Statistics

Statistics is a type of data analysis which practice includes the planning, summarizing, and interpreting of observations of a system possibly followed by predicting or forecasting of future events based on a mathematical model of the system being observed. Statistics is a branch of applied mathematics specifically in the area of statistical theory which uses probability theory in the mathematical models.

Statistical methods

The goal of a statistical research project is to make a conclusion on the effect of changes of an independent variable on a dependent variable. There are two major types of statistical studies, experimental studies and post facto or after the fact studies. In both of these types of studies, the effect of changes of an independent variable on the behavior of the dependent variable are observed. The difference between the two is in how the study is actually conducted.

Related Topics:
Independent variable - Dependent variable

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An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation may have modified the values of the measurements. A post-facto study involves reviewing existing data and making a determination about a correlation between two measurements.

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An example of an experimental study is the famous Hawthorne studies which attempted to test changes to the working environment at the Hawthorne plant of the Western Electric Company. The researchers were interested in whether increased illumination would increase the productivity of the assembly line workers. The researchers first measured productivity in the plant then modified the illumination in an area of the plant to see if changes in illumination would affect productivity. Due to errors in experimental procedures, specifically the lack of a control group, the researchers while unable to do what they planned were able to provide the world with the Hawthorne effect.

Related Topics:
Hawthorne studies - Assembly line - Control group - Hawthorne effect

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An example of a post-facto study is a study which explores the correlation between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then perform statistical analysis. In this case, the researchers would collect observations of both smokers and non-smokers and then look at the number of cases of lung cancer in each group.

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There are four types of measurements or measurement scales used in statistics. The four types or levels of measurement (ordinal, nominal, interval, and ratio) have different degrees of usefulness in statistical research. Ratio measurement,

Related Topics:
Levels of measurement - Research

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where both a zero value and distances between different measurements are defined, provide the greatest flexibility in statistical methods that can be used for analysing the data. Interval measurement, with meaningful distances between measurements but

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no meaningful zero value (such as IQ measurements or temperature measurements in degrees Celsius), is also used in statistical research.

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The basic steps for any statistical research involves

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• plan the research including determining information sources, research subject selection, and ethical considerations for the proposed research and method,
• design the experiment concentrating on the system model and the interaction of independent and dependent variables,
• summarize a collection of observations to feature their commonality by suppressing details (descriptive statistics),
• reach consensus about what the observations tell us about the world we observe (statistical inference),
• document the results of the study.

Some well known statistical tests and procedures for research observations are:

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• Student's t-test
• chi-square
• analysis of variance (ANOVA)
• Mann-Whitney U
• regression analysis
• correlation
• Pearson product-moment correlation coefficient
• Spearman's rank correlation coefficient