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Quantitative Research Methods

Descriptive Statistics

Descriptive statistics capture information about a sample in a single number. There are many statistical measures that fall under the umbrella of descriptive statistics, such as mean, median, standard deviation, and variance. These measures are often divided into two categories:

1. Measures of Central Tendency: Measures of central tendency represent the center or middle of a sample. The most commonly used measures of central tendency are the mean, the median, and the mode, all of which calculate the "center" differently.  

2. Measures of Dispersion: Measures of dispersion show how spread out the data is. Examples of measures of dispersion include standard deviation, variance, and range. Newer methods include the translated biweight S (TBS) estimator and tau measure of scale, which are better when trying to protect against outliers. 

Inferential Statistics

Inferential statistics make inferences about a population from a sample. Two different inferential statistics that will be covered in this online guide are tests of difference and regression. 

1. Tests of Difference: Tests of difference compare two samples to infer whether the populations they represent have different values of some descriptive statistic. Some of the most common tests of difference are t-tests, ANOVA, and Chi-square. Some of the most common non-parametric tests include the Mann-Whitney, Wilcoxon, Kruskal-Wallis, and Friedman tests.  

2. Regression: Regression estimates the relationship between two or more variables in the population. Simple linear regression and multiple regression are commonly used methods. 

Statistical Notation and Symbols

Mathematical shorthand is used throughout statistics. X is often used to represent an independent variable and Y is often used to represent a dependent variable. In addition, you are likely to see Greek letters like μ (pronounced mu), which signifies the population mean. The statistical symbols that represent the population are different from those that represent the sample. For example, the population mean has a different symbol than the sample mean.