INTRODUCTION TO QUANTITATIVE RESEARCH

The objective of quantitative research is to systematically measure observable phenomena using statistical, mathematical, or other computational methods.  Quantitative methods are applicable both to social science and to hard science. 

To be honest, no one wants to see an enormous list of numbers.  What people really care about is what these numbers mean, or why their trends are significant.  That being said, descriptive measures and inferential measures are crucial to effectively summarizing and analyzing your data.  Stata, and to a lesser extent Excel, will be able to do most of these quantitative measures.

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Basic Summary Statistics 

Arithmetic Mean: the average of the numbers

Geometric Mean: the average that mitigates the influences of outlier data points.  It is defined as the nth root of n numbers.  For example, if you have 3 numbers, you multiply them then take the cube root. 

Median: the middle value in a dataset when the data are ordered in ascending or descending order

Mode:  the most frequently occurring value in a dataset

Range: the highest term minus the lowest term in a dataset

Inner Quartile Range: the difference between the first and third quartile

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Variance: a measure of the spread of data points around the mean.  Population variance is rarely used in social science because it requires you know the total population.  Sample variance is much more common as it is used for samples of data. The sample variance is the sum of the squared distances of each term (Xi) from the mean (μ), divided by the number of terms in the distribution (N) minus 1. 

Standard deviation: square root of the variance.  This does two main things 1) if there is data below and above the mean, the variance can be zero, which is useless and 2) technically your units are squared when you use the variance formula so to get normal units again, take the square root.

Different Types of Numbers

• Numbers

  • Categorical

    • Nominal: Order does not have significance

      • Example: Casey’s GWid number is higher than Jillian’s, but that does not mean that Casey is smarter, taller, etc than Jillian

    •  Ordinal: Order matters

      • Casey’s GPA is lower than Jillian’s so Jillian did better in school than Casey did

  • Cardinal

    • Discrete: limited number of intervals between values

      • Example: Number of children.  You can have 1 kid or 2 kids, but you cannot have 1.2 kids.  1 and 2 are the values and there are not options in between them.

    • Continuous: infinite number of intervals between values

      • Example: Casey is 22 years, 29 days, 14 hours, 10 seconds, 45 milliseconds…old

Why on earth does this matter, you ask?  Well I asked the same question.  Turns out that some statistical measures can only be done with certain types of numbers – hence it is important.

This page will be updated throughout the semester with more information about different quantitative measure.  Check back for more if you are interested. 

Good luck!