语言教学 | 普渡大学写作教学系列Research&Citation17-Writing with Statistics(3)

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6、Writing with Inferential Statistics

Writing Statistics Plainly

In general, you should always 'translate' your statistics into some understandable form for your reader.

Poor example: "A t-test (t = 3.59) showed that the two groups were significantly different (p<0.01)."

The example above is complicated and hard to read. It's better to say something plainly first, then provide the statistical evidence afterwards:

Better example: Women scored higher than men on the aptitude test (t = 3.89, p < 0.01).

In the second example, your reader understands the relationship, it's not filled with jargon, but all of the same information is presented. Note that different fields have their own way of writing with statistics—please refer to your field's style guide for specific guidelines.

When using a complicated inferential procedure that your readers would be unfamiliar with, explain it. It may be necessary to go over it in detail. You may want to cite who used it first, and why they used it, and explain how it is applicable to your situation. A footnote or an appendix is a fine place for such an explanation.

If you include statistics that many of your readers would not understand, consider adding the statistics in a footnote or appendix if you can, especially if it is not central to your argument.

Writing Statistics Accurately

If you aren't sure how to calculate a particular statistic, either find out how, or don't use it. Along the same lines, never plug in numbers into a computer program, such as SPSS, and think that the output is "correct." Computer programs don't think for us; they simply allow for fast calculations. They cannot and do not interpret results. You should never interpret the results of a statistic that you don't fully understand. This is extremely important.

When in doubt, keep it simple. If the only thing you can say for certain is that the mean of one group is higher than the mean of another group, then that is fine. This is evidence, albeit it's not as strong as other types of evidence.

Remember that inferential statistics can never "prove" anything. You should think of statistics as a body of evidence (much like a fingerprint at a crime scene) that provides support for your argument. Sometimes it can be used as primary evidence or sometimes it is used in a more supporting role.

Focusing on Statistics

How you frame the use of your statistics is extremely important. In a more scientific field, you'll probably want your statistics as a focal point, but in other fields (say politics, for instance) you may use statistics to support a stance or policy, but it may be only one of many reasons for that policy. Knowing how your audience will react to statistics should affect how you use it. If your audience doesn't use a lot of statistics, you probably shouldn't make statistics the focal point of your argument, or if you do, you need to be very good about explaining the logic behind your statistics.

7、Statistics and Visuals

Tables

Don't be afraid to use graphics. Statistics can contain a lot of information. Visuals can display a lot of information in a manner that can be quickly understood. The same thing applies to tables. For example:

The mean (and standard deviation in parentheses) for group A was 10.5 (2.1), the mean (S.D.) for group B was 12.3 (1.2) the mean (S.D.) for group c was 15.9 (1.8), and the mean (S.D.) for group D was 21.3 (2.5).

It' s hard to read! Imagine trying to make sense of this. Instead, provide your data in a table for easy reading:

A table is much easier to read than blocks of text. It can help sort the information for both you and your readers. It also makes group comparisons easy. For example, suppose you want to point out to the reader the difference between group A and group D (perhaps this was a new weight training program comparing the number of 80 lbs. dumbbell reps).

Or, you could do this:

Don't be afraid to bold, use asterisks, or otherwise highlight important groups or comparisons.

Graphs

Graphs are an excellent alternative to tables, and they are used by virtually everyone in every field. Papers and articles are like faces. Graphics are like makeup. Makeup is always good in small doses, but don't over apply, or you will end up looking worse than if you didn't use any make up at all. Use visuals, but be careful not to over use them. This is a good example of a visual using the data from the previous table:

Consider distributions of information for a moment. Imagine that we are teaching a class and displaying the students' first homework grades to the students for their benefit. This is one of the ways we could display their homework grades.

In this graph, each of these bars represents a student (each student gets a different color). This is an example of using too much make-up. While the graph does convey a lot of information, it is hard to read. The following graph is much better, and it actually gives you some useful information regarding the class:

Now we can clearly see that one person did really poorly, but that most people were clustered between 70-90%. In the first graph of student scores, we can't really 'see' the distribution, but in this second graph we have a much clearer image of the distribution of scores.

8、Key Terms

Data Point: A data point is one particular number or item from a data set.

Data Set: A data set is simply a group of numbers. In formal mathematics, data sets are distinguished from each other by using brackets. A more formal mathematical definition allows a data set to contain other things besides numbers (such as letters, items, or even concepts and ideas). The following data set contains only the numbers 2, 5, and 7.

 {2,5,7}

Distribution: A distribution is simply how the data points are clustered. Are they spread apart evenly, or do most of them cluster in the middle and fall off towards the edge like a bell-shaped curve? Two data sets may have the same mean or median, but having different distributions gives them radically different properties.

Mean: The mean (or arithmetic mean) is what most people are referring to when the say average. It is simply the total sum of all the numbers in a data set, divided by the number of different data points.

Median: The middle data point in a data set.

Mode: The most common data point in a data set. This is the value that occurs with greatest frequency.

Population: A population is all of the members contained within a group. In statistics, the population is the group you want your results to generalize about. For example, if you are studying a particular species of fish. such as a Yellow Fin Tuna, then your population is all Yellow Fin Tuna. Your population would not be all fish, nor would your population be all the different species of tuna.

Sample: A sample is all of the units or members that you have studied, drawn from a larger population. In our tuna example, researchers may have found 50 particular yellow fin tuna to study. The sample therefore would consist of 50 yellow fin tuna. As a researcher, you hope that your sample is as representative of your population as possible. The closer the sample represents the population, the stronger and more accurate an inference drawn from the sample will be. This is why you want a large sample to study from.

T-test: A t-test is a common statistical test used to compare two groups, typically two groups' means (the difference of two means divided by a measure of variability). A t-test takes into account the number of units in the sample.

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