Homework #1: Due Friday Sept. 3, 2004
1. Using your own words, define the terms “descriptive statistics” and “inferential statistics.” (2 points)
Descriptive statistics are a set of procedures that allow us to summarize and/or
simplify a set of data, usually with a single number or very small set of numbers.
Inferential statistics allow us to compute values based on a sample of individuals
and use those sample values as estimates of population values. Inferential statistics allow us to take values computed from a sample and generalize them to a larger population of individuals.
2. A survey researcher asked a group of college students the following question:
I like the Daily Show:
Not at all 1 --- 2 --- 3 --- 4 --- 5 --- 6 --- 7 Very Much
a). Make the argument that this question represents a discrete variable. (1 point)
This variable represents a discrete variable because there are only whole numbers as possible answers.
b). Make the argument that this question represents a continuous variable. (1 point)
Though the measuring instrument itself is limited to whole numbers, the psychological construct of liking is in theory something that ranges in a continuous fashion—with an infinite number of possible values representing it. One could easily imagine using a more fine-grained measuring scale to capture levels of liking than the one used here.
c). Make the argument that this variable is measured using an interval scale. (1 point)
This variable represents an interval scale because (1) the numbers indicate actual amounts (i.e., a value of 7 indicates more liking than a value of 5); and (2) we can reasonably assume that the distance between units is equal (i.e., the interval between 1 and 2 is the same as the interval between 4 and 5).
d). Make the argument that this variable is measured using an ordinal scale. (1 point)
One could argue that this variable is measured using an ordinal scale. The values could be considered just relative – that is, someone who says they like the Daily Show at level 6 has relatively more liking for the show than someone who rates it at 5. But, one could argue that the distances between the units are not all equal. Someone who likes the Daily Showfairly wellmay give it a rating of 5. Someone who likesitverywell may give it a 6. However, someone might need to likethe Daily Showextremely well before giving it the top rating of 7. The psychological distances between “like it fairly well,” “like it very well,” and “like it extremely well” may not be equal. If we cannot assume equal distances between units, then the scale is not interval.
3. Suppose you are interested in investigating if exercise impacts mood. Explain how you might investigate this hypothesis using (a) correlational methods and (b) experimental methods. (4 points)
Correlational method: Obtain a random sample of Miami students and measure how often they exercise and their current mood. Conduct statistical tests to see if those who exercisemore regularly have better moods. The key here is that we are only measuring variables.
Experimental method: Obtain a sample of Miami students and randomly choose half of them to exercise for 30 minutes. The other half of the sample will just sit quietly for 30 minutes (i.e., not exercise). Then, measure each student’s mood using a standard mood questionnaire. Then, conduct statistical tests to determine if the group who exercised reportsbetter moods than those who did not exercise. The key here is that we manipulated an independent variable (in this case exercise) to see its impact on a dependent variable (in this case mood).
4. A market-research firm asked 12 randomly selected people how often they shop at the local mall per month. Their answers are shown below. Use these data to create a simple frequency distribution, a relative frequency distribution, and a cumulative frequency distribution by hand (i.e., do not use SPSS). (6 points)
4, 2, 0, 0, 2, 1, 1, 8, 6, 5, 4, 3
X
/ f / p / % / cf / c%8 / 1 / .083 / 8.3 / 12 / 100
7 / 0 / 0 / 0 / 11 / 91.67
6 / 1 / .083 / 8.3 / 11 / 91.67
5 / 1 / .083 / 8.3 / 10 / 83.33
4 / 2 / .167 / 16.7 / 9 / 75.00
3 / 1 / .083 / 8.3 / 7 / 58.33
2 / 2 / .167 / 16.7 / 6 / 50.00
1 / 2 / .167 / 16.7 / 4 / 33.33
0 / 2 / .167 / 16.7 / 2 / 16.7
5. What type of graphical display is shown below? Is the distribution skewed positively, skewed negatively, or symmetric? What is the mode of this distribution? Is the graphed variable quantitative or categorical? (4 points)
This is a histogram. Histograms look similar to bar charts. The difference is that adjacent bars touch in histograms to reflect the continuous nature of the variable. Bar graphs have gaps between all values because they are used to display categorical data.
The distribution is NOT symmetric. If it were, one side of the distribution would be the mirror image of the other. This isn’t the case. So, the distribution is skewed. Specifically, it is positively skewed. Remember, the skew follows the “tail.”
The bars on this particular histogram represent intervals of values (not one specific value). So, it is technically impossible to say what exact value occurs most frequently. Thus, our best guess is that the mode (most frequently occurring score) is in the range of 250-350 because the bar representing that interval is the tallest. Another acceptable answer is that the mode occurs at the value of 300.0 (b/c that is the value at the center of the 250-350 range).
The graphed variable is quantitative. Histograms are used to display quantitative variables not categorical ones.