Nature and Types of Descriptive Analysis
Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data.
Descriptive statistics are typically distinguished from inferential statistics. With descriptive statistics you are simply describing what is or what the data shows. With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone. For instance, we use inferential statistics 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. Thus, we use inferential statistics to make inferences from our data to more general conditions; we use descriptive statistics simply to describe what’s going on in our data.
Descriptive Statistics are used to present quantitative descriptions in a manageable form. In a research study we may have lots of measures. Or we may measure a large number of people on any measure. Descriptive statistics help us to simplify large amounts of data in a sensible way. Each descriptive statistic reduces lots of data into a simpler summary. For instance, consider a simple number used to summarize how well a batter is performing in baseball, the batting average. This single number is simply the number of hits divided by the number of times at bat (reported to three significant digits). 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. The single number describes a large number of discrete events. Or, consider the scourge of many students, the Grade Point Average (GPA). This single number describes the general performance of a student across a potentially wide range of course experiences.
Every time you try to describe a large set of observations with a single indicator you run the risk of distorting the original data or losing important detail. The batting average doesn’t tell you whether the batter is hitting home runs or singles. It doesn’t tell whether she’s been in a slump or on a streak. The GPA doesn’t tell you whether the student was in difficult courses or easy ones, or whether they were courses in their major field or in other disciplines. Even given these limitations, descriptive statistics provide a powerful summary that may enable comparisons across people or other units.
Descriptive statistics allow you to characterize your data based on its properties. There are four major types of descriptive statistics:
1. Measures of Frequency:
* Count, Percent, Frequency
* Shows how often something occurs
* Use this when you want to show how often a response is given
2. Measures of Central Tendency
* Mean, Median, and Mode
* Locates the distribution by various points
* Use this when you want to show how an average or most commonly indicated response
3. Measures of Dispersion or Variation
* Range, Variance, Standard Deviation
* Identifies the spread of scores by stating intervals
* Range = High/Low points
* Variance or Standard Deviation = difference between observed score and mean
* Use this when you want to show how “spread out” the data are. It is helpful to know when your data are so spread out that it affects the mean
4. Measures of Position
* Percentile Ranks, Quartile Ranks
* Describes how scores fall in relation to one another. Relies on standardized scores
* Use this when you need to compare scores to a normalized score (e.g., a national norm)