 208-209.
· Becky assigns participants a “0” if they do not drink, a "1" if they are a wine drinker, and a "2" if they are a beer drinker. What scale of measurement is this?
Hints: Does larger number (2) refer to more of a quality than a (1)? If so, the data are at least ordinal. If not, do different numbers refer to different types of drinkers? In that case, what scale of measurement do you have? For more, see p. 207
· Becky asks participants: How much do you drink?
1) 0-1 drinks; 2) 1-3 drinks; 3) 3-4 drinks, 4) more than 4, and 5) don't know
Hints: If she includes “5” (don't know), is “5” necessarily more than “4” (more than 4 drinks). If she did not have the “5” option, what kind of data would she have?
4. Assume that facial tension is a measure of thinking.
· How would you measure facial tension?
Facial tension could be measured as the amount of lines a person gets on his/her face during times of stress or by measuring electrical activity of facial muscles.
· What scale of measurement is it on? Why?
You might assume that it is an ordinal scale (more tension means more thinking). Certainly, it would not be safe to assume that you had a ratio scale (twice as much tension means twice as much thinking). Indeed, it would probably not be safe to assume that you had an interval scale (that there is a perfect relationship between increases in tension and increases in thinking).
· How sensitive do you think this measure would be? Why?
The measure of lines on the face might not be sensitive (there would be a small range of scores and some random observer error). However, the measure of electrical activity in the facial muscles might be extremely sensitive.
5. Suppose a researcher is investigating the effectiveness of drug awareness programs.
· What scale of measurement would the investigator need if she were trying to discover whether one drug awareness program was more effective than another?
Hints: Could nominal scale data show that one group was more effective than another? What about ordinal data?
What scale of measurement would the investigator need if she were trying to discover whether one program is better for informing the relatively ignorant than it is for informing the fairly well-informed?
Hints: The investigator needs to compare changes in low scores to changes in high scores. To do that, the investigator needs to be able to assume that a one-unit change, regardless of whether it happens to a low score, a medium score, or a high score, represents the same amount of change. What scale of measurement is needed to assume that the intervals between numbers are equal?
6. In an ideal world, car gas gauges would be on what scale of measurement? Why?
Ratio. You would want the best measurement possible. It would be nice to know that if you registered having half a tank you really had half a tank.
In practice, what is the scale of measurement for most gas gauges? Why do you say that?
Ordinal. You know that if your gauge registers full, it has more gas than if it registers half-full. So, your gas gauge does tell you something about quantity. Therefore, it’s not nominal. However, gas gauges tend to go down slowly until they register about half-full and then quickly thereafter. That is, it isn’t an equal-interval scale, so it can’t be interval or ratio.
7. Find or invent a measure.
· Describe the measure.
Hints: That obviously depends on the measure. To find a measure, you might use one of these links:
· Discuss how you could improve its sensitivity.
Hints: See green headings on pages 198-203
· What kind of data (nominal, ordinal, interval, or ratio), do you think that measure would produce? Why?
Hints: See Table 6.3 (p. 216). If you are still stuck, see Table 6.1 (p.214)