Dungeons & Dragons

“conditions”

“Given”

A frequency polygon for 642 psychology test scores shown in Figure 2.2.82.2.8\PageIndex{8} was constructed from the frequency table shown in Table 2.2.22.2.2\PageIndex{2}.

Frequency polygons are also a good choice for displaying cumulative frequency distributions

The histogram makes it plain that most of the scores are in the middle of the distribution, with fewer scores in the extremes. You can also see that the distribution is not symmetric: the scores extend to the right farther than they do to the left. The distribution is therefore said to be skewed. (We'll have more to say about shapes of distributions in Chapter 3.)

Interval's Lower Limit Interval's Upper Limit Class Frequency

Notice that each stem value is split into five parts: 0-1, 2-3, 4-5, 67, and 8-9.

Observe that the figure contains a row headed by “0” and another headed by “-0.” The stem of 0 is for numbers between 0 and 9, whereas the stem of -0 is for numbers between 0 and -9.

Thus, the value 43.2 is rounded to 43 and represented with a stem of 4 and a leaf of 3. Similarly, 42.9 is rounded to 43. To represent negative numbers, we simply use negative stems.

First, the data are limited to whole numbers that can be represented with a one-digit stem and a one-digit leaf.

Figure 2.2.42.2.4\PageIndex{4}: Back-to-back stem and leaf display. The left side shows the 1998 TD data and the right side shows the 2000 TD data.

To make this clear, let us examine Figure 2.2.22.2.2\PageIndex{2} more closely. In the top row, the four leaves to the right of stem 3 are 2, 3, 3, and 7. Combined with the stem, these leaves represent the numbers 32, 33, 33, and 37, which are the numbers of TD passes for the first four teams in Figure 2.2.12.2.1\PageIndex{1}.

The numbers to the right of the bar are leaves, and they represent the 1’s digits. Every leaf in the graph therefore stands for the result of adding the leaf to 10 times its stem.

A stem of 3, for example, can be used to represent the 10’s digit in any of the numbers from 30 to 39.

Scatter plots are used to show the relationship between two variables.

inally, we note that it is a serious mistake to use a line graph when the X-axis contains merely qualitative variables. A line graph is essentially a bar graph with the tops of the bars represented by points joined by lines (the rest of the bar is suppressed).

Figure 2.1.52.1.5\PageIndex{5}: A redrawing of Figure 2.1.22.1.2\PageIndex{2} with a lie factor greater than 8.

For example, 3-dimensional bar charts such as the one shown in Figure 2.1.42.1.4\PageIndex{4} are usually not as effective as their two-dimensional counterparts.

Figure 2.1.32.1.3\PageIndex{3}: A bar chart of the number of people playing different card games on Sunday and Wednesday.

Bar charts Bar charts can also be used to represent frequencies of different categories.

For example, if just 5 people had been interviewed by Apple Computers, and 3 were former Windows users, it would be misleading to display a pie chart with the Windows slice showing 60%.

Pie charts are effective for displaying the relative frequencies of a small number of categories. They are not recommended, however, when you have a large number of categories.

The pie chart in Figure 2.1.12.1.1\PageIndex{1} shows the results of the iMac study. In a pie chart, each category is represented by a slice of the pie. The area of the slice is proportional to the percentage of responses in the category. This is simply the relative frequency multiplied by 100. Although most iMac purchasers were Macintosh owners, Apple was encouraged by the 12% of purchasers who were former Windows users, and by the 17% of purchasers who were buying a computer for the first time.

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All of the graphical methods shown in this section are derived from frequency tables. Table 1 shows a frequency table for the results of the iMac study; it shows the frequencies of the various response categories. It also shows the relative frequencies, which are the proportion of responses in each category. For example, the relative frequency for “none” of 0.17 = 85/500.

The key point about the qualitative data that occupy us in the present section is that they do not come with a pre-established ordering (the way numbers are ordered).

Non-Experimental Designs

Quasi-Experimental Designs

Experimental Designs

To solidify your understanding of sampling bias, consider the following example. Try to identify the population and the sample, and then reflect on whether the sample is likely to yield the information desired.

We are interested in examining how many math classes have been taken on average by current graduating seniors at American colleges and universities during their four years in school.

It is not practical to ask every single American how he or she feels about the fairness of the voting procedures. Instead, we query a relatively small number of Americans, and draw inferences about the entire country from their responses. The Americans actually queried constitute our sample of the larger population of all Americans.

For example, experimental subjects may be asked to rate their level of pain, how much they like a consumer product, their attitudes about capital punishment, their confidence in an answer to a test question.

Ratio scales

Interval scales

Ordinal scales

Nominal scales

The essential point about nominal scales is that they do not imply any ordering among the responses.

Other variables such as “time to respond to a question” are continuous variables since the scale is continuous and not made up of discrete steps

Variables such as number of children in a household are called discrete variables since the possible scores are discrete points on the scale. For example, a household could have three children or six children, but not 4.534.534.53 children

Some examples of quantitative variables are height, weight, and shoe size

Qualitative variables are those that express a qualitative attribute such as hair color, eye color, religion, favorite movie, gender, and so on.

If an experiment were comparing five types of diets, then the independent variable (type of diet) would have 555 levels

control

experimental

systematically

39,000 women aged 45 and up

However, a study published in the Journal of the National Cancer Institute suggests this is false

Does beta-carotene protect against cancer?

Although all supplemented rats showed improvement

blueberry, strawberry, or spinach powder

Can blueberries slow down aging?

In this example, relief from depression is called a dependent variable. In general, the independent variable is manipulated by the experimenter and its effects on the dependent variable are measured.

In this case, the variable is “type of antidepressant.” When a variable is manipulated by an experimenter, it is called an independent variable

Many of the numbers thrown about in this way do not represent careful statistical analysis

People tend to be more persuasive when they look others directly in the eye and speak loudly and quickly.

Almost 85%85%85\% of lung cancers in men and 45%45%45\% in women are tobacco-related.

If you cannot distinguish good from faulty reasoning, then you are vulnerable to manipulation and to decisions that are not in your best interest.

many students view statistics as a math class, which is actually not true

In addition, the statistic provided does not rule out the possibility that the number of interracial marriages has seen dramatic fluctuations over the years and this year is not the highest.

The more churches in a city, the more crime there is. Thus, churches lead to crime.

This effect is called a history effect