Descriptive Statistics

The world is filled with uncertainties. Consumer prices, economic fluctuations, political candidate popularity, water quality, portfolio investment management, and everyday decisions, among others, are often ambiguous, unclear, and indeterminate. Statisticians help individuals resolve the vagueness of life by developing characterizations and drawing conclusions surrounding these questions (American Statistical Association [ASA], 2008). Statistics is a division of mathematics that centers on the collection and evaluation of data, which can be drawn upon to make conclusions (Aron, Aron, & Coups, 2006, 2). Two branches of statistics exist, including descriptive and inferential domains. Extrapolation beyond the data is where the real difference emerges. Indeed, these two subcategories vary in function and definition. However, a relationship exists between descriptive and inferential statistics, irrespective of the distinction in purpose and meaning.

The function of statistics is the “collecting, analyzing, presenting, and interpreting of data (Statistic, 2008). Statistics have become a valuable tool that many fields use which include but are not limited to business, healthcare, politics, sports, gambling, and all sciences. The government census reports that keep track of the population and the economics of everyday life that is played out on Wall Street and the stock market are two examples of where statistics influence every individual. In psychology statistical methods are used on the data collected regarding a theory or question about human and animal behavior in order to discover the truth about the behavior. For example, a research study on the effects of stress levels of a student and how well the student performs on a test.

Through the collection of quantitative and qualitative data a researcher uses statistical analysis to make sense of the data collected. Statistics can have both a positive and negative impact. The positive impact would be that the data collected would be translated into information that is useful, will give answers to questions or provide a means of protection from unnecessary outcomes like the effects of too much stress. The negative impact would be if the information is used to mislead, would cause harm or was too biased by the views of the researcher. The overall function of statistics is a mathematical tool used in the interpretation of data.

Statistics combine two or more numbers from an algebraic equation into a single number. In Statistics for Psychology (2006), the authors state that “Psychologists use statistical methods to help them make sense of numbers they collect when conducting research.” The gathering of information and placing in a frequency table or a frequency graph is a good way to analyze said information. A frequency table shows how often a particular score is given. This table can help make the information being analyzed easier to understand. The necessity of using a grouped frequency table comes into effect when a significant amount of values are used and cannot be tolerated on a regular frequency table. A grouped frequency table uses number groupings within a certain range to simplify the scores of acquired data. According to Statistics for Psychology (2006), “A graph is another good way to make a large group of scores easy to understand. A straightforward approach is to make a graph of the frequency table.” The two main graphs are histograms and frequency polygons. The histogram is a sort of bar chart and the frequency polygon is a line graph going from point to point.

Frequency tables are usually found in survey studies. In Statistics for Psychology (2006), the claim is made that “Frequency tables in research articles are often used to summarize the characteristics of the people in the study.” Frequency tables should be used to find the number of individuals within each category of a categorical variable, such as gender, race or age. Frequency tables give information like counts and percentages. A frequency table is a systematic listing of the number of scores of each value in the group studied and is as a significant tool in the area of statistics because it groups together the frequencies of adjacent values into intervals.

A histogram is the most common way to display data graphically (Aron et al., 2006). The horizontal axis gives the interval of observations involved. The vertical axis gives the number of observations that fall in each interval. In result the number of data points of the observation in each interval will be given. The graph of a histogram can be described as some what like a sky line and is also a valuable tool when explaining statistics.

Without these types of functions, difficulty comprehending the mathematical concepts behind the world of statistics would arise. On occasion graphs and other tools may mislead. One must recognize these lies and misuses in contrast to the truth about statistics. Undoubtedly, skepticism and lack of trust will exist in measure with regard to statistics. Consequently, proper use and illustration of the tools and functions of ones research is vital and lead to the ever-elusive truth behind the numbers.

As mentioned before, two main types of statistics exists: descriptive statistics and inferential statistics. Descriptive statistics is tools used to collect data using a variety of methods that help researchers understand the data collected. Descriptive statistics simplify what the data shows. Findings and statements from the descriptive research can be verified. This form of statistical research focuses on a particular area and outcome of the findings, without making any conclusions beyond what can be verified from collection.

Conversely, inferential statistics uses a broader way of collecting data that attempts to reach a conclusion that extends beyond immediate information alone. Inferential statistics is a set of methods used to make generalizations, estimations, predictions, or decisions. Both inferential and descriptive statistics are for processing, collecting, comparing, and making conclusions regarding statistical information. Descriptive statistics are used to describe the features being studying through numerical data. With descriptive statistics you describe what the data is showing. With inferential statistics you are drawing a conclusion that goes beyond the data shown. Inferential statistics also makes a prediction with the data given and are used to try to infer from the sample data what the population might think.

Or, we use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study (Research, 2006). Let’s say a P.E. coach is interested in how many sit ups her classes can do in a minute. The population is all her students. She tested each student in all seven of her classes. The average sit ups for the minute were 35. There could be some factors for students not doing as well as they could. For instance students might do better in the second class instead of the last class or the class after lunch. Descriptive statistics can reduce a great deal of data into a small summary. An example of descriptive statistics is a baseball player’s batting average. A batter who is hitting .333 is getting a hit one time in every three at bats. One batting .250 is hitting one time in four (Research, 2006).

Many descriptive techniques are also used for inferential data. Psychologist use descriptive statistics to summarize data and to make the data understandable. Inferential techniques are used to draw conclusions and make predictions. Although, descriptive and inferential statistics have differences the relationship that exist between the two can be used for the outcome of research.

In conclusion, a relationship exists between descriptive and inferential statistics, despite significant differences. Dissimilarities in function and definition exist. Overall, descriptive and inferential statistics provide guidance to individuals as to what information is reliable and what predictions can be trusted. With such scientific guidance, one can better address the world’s uncertainties.

References

American Statistical Association (2008). What is statistics? What do statisticians do?. Retrieved June 4, 2008, from http://www.amstat.org/careers/index.cfm?fuseaction=whatisstatisticsAron, A., Aron, E., & Coups, E. (2006). Statistics for psychology (4th ed.). Upper Saddle River, NJ: Pearson/Allyn Bacon.

Habermas (2008). Retrieved June 8, 2008, from www.habermas.org/statzf98.htmlInfinity.cos.edu (2008). Retrieved June 8, 2008, from www. infinity.cos.edu/faculty/woodbury/stats/tutorial/data_descr_infer.htmlResearch Methods. (2006). Inferential Statistics. Retrieved July 13, 2008, fromhttp://www.socialresearchmethods.net/kb/statinf.phpResearch Methods. (2006). Descriptive Statistics. Retrieved July 13, 2008,
fromhttp://www.socialresearchmethods.net/kb/statdesc.phpStatistics for Psychology, Fourth Edition, by Arthur Aron, Elain N. Aron, and Elliot J. Coups.

Published by Pearson Prentice Hall. Copyright © 2006 by Pearson Education.

Statistics. (2008). In Encyclopædia Britannica. Retrieved July 13, 2008, from EncyclopædiaBritannica Online: http://www.search.eb.com.ezproxy.apollolibrary.com/eb/article-9108592