Statistics in Descriptive Research

The description of a sample implies that a researcher defines variables, measures them, and for each measure calculates one or more of the following descriptive statistics: measures of central tendency and measures of variability. Measures of central tendency are: mean, median and mode. Measures of variability are: standard deviation, variance and range. The researcher can also calculate the derived scores which help interpreting the sample's scores on the variables that were measured. Derived scores aid the interpretation by providing a quantitative measure of each individual's performance relative to a comparison group. Age equivalents, grade equivalents, percentiles, and standard scores are examples of derived scores commonly used in descriptive research.

Some descriptive research provide statistical information about aspects of education that interest  policy makers and educators. This type of research is the specialty of the National Center for Education Statistics. Many of this center's research results are published in an annual volume called the Digest of Educational Statistics. This center also administers the National Assessment of Educational Progress (NAEP), which is a collection of descriptive information about the performance of youth in the different subjects taught in public schools. A noticeable NAEP publication is the Reading Report Card, which reports descriptive statistics about student's performance in reading at different levels. At a higher level the International Association for the the Evaluation of  Educational Achievement (IEA) does descriptive studies of the academic achievement of students in many nations including the United States.

The two main types of descriptive research differ by the time the variables are measured. In the first type the variables or the characteristics of a sample are measured at one point in time. In the second type which is called longitudinal a sample is followed over time.    

Statistical techniques

Definition of Statistics

Statistics are mathematical techniques  for analyzing numerical data to accomplish various purposes. For example the calculation of a mean leads to a single score that represents many scores such as the scores of all students who took a particular test.

Types of Statistics

There are four types of Statistics: descriptive, correlational, inferential and psychometric.

Descriptive Statistics

Descriptive Satistics are mathematical techniques for organizing and summarizing a set of numerical data. In Educational Research they are used to describe educational phenomena. They describe the score on a single variable

Correlational Statistics

Correlational Statistics are used to describe relationships between two or more variables.

Inferential Statistics

Inferential Statistics are mathematical techniques for using probabilities and information about a sample to draw conclusions about the population from which the sample originated.

Psychometric Statistics

They are Statistics used to describe the psychometric properties of tests and he appropriateness of information and uses of outcomes from tests and other measures.


Example of Statistical Analysis in a Research Study


Statistics are used in virtually all quantitative studies but in many qualitative studies also. An example is the case study of reading groups in a first grade classroom conducted by James Collins. The study was part of a large ethnographic study of language differences between working class black children and middle class white children in their home and school environments.

Types of Scores 

Measurements in educational research are expressed usually in three forms: continuous scores, ranks, or categories. It is important to understand the differences between the score types because the forms in which the scores are expressed reflect the choice of statistical analysis procedure. If the research data consist of continuous scores on two groups group differences are analyzed by calculating a mean score and a statistic known as t. However if the scores are in thew forms of categories the group differences are analyzed by a Chi-square test, which compares categories frequencies between two or more groups. There are 3 types of scores: continuous, age and grade equivalents and rank.