Statistics are mathematical computations used to analyze data. Tools of statistical analysis can describe, summarize and compare data. There are various tools that can analyze statistical data. These range from relatively simple computations to advanced analysis. Basic analyses can be easily computed, while more advanced methods require a solid understanding of advanced statistics as well as specialized computer software.
Descriptive analysis uses specific tools to describe data. These are relatively simple calculations that give a basic picture of what the data looks like overall. Descriptive tools include: frequency, percentages and measures of central tendency. Frequency tells how many times something has occurred in a data set. Percentages are calculations that show a proportion. Measures of central tendency are represented by the mean, median and mode. These tools describe the central point (median), the most common (mode) or the average (mean) for a specific variable.
Moderate statistical analysis tools look at the relationships between variables -- what the nature of these relationships are and if they are significant. These include correlation and regression. A correlation describes the relationship between two variables as well as the direction and strength of that relationship. Regression can show if a variable predicts another variable. Like correlation, however, regression does not show causation.
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Advanced analyses include calculations of variance. These can help a researcher see what variety exists in the data, as well as positive outcomes in the research. In order to calculate variance, a researcher must use the standard deviation. A standard deviation measures the degree that an individual value varies from the mean or average. Once the standard deviation is known, analysis of variance can be conducted. An analysis of variance or ANOVA is used to compare the difference in the means or averages of variable groups. This will show if an outcome from one group is statistically different from the outcome for another group. An Analysis of Covariance, or ANACOVA, is a tool that can be used for experimental research designs. ANACOVA will tell the researcher the variance between pre- and post-test data.