Decile

As with all quantiles, a decile is a rank-order statistic. A decile divides a distribution of data into 10 equally sized groups determined after ranking the data according to some measure or combination of measures. After offering two meanings for the term decile, this entry provides an explanation of how decile values can be utilized in educational settings, including an example of its use in New Zealand.

The most common quantiles are percentiles, quartiles, deciles, and sometimes quintiles. Percentiles offer too many groups to visualize and to make sense of each group, but deciles provide a fairly large number of groups that can still be treated at one time while still allowing the analyst to deal with each of them as separate entities.

The term decile can have two meanings—a point on the distribution that divides two of the 10 groups and the group to which a member of the distribution belongs. There are nine decile values that separate the data into the 10 groups. The ninth decile value is the point in the distribution where nine tenths of the data lies below that value. The second decile is the point below which two tenths of the distribution lies. If a point on the distribution lies between the second and third decile, then it is a member of Decile 3. If data are normally distributed, then areas under the normal curve tables can be used to identify deciles. For example, normally the mean is the fifth decile and the sixth decile is around a Z of .25 or .25 standard deviations above the mean.

When an analyst breaks data into quantile groups, the purpose is to simplify the way in which the analyst can visualize the data to look for patterns and trends or to compare and [Page 475]contrast high-performing and low-performing groups. Deciles are used in the real-world decision making in a number of ways. For example, they have been used for equity funding of state and state-integrated schools in compulsory education in New Zealand. Unlike other jurisdictions overseas, schools in New Zealand are not permitted to collect family demographic data such as parental qualifications or income in order to assess the socioeconomic background of students attending the school.

For each school, the home address of students is extracted and compared with mesh block data from the most recent 5-year census on five indicators: household income, occupation of employed adults, household crowding, educational qualifications, and income support (i.e., receipt of social welfare support). These indicators are combined, each school is ranked, and 10 groups with approximately equal numbers of schools are obtained.

Decile 1 schools have the highest proportion of students from low-income communities, and Decile 10 schools have the lowest proportion of these students. Although there are some funding components that are equally applied to all schools and students (e.g., the basic per capita grant), differential funding on other specific targeted equity components is applied to enable schools to address the challenges that are faced by schools in low-income communities.

See also Box Plot; Descriptive Statistics; Percentile Rank;

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