Statistics are mathematical methods to collect, organize, summarize, and analyze data. Statistics provide valid and reliable results only when the data collection and research methods follow established scientific procedures. With the development of the computer, the science of statistics has changed dramatically.
Basic statistical procedures include:
descriptive statistics,
sample distribution, and
data transformation.
In descriptive statistics, the chapter presents the concept of data distribution, frequency distribution, cumulative frequency, histogram, bar chart, frequency polygon, normal curve, and skewness.
Summary statistics make data more manageable by measuring two basic tendencies of distributions: 1) central tendency; and 2) dispersion (variability). These statistics make it easier for researchers to understand data.
Central tendency statistics provide information about the grouping of numbers in a distribution by giving a single number that characterizes the entire distribution. Using the mode, median, and mean, researchers can figure out a typical score of a distribution.
In addition, dispersion measures describe the way scores are spread out about a central point. Using range, variance, and standard deviation, allows researchers to understand the characteristics of the data.
The term sample distribution—the distribution of some characteristic measured on an individual or other unit of analysis that were part of a sample. Additionally, it's important to understand the notion of a sampling distribution—a theoretical probability distribution of all values of a variable for a given sample size.
Most statistical procedures are based on the assumption that the data are normally distributed. When some anomalies arise, researchers can attempt to transform the data to achieve normality. Data transformation can be possible by multiplying or dividing each score by a certain number, or taking the square root or log of the scores.
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