Methodology tutorial - descriptive statistics and scales
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This is part of the methodology tutorial (see its table of contents).
Introduction
This tutorial is a short introduction to simple descriptive statistics for beginners.
- Learning goals
- Understand the concept of a statistical variable
- Be able to distinguish between data types
- Understand simple measures of centrality and dispersion
- Prerequisites
- None
- Moving on
- Level and target population
- Quality
- under construction !!
Variables, scales and "data assumptions"
Variables
Statistical variables are:
- what we measure with various methods (e.g. survey questions, test items, observations, elements of logfiles)
- what we manipulate, e.g. two experimental conditions.
Let's also recall the distinction between independant and dependant variables:
- Independent variables are measures or conditions that we will used to explain (i.e. predict) other variables
- Dependant variables are the ones that are explained
Descriptive statistics don't make a difference of these variables. It's up to you to decide which variables should explain something and what they should explain. The purpose of descriptive statistics is simply to summarize data distributions.
Finally, descriptive statics (in particular the mean and standard deviation) are the basis of most statistical analysis techniques.
Types of quantitative variables
Quantitative data come in different types or forms . Depending on the data type you can or cannot do certain kinds of analysis. There exist three basic data types and the literature uses various names for these. E.g.
|
Types of measures |
Description |
Examples |
|---|---|---|
|
nominal or category |
enumeration of categories |
male, female district A, district B, software widget A, widget B |
|
ordinal |
ordered scales |
1st, 2nd, 3rd |
|
interval or quantitative or "scale" (in SPSS) |
measure with an interval |
1, 10, 5, 6 (on a scale from 1-10) 180cm, 160cm, 170cm |
In quantitative research designs, it is not very interesting to present descriptive statistics. But they play an important role in early stages of data analysis, e.g. you can check data distributions and make more informed decisions about data analysis techniques. Simple data distributions are most often uninteresting, you should aim to explain these...
On the other hand, descriptive statistics are often used to compare different cases in comparative systems designs or they are used to summarize qualitative data in more qualitative studies.
In any case, avoid filling up pages of your thesis with tons of Excel diagrams. !!
Descriptive statistics =
Some popular summary statistics for interval variables
- Mean
- Median: the data point that is in the middle of "low" and "high" values
- Standard deviation: the mean deviation from the mean, i.e. how far a typical data point
is away from the mean.
- High and Low value: extremes a both end
- Quartiles: same thing as median for 1/4 intervals