Statistical Methods for Psychology

Report: RxTime

NStim N Mean Median Std. Deviation Variance

1 100 53.27 50.00 13.356 178.381

3 100 60.65 60.00 9.408 88.513

5 100 66.86 65.00 12.282 150.849

Total 300 60.26 59.50 13.011 169.277

Exhibit 2.1 SPSS analysis of reaction time data

2.11 Percentiles, Quartiles, and Deciles

A distribution has many properties besides its location and dispersion. We saw one of these

briefly when we considered boxplots, where we used quartiles, which are the values that

divide the distribution into fourths. Thus, the first quartile cuts off the lowest 25%, the sec-

ond quartile cuts off the lowest 50%, and the third quartile cuts off the lowest 75%. (Note

that the second quartile is also the median.) These quartiles were shown clearly on the

growth chart in Figure 2.11. If we want to examine finer gradations of the distribution, we

can look at deciles,which divide the distribution into tenths, with the first decile cutting

off the lowest 10%, the second decile cutting off the lowest 20%, and so on. Finally, most

of you have had experience withpercentiles,which are values that divide the distribution

into hundredths. Thus, the 81st percentile is that point on the distribution below which 81%

of the scores lie.

Quartiles, deciles, and percentiles are the three most common examples of a general

class of statistics known by the generic name of quantiles,or, sometimes, fractiles. We

will not have much to say about quantiles in this book, but they are usually covered exten-

sively in more introductory texts (e.g., Howell, 2008). They also play an important role in

many of the techniques of exploratory data analysis advocated by Tukey.

2.12 The Effect of Linear Transformations on Data

Frequently, we want to transform data in some way. For instance, we may want to convert

feet into inches, inches into centimeters, degrees Fahrenheit into degrees Celsius, test

grades based on 79 questions to grades based on a 100-point scale, four- to five-digit in-

comes into one- to two-digit incomes, and so on. Fortunately, all of these transformations

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RxTime

52 Chapter 2 Describing and Exploring Data

deciles

percentiles

quantiles

fractiles