descriptive statistics essay

descriptive statistics essay

Exploring the Importance and Application of Descriptive Statistics in Research

1. Introduction to Descriptive Statistics

Descriptive statistics are also used to describe how many, how much, how often, and how well, in terms of either the proportion of values that fall into specific categories, the amount of a particular variable, or the average value of that variable. Researchers carefully choose the particular descriptive statistics they seek to calculate, based on the study question and the level of measurement of the variable being studied. For example, if the study is designed to describe the gender differences in a weight loss program, the sample proportion (percentage) of women and men in the program is of great interest. Descriptive statistics aid in the description and interpretation of the properties of the underlying body of data. When a very large number of variables are provided in a research study, the properties can seem overwhelming. When the data analysis plans include statistical tests of group differences, the utility of descriptive statistics is even greater, because their magnitudes help to prioritize which variables to address first in the results of the study.

Descriptive statistics serve to summarize data in a clear and understandable way. Often, these summaries become the results that emerge from research studies. For example, researchers often analyze data to describe the demographic characteristics of the people in their studies. They do this for a number of reasons, but some of the most important are to help make the sample “come alive” in the reader’s mind and to allow readers, when they read the findings in the rest of the paper, to relate the groups in the study, such as the gender and ethnicity of subjects, to the results, and how they might apply to people in other groups like themselves.

2. Key Concepts and Measures in Descriptive Statistics

When we use descriptive statistics techniques to discuss our data, the measures we typically discuss include measures of central tendency or measures where the center is located in the distribution of a variable. We also utilize measures of variability or measures that indicate the extent to which the scores of a variable are spread out or dispersed in a data set. We usually examine and would like to find a balance between the measures of central tendency and variability when examining and answering questions about the data using statistics. Finally, we typically use bar, pie, and histogram charts to demonstrate many of the basic characteristics and properties – both descriptive and inferential – of a set in statistics.

What do we mean by descriptive statistics? Any class involves the collection and analysis of data set(s), and answering research question(s) about the data. In order to answer the research questions, we generally have to apply some sort of mathematics to help analyze and summarize (hence the term descriptive) the data we have already collected. Descriptive statistics involves the summarizing, organization, and describing of data so they can be more easily understood and interpreted. Descriptive statistics for a single variable are known as univariate, where univariate means ‘a variable.’ For two variables, the term is bivariate, where bi- means ‘two.’ Using statistical software programs can greatly facilitate the calculations that are typically made in computing the descriptive statistics for a data set.

3. Methods and Techniques for Descriptive Data Analysis

In order to provide an overall summary of the data in a manner that allows a succinct response to the research questions, we will explore approaches that should be considered to summarize numeric data objectively and succinctly. The basic margin statistical measures for a numeric distribution include: the mean, median, and the mode. These measures summarize the center of the distribution, and the variability of the distribution. However, they do not give satisfactory description of the shape of the distribution. The three basic margin statistical measures focus only on the center of the distribution. Therefore, the usefulness of these measures depends upon how well they reflect the actual distribution of interest. The histogram or the box plot is an essential tool for understanding the data to validate the assumption that the distribution of interest should have.

It is good to point out that boxed graphical displays and numerical summaries are, in fact, a typical way of presenting data when they are first collected, during an exploratory phase of the research. It is also important to note that descriptive statistics does not involve the use of the standard distribution tables or the drawing of inferences about populations on the basis of samples. Instead, the goal of descriptive statistics is to transform a significant body of data in a manner that communicates a general understanding and possible patterns of the data to the target audience. Data analysts should never underestimate the importance of visual displays to provide an understanding of overall problems, or noteworthy characteristics of the data. However, the shortcomings of visual displays are numerous: many features of the data may escape notice, due to inadequate length converted to bars (over-stretching the non-zero axis units), or due to the absence of a non-zero baseline (which can cause misleading locations of category proportions), etc.

4. Interpreting and Presenting Descriptive Statistics

Explanation and interpreting the results of descriptive statistics begin with the identification of the location of various types of data. These are data, including percentages of the main scores and ranges in distributions, measures of variability, such as the standard deviation, and assessment of normal distribution. Determining the statistical method to be used in subsequent examination is critically important in interpreting hypothesis-testing results. For example, a mistake all too often made in interpreting hypothesis testing results is concluding that the null hypothesis has been proved. In fact, an analyst who uses descriptive statistics can do only one of three things: accept the null hypothesis, reject the null hypothesis or tentatively accept or reject the null hypothesis for further hypothesis testing. The hypothesis test is not proof of anything. Thus, especially when the result is not as predicted, it may be better termed a “null hypothesis.”

5. Applications of Descriptive Statistics in Various Fields

The applications of descriptive statistics are not limited, however, to those areas in which it is used. In sports, descriptive statistics plays an important role in determining the usefulness of the data that is obtained, and in turn aids in determining the possible success of different ideas. IBM developed SPSS, which has been adopted by most schools, to analyze the performance of first and second round players from past NCAA tournaments. SPSS produces descriptive statistics which measures the sum of round 1 scores, sum of round 2 scores, standard deviation, the mean, and skewness. Then you can use these findings to develop questions to help see if this model, the sum of round one scores and the standard deviation of round two, are reliable indicators of team success in the big dance. Any worthy data analysis of a sample must use the tools that we have learned in our discussion of descriptive statistics.

Descriptive statistics is a tool that has been developed to help understand various forms of data. It can be used for data analysis, but also for data collection. Whether you are talking about data types or methods of data collection, descriptive statistics provides helpful tools for understanding the extensive variety of data that exists.