Statistical Analysis: How to Choose a Statistical Test

This article provides a guide for selection of the appropriate statistical test for different types of data. Examples are given to demonstrate how the guide works. This is an ideal read for a beginning researcher.

One of the difficulties encountered by many of my students in the advanced statistics course is how to choose the appropriate statistical test for their specific problem statement. In fact, I had this difficulty too when I started analyzing data for graduate students more than 15 years ago.

The computation part is easy as there are a lot of statistical software applications available, as stand-alone applications, or part of the common spreadsheet applications such as Microsoft Excel. If you really want to save money and is a Linux user, Gnumeric is an open source statistical application software that performs as well as MS Excel. I discovered this free application when I decided to use Ubuntu Linux as my primary operating system. The main reason for the switch was my exasperation with having to spend much time, as well as money for antivirus subscriptions, in an effort to remove persistent windows viruses.

Back to the issue of identifying the appropriate statistical test, I would say that experience counts a lot. But this is not the only basis for judging which statistical test is best for a particular research question, i.e., those that require statistical analysis. A guide on the appropriate statistical test for certain types of variables can steer you towards the right direction.

Guide to Statistical Test Selection

Table 1 below shows what statistical test should be applied whenever you analyze variables measurable by a certain type of measurement scale. You should be familiar with the different types of data in order to use this guide. If not, you need to read the 4 Statistical Scales of Measurement first before you can effectively use the table.

Type of Data
# of Groups
Test Hypothesis for
Statistical Test
1. Ratio/Interval
2
CorrelationKendall’s Tau/Pearson’s r
-do-
2
VariancesFmax test
-do-
2
Meanst-test
-do-
2+
VariancesAnalysis of Variance
2. Ordinal
2
CorrelationSpearman’s rho
-do-
2+
CorrelationKruskal-Wallis ANOVA*
3. Nominal (frequency data)
2 Categories
AssociationChi-Square
Table 1. Type of data and their corresponding statistical tests [modified from Robson (1973)].

*Used if samples are independent; if correlated, use Friedman Two-Way ANOVA

Some Examples to Illustrate Choice of Statistical Test

Refer to Table 1 as you go through the following examples on statistical analysis of different types of data.

Null Hypothesis: There is no association between gender and softdrink preference.
Type of Data: Gender and sofdrink brand are both nominal variables.
Statistical Test: Chi-Square

Null Hypothesis: There is no correlation between Mathematics score and number of hours spent in studying the Mathematics subject.
Type of Data: Math score and number of hours are both ratio variables
Statistical Test: Kendall’s Tau or Pearson’s r

Null Hypothesis: There is no difference between the Mathematics scores of Sections A and B.
Type of Data: Math scores of both Sections A and B are ratio variables.
Statistical Test: t-test

Once you have chosen a specific statistical test to analyze your data with your hypothesis as a guide, make sure that you encode your data properly and accurately (see The Importance of Data Accuracy and Integrity for Data Analysis). Remember that encoding a single wrong entry in the spreadsheet can make a significant difference in the computer output. Garbage in, garbage out.

Reference

Robson, C. (1973). Experiment, design and statistics in Psychology, 3rd ed. New York: Penguin Books. 174 pp.

©2015 February 18 P. A. Regoniel